Breaking Math Podcast

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Breaking Math is a deep-dive science, technology, engineering, AI, and mathematics podcast that explores the world through the lens of logic, patterns, and critical thinking. Hosted by Autumn Phaneuf, an expert in industrial engineering, operations research, and applied mathematics, and Noah Giansiracusa, a mathematician and leading voice in algorithmic literacy and technology ethics, the show is dedicated to uncovering the mathematical structures behind science, technology, and the systems shaping our future.

What began as a conversation about math as a pure and elegant discipline has evolved into a platform for bold, interdisciplinary dialogue. Each episode of Breaking Math takes listeners on an intellectual journey—into the strange beauty of chaos theory, the ethical dilemmas of AI and algorithms, the hidden math of biology and evolution, or the physics governing black holes and the cosmos. Along the way, Autumn and Noah speak with working scientists, researchers, and thinkers across fields: computer scientists, physicists, chemists, engineers, economists, philosophers, and more.

But this isn’t just a podcast about equations. It’s a show about how mathematics shapes the way we think, decide, build, and understand the world. Breaking Math pushes back against the idea that STEM belongs behind a paywall or an academic podium. It’s for the curious, the critical, and the creative—for anyone who believes that ideas should be rigorous, accessible, and infused with wonder.

If you’ve ever wondered:

  • What’s the math behind machine learning and modern algorithms?
  • How do we quantify uncertainty in climate and economic models?
  • Can intelligence or consciousness be meaningfully described in AI?
  • Why does beauty matter in an equation?

You’re in the right place.

At its heart, Breaking Math is about building bridges—between disciplines, between experts and the public, and between abstract mathematics and the messy, magnificent reality we live in. With humor, clarity, and deep respect for complexity, Autumn and Noah invite you to rethink what math can be—and how it can help us shape a better future.

Listen wherever you get your podcasts.

Website: https://breakingmath.io

Linktree: https://linktr.ee/breakingmathmedia

Email: breakingmathpodcast@gmail.com

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Episodes

Published 2026-05-13

Are We Being Misled by Data? Ron Wasserstein on AI, Bias, and Statistical Truth

47 min
Open

In this episode of Breaking Math, Autumn and Noah speak with Ron Wasserstein, Executive Director of the American Statistical Association, about what statistics means in a world increasingly shaped by AI, misinformation, and fragile public trust. Wasserstein argues that statistics is not merely a “bag of tools,” but a way of thinking: asking where data comes from, what it leaves out, how uncertainty should be communicated, and when numbers are being used to illuminate rather than manipulate.

Chapters

00:00 The Golden Age of Statistics

02:36 AI's Impact on Statistics

08:16 Data as Fuel for AI

10:55 Bias in AI and Statistics

14:01 Preparing Future Statisticians

16:58 Bridging the Gap: Academia and Industry

22:58 The Misconception of Statistics

23:08 The Role of Statistics in Public Discourse

26:20 The American Statistical Association's Mission

32:18 Statistics and Politics: A Historical Perspective

36:02 Addressing Misinformation and Misuse of Data

39:51 The Importance of Statistical Literacy

44:01 Misconceptions About Statistics and Expertise

46:57 The Essence of Statistics

47:22 Statistics as a Way of Thinking

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Published 2026-05-05

How Ransomware Became a Global Industry with Anja Shortland on Dark Screens

41 min
Open

What if ransomware did not begin with criminals, but with curiosity? In this episode of Breaking Math, Autumn and Noah talk with Anja Shortland, professor of political economy at King’s College London and author of Dark Screens.

This conversation explores how playful hacking evolved into professionalized cybercrime, why ransomware gangs operate like morally questionable internet startups, how cryptocurrency made ransomware scalable, and why hospitals, governments, universities, and critical infrastructure remain especially vulnerable. We also dig into the mathematics behind encryption, asymmetric cryptography, game theory, negotiation, cyber insurance, and the uncomfortable trade-offs between freedom, privacy, and regulation.

Chapters

00:00 The origins of ransomware and early hacker culture

02:13 The evolution of ransomware attacks since 2013

03:14 The paradox of cybercriminals as entrepreneurs

06:19 Early hackers: Steve Jobs and Wozniak as pioneers

12:34 The moral and legal landscape of hacking and cybercrime

13:39 The importance of cybersecurity awareness for individuals

15:03 The arms race: attackers vs defenders and the role of math

16:02 The technological innovations behind ransomware

19:21 Asymmetric encryption and cryptocurrency in ransomware

20:53 Bitcoin and the dark web: enabling cybercrime

22:45 The impact of AI on future cyber threats and defenses

34:07 The future of ransomware and cybersecurity challenges

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Published 2026-04-28

Explaining Huge Numbers with Richard Elwes

56 min
Open

What does it actually mean for a number to be “big”? In this episode of Breaking Math, Autumn chats with mathematician Richard Elwes to explore how huge numbers reveal the limits of human intuition, language, and even mathematics itself. The discussion moves from exponential growth in pandemics and finance to numbers larger than the universe itself, emerging in games like chess and abstract possibility spaces. Finally, it reaches one of the most profound ideas in modern mathematics: that there are true statements about numbers that can never be proven. This episode challenges how we think about scale, complexity, and the systems we rely on to make sense of reality.

Key Topics

Limits of ancient numeral systems like Roman numerals

Mathematical logic and the concept of huge numbers

Evolution of number notation from Roman to Hindu-Arabic systems

The significance of place value in expressing large numbers

The Mayan long count and its implications for understanding time scales

Chapters

00:00 Introduction and Inspiration for the Book

01:39 Redefining Big Numbers

01:55 Limits of Numerical Systems

05:33 Evolution of Number Sense

10:02 Language and Numerical Understanding

11:53 Cultural Influences on Numerical Systems

14:18 Hacks in Ancient Number Systems

16:55 Archimedes and the Concept of Infinity

22:01 The Importance of Place Value

25:45 Mayan Cosmology and Time Scales

31:55 Exponential Growth and Its Dangers

32:20 Understanding Exponential Growth

36:14 The Dangers of Exponential Growth

37:23 Limits of Exponential Growth in the Physical World

39:42 Exploring Possibility Space

45:38 Goodstein's Theorem and Mathematical Logic

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Published 2026-04-26

AI Isn’t Replacing You—It’s Changing the Rules with Sheamus McGovern

35 min Transcript
Open

In this episode we sit down with Sheamus McGovern, founder of the Open Data Science Conference (ODSC AI), to unpack what AI actually looks like. Sheamus shares what’s really happening behind the scenes of the AI boom and why the biggest shift isn’t job loss, but a complete transformation of skills. From explaining why AI is reshaping—not replacing—jobs, to breaking down the gap between hype and real-world applications, this conversation explores how early algorithmic trading foreshadowed today’s AI revolution, why open-source tools like TensorFlow and PyTorch changed everything, what the “AI Skill Flip” means for your career, and why even data scientists are questioning their future. Along the way, the biggest mistake people make when trying to learn AI, and why the smartest approach isn’t to learn everything—but to start intentionally and build from there.

Timestamps

00:00 – The biggest misconception about AI

02:00 – Algorithmic trading and the origins of AI in finance

05:00 – The birth of ODSC AI and the data science movement

09:30 – Breakthrough moments in AI

16:30 – Democratization of AI and open-source tools

19:00 –The AI Skill Flip

24:00 – The truth about AI replacing jobs

27:00 – Real-world AI success stories

32:30 – How to actually start learning AI today

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Published 2026-04-14

Math and Magic with Matt Baker

50 min Transcript
Open

In this episode, mathematician and award-winning magician Matt Baker explores the fascinating intersection of mathematics and magic, revealing how mathematical principles, intuition, and storytelling create unforgettable illusions. From a mind-reading trick based on the classic concept of “casting out nines” to his groundbreaking research on the Riemann–Roch theorem for graphs, Baker demonstrates how creativity and pattern recognition drive both mathematical discovery and magical performance.

Chapters

00:00 The Interplay of Math and Magic

04:58 Aesthetic Connections in Math and Magic

08:57 Balancing Family, Math, and Magic

12:34 The Impact of Magic on Mathematical Thinking

16:32 The Art of Clarity in Communication

16:44 A Live Magic Demonstration

25:14 Intuition and Pattern Recognition in Math

30:03 The Riemann-Roch Theorem for Graphs

41:42 The Role of AI in Mathematics and Magic

50:21 The Art of Communicating Mathematics

50:47 The Magic of Math and Performance

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Published 2026-04-07

Credibility Crisis in Science with Thomas Plümper and Eric Neumayer

38 min Transcript
Open

In this episode, Thomas Plümper and Eric Neumayer explore the hidden challenges in modern science, from outright fraud to the subtler practice of “tweaking” data that distorts results. They examine why the self-correcting nature of science often falls short, how incentives and academic pressure drive misconduct, and the double-edged role of AI in both enabling and detecting fraud. The conversation also tackles debates around p-values and statistical reasoning, shares cautionary case studies, and proposes solutions like greater data transparency and stronger verification standards.

Chapters

00:00 Introduction to Fraud in Research

06:21 The Nature of Fraud Detection

08:56 Incentives and Motivations for Fraud

10:43 Self-Correction in Science

12:13 Understanding Statistical Significance

13:04 The Role of Replication in Research

14:32 Bayesian vs Frequentist Approaches

23:09 Understanding Bayesian Statistics and Its Implications

26:24 The Humility of Empirical Science

27:16 Concrete Examples of Scientific Fraud

32:52 Proposed Solutions to Scientific Fraud

34:50 The Reality of Scientific Fraud and Human Nature

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Published 2026-03-27

Denied, Then Unstoppable: The Story of Mary T. Washington Wylie

8 min
Open

This Women in History Mini-Series episode with Dr. Victoria Bateman explores the inspiring story of Mary T. Washington Wylie, the first African-American woman CPA, her challenges, achievements, and legacy in breaking racial and gender barriers in the early 20th century. Mathematics is supposed to be objective—but access to it has never been equal.

Chapters

00:00 Introduction to Mary T. Washington Wylie

00:48 Early Life and Challenges

02:58 Breaking Barriers in Accountancy

05:25 Pioneering a Path for Others

07:21 Legacy and Impact

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Published 2026-03-24

The Power of Connection in Math: Insights from Hortensia Soto

40 min
Open

In this episode of Breaking Math, we sit down with Dr. Hortensia Soto, former president of the Mathematical Association of America, to explore the role of mathematics in a world shaped by AI, education, and access. We discuss how debates in math are often really about opportunity and inclusion, how educators can navigate the rapid pace of AI, and why communication and human connection matter more than ever. The conversation also highlights the importance of financial literacy, embodied learning, and collaboration, reframing mathematics not as a set of answers, but as a way of thinking grounded in curiosity, effort, and relationships.

Chapters

00:00 Introduction to Hortensia Soto and the Math Community

02:48 The Role of AI in Mathematics

05:17 Access to Mathematics and Its Political Nature

07:34 The Importance of Financial Literacy in Math Education

10:19 Communication Skills for Mathematicians

13:06 The Culture of the Mathematical Association of America

15:29 Reflections on Leadership in the Math Community

25:01 Innovative Approaches to Mathematics Education

25:50 Recognizing Math Identity in Students

27:02 Nurturing Student Potential

35:31 The Role of AI in Learning

38:26 The Human Element in Mathematics

39:51 Mathematics Beyond Symbols and Procedures

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Published 2026-03-20

Florence Nightingale: Data-Driven Reformer of Medicine

12 min
Open

This Women in History Mini-Series episode with Dr. Victoria Bateman explores the groundbreaking contributions of Florence Nightingale, highlighting her use of data and statistics to revolutionize healthcare and public health during the 19th century. Discover how her innovative use of data visualization and her perseverance against gender biases transformed modern nursing and public health policy.

Chapters

00:00 Introduction to Florence Nightingale's Legacy

02:21 The Crimean War and Nightingale's Impact

05:18 Data Collection and Analysis in Healthcare

07:18 Overcoming Gender Bias in Medicine

09:23 Innovations in Data Visualization

11:59 Nightingale's Lasting Influence and Conclusion

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Published 2026-03-17

The Math Behind Gerrymandering, Fair Representation, and Politics with Karen Saxe

35 min
Open

Mathematics quietly shapes some of the most important decisions in public life, from redistricting and congressional apportionment to federal research funding and AI policy. In this episode, Autumn and Noah speak with Dr. Karen Saxe, Senior Vice President of Government Relations at the American Mathematical Society, about how mathematical ideas influence representation, fairness, education, and the future of research. From gerrymandering and geometric compactness to life inside the U.S. Senate and the growing policy debates around AI, Karen reveals how deeply math is woven into the systems that govern everyday life.

Chapters

00:00 Introduction to the Conversation

01:15 The Hot Tea in DC

01:24 Gerrymandering and Mathematics

03:42 Understanding Gerrymandering and Redistricting

08:07 The Role of Mathematicians in Politics

12:19 Experiences in the Senate with Al Franken

19:32 Government Relations and the Role of Mathematics

23:01 The Impact of AI on Mathematics and Policy

28:41 Community Readiness for AI Transformations

29:22 Diversity in Education and Its Challenges

29:40 Bridging Mathematics and Politics

29:58 Career Pathways: Academia to Policy

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Published 2026-03-13

Anna Schwartz: The Economist Who Changed How We Study Economies

14 min
Open

This Women in History Mini-Series episode with Dr. Victoria Bateman explores the groundbreaking work of Anna Schwartz, a pioneering economist who transformed macroeconomics through data-driven research. Discover how her meticulous analysis of monetary history shaped economic policy and the legacy she left for future generations.

Chapters

00:00 Introduction to Anna Schwartz and Her Impact

01:45 The Historical Context of Economic Data

04:10 Challenges Faced by Women in Economics

06:03 A Monetary History of the United States

09:04 The Methodology of Anna Schwartz

11:46 Legacy and Personal Insights on Anna Schwartz

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Published 2026-03-11

Disappearing Grants, Genius Grants, and the AI Proofs with Lauren K. Williams

25 min
Open

In this episode, Lauren Williams, professor of mathematics at Harvard University and a 2025 MacArthur Fellow, speaks about the surprising and often messy reality of mathematical research. The conversation begins with a turbulent moment in academia, when federal grants supporting her work were suddenly canceled—only months before she received the MacArthur “Genius Grant,” an unexpected recognition that allowed her to continue her research. Williams explains her work in algebraic combinatorics, illustrating how abstract mathematics can connect to real-world systems. The discussion also explores the human side of discovery, from collaborations that span continents to the strange coincidence of research papers and babies arriving the same week. Finally, the episode dives into one of the most intriguing experiments in modern mathematics: the First Proof project, which tests whether artificial intelligence can produce genuine mathematical proofs, revealing both the promise and the current limitations of AI-generated reasoning.

Chapters

01:27 Winning the MacArthur Genius Grant

01:43 Becoming a Woman in Mathematics at Harvard

04:25 Research Applications

10:04 The Human Side of Research

12:20 The First Proof Project

18:29 Advice for Young Mathematicians

22:51 The Intersection of Mathematics and AI

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Published 2026-03-06

Priscilla Wakefield: Empowering Women Through Financial Literacy

9 min
Open

This Women in History Mini-Series with Dr. Victoria Bateman explores the life and contributions of Priscilla Wakefield, a revolutionary figure in financial literacy and women's empowerment during the Industrial Revolution. Wakefield's work in establishing savings banks and community insurance schemes for women highlights her belief in the practical application of mathematics for everyday life. The discussion also addresses the challenges women faced in finance during her time and her lasting impact on feminist economics.

Takeaways

  • Priscilla Wakefield taught ordinary people how to use numbers.
  • She established England's first savings bank for women and children.
  • Wakefield's work was pivotal during the British Industrial Revolution.
  • She recognized the need for financial education among women.
  • Her community insurance scheme empowered women financially.
  • Wakefield's approach to mathematics was practical and accessible.
  • She published influential works on women's rights and economics.
  • Her philosophy emphasized the importance of financial literacy.

Chapters

00:00 Introduction to Priscilla Wakefield

01:19 Priscilla Wakefield: A Revolutionary Mathematician

04:28 The Financial Landscape of Georgian Britain

06:34 Groundbreaking Contributions to Banking and Finance

07:41 Fun Facts and Legacy of Priscilla Wakefield

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Published 2026-03-03

Why Mathematicians Must Speak Up with Bryna Kra

31 min
Open

In this conversation, Dr. Bryna Kra discusses her journey in mathematics, focusing on her research, dynamical systems, the importance of collaboration, and the role of the American Mathematical Society. She emphasizes the need for better communication within the mathematics community and the challenges it faces, particularly regarding diversity and inclusion. Bryna shares her experiences in mentoring women in mathematics and reflects on her career achievements while looking forward to future contributions in the field.

Takeaways

Mathematics is a dynamic field that evolves over time.

Explaining the applications of mathematical research is essential.

Collaboration often starts in unexpected places.

Dynamical systems connect seemingly unrelated mathematical fields.

The AMS plays a crucial role in supporting mathematicians.

Communication is key to addressing challenges in the mathematics community.

Women in mathematics need more support and mentorship.

Creating pathways for underrepresented groups is vital.

Asking for help can lead to significant changes in academia.

Reflecting on one's career can inspire future generations.

Chapters

00:00 Introduction to Dynamical Systems

01:33 The Intersection of Number Theory and Dynamical Systems

03:23 Communicating Abstract Mathematics

05:21 The Evolution of Mathematical Fields

07:09 Quirky Anecdotes in Mathematics

09:49 Leading the American Mathematical Society

15:01 Challenges Facing the Mathematics Community

18:08 Roles in the National Mathematics Community

21:11 Women in Mathematics and Mentorship

27:02 Reflections on a Successful Career

Bryna does not have social media, but you can email us to contact her,

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Published 2026-02-24

Reaching for the Extreme with Ian Stewart

43 min
Open

In this conversation, Ian Stewart discusses the nature of mathematical inquiry, the motivations behind problem-solving in mathematics, and the importance of storytelling in making math relatable. He explores the relationship between nature and mathematics, emphasizing how patterns in nature inspire mathematical concepts. Stewart also addresses the role of AI in mathematical discovery and the importance of choosing meaningful problems to work on. He concludes by highlighting the vital role of mathematics in society and its significant contributions to the economy.

Takeaways

-Mathematics is driven by curiosity and the desire to solve problems

-Nature serves as a significant source of inspiration for mathematical ideas.

-Mathematicians often seek deeper understanding beyond just solving problems.

-AI can be a powerful tool in mathematical discovery, but it raises questions about understanding

-Choosing problems that interest you is crucial for success in mathematics.

-Mathematics has a profound impact on various industries and the economy.

Chapters

00:00 The Origins of Mathematical Problems

06:12 Breaking Down Complex Problems

09:57 The Beauty of Mathematical Proofs

15:21 The Role of Storytelling in Mathematics

20:10 Nature as Inspiration for Mathematics

24:30 The Pursuit of Mathematical Extremes

27:00 The Complexity of the Four Color Theorem Proof

28:38 The Impact of Computer-Aided Proofs on Understanding

31:21 The Quest for Deeper Mathematical Insights

32:11 AI and the Evolving Boundaries of Mathematics

34:35 The Dilemma of Solving Without Understanding

38:49 Guiding the Next Generation of Mathematicians

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Published 2026-02-17

Rethinking Mathematical Value in the Age of AI with Ravi Vakil

42 min
Open

In this conversation, Ravi Vakil discusses the beauty of mathematics, the impact of AI on the field, and the importance of human interaction in mathematical education. He emphasizes the social nature of mathematics and the potential dangers of AI-generated content flooding the mathematical community. The discussion also touches on the future of education, the role of leadership in mathematics, and the balance between mathematics and other disciplines. Throughout, Vakil encourages aspiring mathematicians to embrace the beauty and interconnectedness of the subject.

Takeaways

  • Mathematics is fundamentally about curiosity and connection.
  • The beauty of mathematics can be shared and experienced collectively.
  • AI poses both opportunities and challenges for the field of mathematics.
  • Mathematics thrives on social interaction and collaboration.
  • The influx of AI-generated content may dilute the quality of mathematical research.
  • Education in mathematics requires human interaction and cannot be fully replaced by technology.
  • Leadership in mathematics should focus on long-term investments in education.

Chapters

00:00 Introduction and Setting the Stage

01:11 The Beauty of Mathematics

03:57 The Intersection of Mathematics and Technology

05:41 AI's Role in Mathematics

07:36 Emerging Mathematical Ideas in the Age of AI

09:12 Community Dynamics in Mathematics

13:32 Challenges of AI in Academic Publishing

17:08 The Future of Writing and Learning in Mathematics

19:42 The Value of Human Interaction in Education

22:33 The Future of Mathematics and AI

30:15 Leadership in Mathematics and Education

35:47 Balancing Mathematics with Liberal Arts

39:48 Encouragement for Aspiring Mathematicians

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Published 2026-02-10

AI, Pi, Dynamic Pricing, and Math History Lessons

26 min
Open

Summary

In this episode, Autumn and Noah explore the intersection of AI and mathematics, discussing why AI struggles with math, the differences between calculus and algebra, and the historical contributions of women in mathematics. They delve into the concept of infinity, the significance of pi, and the implications of dynamic pricing in today's economy. The conversation highlights the importance of understanding mathematical tools and the ethical considerations surrounding personalized pricing.

Takeaways

AI is not monolithic; it has varying capabilities.

The difference between calculus and algebra lies in their focus on relationships and change.

Infinity is a concept that exists in mathematics but not necessarily in the physical world.

Pi is fundamental in understanding circular motion and symmetry.

Dynamic pricing is a modern phenomenon influenced by technology and data.

Choosing the right mathematical tool is crucial for problem-solving.

Personalized pricing raises ethical questions about fairness and transparency.

Chapters

00:00 Introduction and Overview

00:22 AI and Mathematics: The Dual Nature

03:25 Understanding Calculus vs. Algebra

07:40 Historical Perspectives: Women in Mathematics

13:11 The Concept of Infinity in Mathematics

16:55 The Origins of Pi

21:33 Dynamic Pricing and Its Implications

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Published 2026-02-03

A New Chapter of Breaking Math: Get to Know Your Hosts

39 min
Open

In this episode, Autumn and Noah celebrate the ninth anniversary of the Breaking Math podcast, reflecting on its journey and growth. They introduce Noah Giansiracusa as the new co-host and discuss the importance of engaging with the audience, storytelling in math, and the interdisciplinary nature of the topics they plan to cover. The conversation also touches on personal experiences, defining success in podcasting, and the dynamics of co-hosting, all while embracing their nerdy sides and fostering curiosity in their listeners.

Takeaways

  • Noah is introduced as the new co-host.
  • Engagement with the audience is a priority.
  • Storytelling is crucial in teaching math.
  • Math communication can impact people's understanding of their lives.
  • Success is defined by personal fulfillment, not just metrics.
  • The hosts aim to humanize math and its applications.
  • Embracing nerdiness fosters a relatable and engaging atmosphere.

Chapters

01:55 Welcoming Noah as Co-Host

05:37 Engaging with the Audience

07:26 Expanding the Narrative and Storytelling

09:34 The Power Dynamic in Education

11:18 The Importance of Storytelling in Math

13:44 Communicating Math Beyond the Classroom

15:33 Interdisciplinary Approach to Math

17:40 Future Topics and Directions

20:37 Personal Insights and Fun Facts

25:32 Defining Success in the Podcasting World

30:13 Personal Reflections on Success

36:19 Embracing Nerdiness and Authenticity

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Published 2026-01-21

The Elements of Power: Supply Chains, Technology, and Energy with Nicolas Niarchos

40 min
Open

In this episode of Breaking Math, Autumn and Nicolas Niarchos critique the "green" narrative of lithium-ion technology. Tracing the industry from its 1991 commercialization to modern geopolitical tensions, the hosts expose the exploitation and environmental degradation inherent in global mining, particularly in the Democratic Republic of the Congo. By challenging the presumed sustainability of electric vehicles, they emphasize the need for supply chain transparency and urge listeners to adopt a more informed, ethically-conscious approach to modern consumption.

Takeaways

  • What does it really cost to power the future?
  • The bargain as stated is clean energy in one part and at the other end, you have corruption, pollution, and human suffering.
  • The greenest vehicle is not always the electric one; it depends on the entire lifecycle of the product.
  • We need to improve conditions on the ground, not just extract resources.
  • Corruption is unfortunately a fact of life and is very closely related to extraction.

Chapters

  • 00:00 Introduction and Background
  • 03:24 The Journey to Congo and Corruption
  • 07:13 The Birth of Lithium-Ion Batteries
  • 09:35 The Uneven Global Bargain
  • 12:16 Mining vs. Oil: A Different Kind of Harm
  • 13:56 Onshoring Battery Production: Challenges and Opportunities
  • 17:13 China's Dominance in Battery Manufacturing
  • 18:51 The Race in Battery Technology
  • 21:39 Corruption and Poverty in the Congo
  • 24:31 The Human Cost of Mining
  • 29:12 Health Impacts of Mining
  • 31:52 Colonial Legacy and Modern Mining
  • 34:00 The Future of Battery Technology
  • 39:12 Introduction to Complex Narratives
  • 39:53 The Reality of Resource Extraction
  • 39:59 Embracing Curiosity and Reflection

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Published 2026-01-14

The Score: Gamifying the Nature of Metrics with Thi Nguyen

57 min
Open

In this conversation, the discussion with C. Thi Nguyen revolves around the nature of metrics, qualitative knowledge, and the duality of scoring systems, particularly in the context of climbing. The speaker shares personal experiences with climbing as a case study to illustrate how scoring systems can both enhance and detract from the experience. The conversation delves into the beauty of climbing, the subtlety of value in metrics, and the importance of savoring moments in games. It also explores the tension between purpose and game mechanics, the role of enjoyment, and the complexities of scoring systems in both games and life. Ultimately, the conversation highlights the challenges of balancing values in decision-making and the risks associated with the gamification of various aspects of life.

Takeaways

  • Metrics can miss the subtlety of qualitative knowledge.
  • Scoring systems can enhance or detract from experiences.
  • Climbing serves as a unique case study for scoring systems.
  • The beauty of climbing lies in its scoring system.
  • Values can become obscured when metrics are prioritized.
  • Games allow for exploration of different scoring systems.
  • Achievement play focuses on winning, while striving play values the process.
  • External expectations can pressure individuals to conform to metrics.
  • The addictive nature of games can lead to negative experiences.

Chapters

  • 00:00 The Intricacies of Portability and Judgment
  • 01:12 Introduction and Social Media Presence
  • 03:40 The Value of Climbing and Scoring Systems
  • 07:16 The Impact of Numbers in Climbing
  • 09:42 Savoring the Moment vs. Obsession with Scoring
  • 10:59 Goals vs. Purpose in Games
  • 12:39 Understanding Value Capture
  • 17:53 The Shift in Standards of Success
  • 20:33 The Limitations of Metrics
  • 21:42 Games as a Reflection of Human Desire
  • 24:37 The Purpose Behind Scoring Systems
  • 26:07 The Magic Circle of Games
  • 29:15 Achievement Play vs. Striving Play
  • 34:47 When Games Become Unsafe
  • 38:21 The Pitfalls of Portability in Metrics

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Published 2026-01-12

The Art of Physics: Bridging Science and Creativity with Ronald Gamble

48 min
Open

This conversation explores the fascinating intersection of math, physics, and art, highlighting how these disciplines inform and inspire one another. Dr. Ronald Gamble discusses his journey as a theoretical physicist and artist, emphasizing the importance of recognizing patterns in nature and the role of creativity in scientific discovery. The dialogue delves into various topics, including the significance of symmetry in physics, the visualization of complex concepts like black holes and gravitational waves, and the influence of mathematical principles on artistic expression. Ultimately, the conversation underscores the idea that art and science are deeply interconnected, each enhancing the understanding and appreciation of the other.

Takeaways

  • Inspiration is pattern recognition.
  • Math serves as a language to describe physics.
  • Art and physics both seek to decode patterns in the universe.
  • Studying nature can enhance understanding of physics concepts.
  • Creativity is essential in theoretical physics.
  • Symmetry plays a crucial role in understanding the universe.
  • Art can influence scientific thought and vice versa.

Chapters

  • 00:00 The Intersection of Math, Physics, and Art
  • 03:57 Finding Inspiration in Nature
  • 06:16 The Art of Storytelling in Physics
  • 08:31 Patterns in Nature and Art
  • 10:13 The Influence of Physics on Art
  • 12:23 Understanding Symmetry in Physics
  • 16:46 Exploring Black Holes and Particle Physics
  • 21:03 The Role of Tessellations in Physics
  • 25:24 Celebrating Scientific Collaborations
  • 27:24 The Art of Tessellation and Structure
  • 29:06 The Power of Minimalism in Art and Science
  • 31:05 Exploring Black Holes and Gravitational Waves
  • 38:59 The Artistic Journey into Physics Course

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Published 2025-11-19

Intelligent Systems: Digital Culture Shock

38 min
Open

In this conversation, Dr. Katharina Reinecke explores the intersection of technology and culture, discussing how cultural assumptions shape the design and functionality of technology. She delves into the implications of self-driving cars, the importance of understanding diverse user experiences, and the challenges posed by a predominantly Western perspective in technology development. The discussion highlights the need for greater cultural sensitivity in technology design and the potential consequences of ignoring these differences.

Takeaways

  • Technology is not culturally neutral; it reflects the values of its creators.
  • Self-driving cars are based on American commuting assumptions.
  • Cultural differences significantly impact user experience and technology design.
  • Efficiency in technology can undermine social interactions and relationships.
  • WEIRD populations dominate technology research, leading to biased outcomes.
  • Universal design principles often fail when applied globally.
  • Stack Exchange exemplifies individualistic design, contrasting with collectivist values.
  • AI systems must be designed with cultural sensitivity to avoid reinforcing biases.

Chapters

  • 00:00 Understanding Digital Culture Shock
  • 03:53 The Challenges of Autonomous Vehicles
  • 06:21 Cultural Assumptions in Technology
  • 08:37 The Impact of AI and Data Bias
  • 10:32 Efficiency vs. Social Interaction in Design
  • 12:14 The Concept of 'Weird' Populations
  • 14:24 Cultural Values in Digital Platforms
  • 21:53 The Simplicity of Design and Its Cultural Impact
  • 22:51 Efficiency vs. Community: The Stack Exchange Debate
  • 25:41 Adapting Global Platforms to Local Norms
  • 31:52 The Implications of AI and Digital Infrastructure
  • 34:34 Recognizing Cultural Bias in Technology Design
  • 37:42 Technology as Culture

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Published 2025-11-11

Who is Francis Crick?

50 min
Open

This conversation delves into the life and legacy of Francis Crick, co-discoverer of the DNA structure. Dr.  Matthew Cobb, the guest, explores Crick's multifaceted personality, his poetic inspirations, collaborative nature, and his later pursuits in consciousness. The discussion also touches on the controversies surrounding his work, particularly regarding the contributions of Rosalind Franklin, and reflects on Crick's complex character, blending modern scientific thought with outdated socio-political ideas.

Takeaways

  • Crick's story is often simplified to his DNA discovery.
  • He had a deep appreciation for poetry and its connection to science.
  • Collaboration was a key aspect of Crick's success.
  • His early life was marked by average academic performance.
  • Crick's transition to biology was driven by a desire to understand life.
  • The discovery of DNA was a complex, collaborative effort.
  • Controversies exist regarding the ethics of scientific discovery.
  • Crick's later work focused on the nature of consciousness.
  • He had a unique blend of intuition and logical thinking.
  • Crick's outdated socio-political views contrast with his scientific modernity.

Chapters

  • 00:00 The Legacy of Francis Crick
  • 01:13 Introduction to Matthew Cobb and His Book
  • 03:43 The Influence of Francis Crick
  • 06:19 Crick's Unique Approach to Science
  • 07:19 Crick's Early Life and Self-Perception
  • 10:04 The Impact of Naval Service on Crick
  • 12:34 Crick's Transition to Biology
  • 15:06 The Role of Schrodinger's Work
  • 17:26 The Dynamic Between Watson and Crick
  • 20:13 The Discovery of the Double Helix
  • 23:02 The Controversy of Rosalind Franklin's Contribution
  • 28:23 The Diplomatic Row and Pauling's Mistake
  • 29:38 The Discovery of DNA's Structure
  • 34:31 Crick and Brenner's Collaboration
  • 38:41 Crick's Exploration of Consciousness
  • 43:03 Crick's Complex Legacy

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Published 2025-11-04

Mathematics and Humanity: The Untold Stories of the Great Math War

43 min
Open

This conversation explores the intersection of mathematics and human experience, focusing on historical figures, philosophical debates, and the ethical implications of scientific progress. Jason Socrates Bardi discusses his book 'The Great Math War', which delves into the personal stories of mathematicians, the challenges of teaching math, and the relevance of these themes in today's world, particularly in the context of AI and misinformation.

Takeaways

  • The personal experiences of mathematicians shape their work.
  • Philosophical clashes in mathematics reflect broader societal issues.
  • Hilbert's optimism about problem-solving parallels today's AI discussions.
  • Historical context is crucial in understanding mathematical developments.
  • Ethics in science must be prioritized to avoid past mistakes.
  • There are limits to human knowledge that we must acknowledge.
  • Mathematics is a fundamental human skill, not just for the gifted.
  • The future of mathematics will be influenced by AI and technology.
  • Understanding historical fallacies can inform current practices.
  • Kovalevsky's story is an inspiring example of overcoming barriers.

Chapters

  • 00:00 The Personal Journey Behind The Great Math War
  • 03:08 The Philosophical Clash in Mathematics
  • 05:13 The Great Math War: Key Players and Their Missions
  • 07:38 The Foundations of Mathematics: Paradoxes and Theories
  • 08:55 The Role of Historical Context in Mathematics
  • 10:00 The Human Side of Mathematics: Stories of Resilience
  • 12:36 Ethics in Science and the Modern Age
  • 14:56 The Future of Mathematics and Technology
  • 25:32 The Spectrum of Idealism and Realism
  • 26:13 Understanding Ignoramus et Ignoramnibus
  • 29:04 Neuroscience and the Evolution of Mathematics
  • 33:12 The Future of AI and Consciousness
  • 35:31 Fallacies and Paradoxes in Mathematics
  • 38:31 The Legacy of Sofia Kovalesky
  • 43:10 The Great Math War: A Reflection on Logic and Humanity

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Published 2025-10-28

The Future of Physics: Portals to a New Reality

48 min
Open

In this conversation, Dr.Vlatko Vedral discusses the complexities of quantum mechanics and its implications for our understanding of reality. He explores the stagnation in physics, the importance of thought experiments, and the potential for new discoveries through technological advancements. Vlatko emphasizes the need for adventurous research and the role of quantum information in shaping future scientific inquiries. He also speculates on the transformative possibilities of quantum technologies and their impact on human perception.

Takeaways

  • Quantum mechanics challenges our understanding of reality.
  • The observer effect is central to quantum mechanics.
  • Physics has been stagnant with two main theories for over a century.
  • Technological advancements are paving the way for new experiments.
  • Thought experiments can guide genuine scientific discovery.
  • The integration of quantum mechanics and general relativity is crucial.
  • Quantum information theory expands our understanding of computation.
  • New theories may emerge from the intersection of quantum mechanics and technology.
  • The perception of reality may evolve with quantum technologies.
  • Funding and research approaches need to be more adventurous.

Chapters

  • 00:00 Exploring Quantum Reality
  • 04:48 The Stagnation of Physics
  • 08:41 The Clouds of Uncertainty
  • 12:46 Thought Experiments and Their Power
  • 16:01 Five Experiments for the Future
  • 24:54 Technological Feasibility of Experiments
  • 28:27 Quantum Theory and Its Foundations
  • 34:08 The Role of Quantum Information
  • 39:35 Imagining New Realities Through Portals

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Published 2025-10-25

AI vs Human Intelligence: The Emergent Mind

50 min
Open

In this conversation, Drs. Gaurav Suri and Jay Mcclelland delves into the intricate relationship between artificial intelligence and human cognition, exploring similarities and differences, the evolution of AI from rule-based systems to learning models, and the concept of emergence in both fields. The discussion also touches on the efficiency of human learning compared to AI, the role of consciousness, and the ethical implications of AI technology.

Takeaways

  • AI and human intelligence share similarities in neural network frameworks.
  • Artificial systems lack the goal-directed nature inherent in humans.
  • Humans learn more efficiently than current AI systems.
  • Neural networks can adapt to language nuances better than rule-based systems.
  • Emergence explains how collective intelligence arises from individual components.
  • Memory in neural networks is represented through connections, not individual units.
  • Mathematics is both invented and discovered, shaped by human needs.
  • Understanding consciousness is crucial for AI development.
  • Human misuse of AI poses significant risks.
  • Recognizing ourselves as processes can foster empathy and morality.

Chapters

  • 00:00 Introduction and Backgrounds
  • 01:00 AI vs Human Mind: Similarities and Differences
  • 03:32 The Shift from Rule-Based AI to Learning Systems
  • 09:07 Emergence in Cognition: Ant Colonies and Intelligence
  • 15:25 Distributed Representations and Memory Storage
  • 23:53 The Nature of Memory and Its Malleability
  • 25:40 Emergence of Mathematical Concepts
  • 29:50 The Invention vs. Discovery Debate in Mathematics
  • 32:19 Learning Mechanisms: Brain vs. AI
  • 36:48 Consciousness: Function and Implications
  • 41:13 AI Risks: Human Misuse vs. AI Autonomy
  • 43:45 Living with Emergence: Understanding Ourselves and Others
  • 48:22 Exploring the Emergent Mind

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Published 2025-10-21

The Giant Leap

56 min
Open

In this conversation, Dr. Caleb Scharf discusses the evolution of space exploration, drawing parallels to historical figures like Darwin. He explores the implications of humanity's expansion into space, the challenges of microgravity, and the allure of Mars as a potential habitat. Scharf emphasizes the interconnectedness of space exploration with our daily lives and the future of humanity as a dispersed entity across the solar system.

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Takeaways

  • Humanity's move into space is a new phase of evolution.
  • Space exploration is a continuation of life's four billion year experiment.
  • Microgravity affects human physiology in profound ways.
  • Mars presents both challenges and opportunities for human exploration.
  • Lagrange points offer stable locations for spacecraft in orbit.
  • The moon's composition is closely related to Earth's.
  • Understanding space exploration is crucial for our future as a species.

Chapters

  • 00:00 The Concept of Dispersal in Space Exploration
  • 04:54 The Universe's Self-Awareness and Its Implications
  • 08:32 Darwin's Influence on Space Exploration
  • 14:14 Historical Figures in Science and Their Impact
  • 21:59 The Moon Landing: A Complicated History
  • 28:14 Challenges in Spacecraft Navigation
  • 30:13 Effects of Microgravity on Humans and Animals
  • 33:50 The Drive for Interplanetary Exploration
  • 36:39 Understanding Lagrange Points
  • 42:06 Life on Other Planets: Mars and Beyond
  • 48:40 The Future of Humanity in Space
  • 54:41 The Essence of Curiosity
  • 54:57 Embracing the Unknown

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Published 2025-10-14

Dinosaurs with Rachel Ignotofsky

30 min
Open

In this engaging conversation, Rachel Ignotofski discusses her new book Dinosaurs, exploring the fascination with these ancient creatures, the impact of mass extinctions, and the evolution of life on Earth. She highlights the importance of paleontology, the legacy of Mary Anning, and the artistic choices made in illustrating the book. The discussion also touches on the audience for the book, quirky anecdotes from paleontological history, and the significance of understanding deep time in relation to our current ecosystem.

Takeaways

  • Most of us fall in love with dinosaurs around the age of six.
  • Dinosaurs and birds evolved together, sharing the Earth.
  • There have been five major mass extinctions in Earth's history.
  • Nature always bounces back after mass extinctions.
  • Paleontology is constantly evolving with new discoveries.
  • Mary Anning was a pioneer in paleontology, often overlooked.
  • Dinosaurs were not just big lizards; they were diverse and complex.
  • The Cambrian explosion marked a significant evolutionary milestone.

Chapters

  • 00:00 The Fascination with Dinosaurs
  • 03:42 Mass Extinctions and Geological Time
  • 06:16 Paleontology and Misconceptions
  • 09:08 Mary Anning: The Mother of Paleontology
  • 11:53 Evolution of Dinosaurs and Marine Reptiles
  • 13:06 The Evolution of Whales
  • 13:42 The Cambrian Explosion and Ancient Creatures
  • 16:12 Favorite Time Periods in Prehistory
  • 18:48 The Book's Audience and Its Appeal
  • 19:03 Anecdotes from the Fossil World
  • 21:53 Art and Illustrations in Science
  • 26:11 The Vastness of Earth History
  • 28:21 Upcoming Events and Future Projects

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Published 2025-10-07

Charlatans with Quico Toro

39 min
Open

In this conversation, Quico discusses the nature of gullibility and the tactics used by charlatans to exploit people's beliefs. He provides insights into various case studies, including astrology and blood types, and highlights notable charlatans like Baba Ramdev and the impact of mega churches. The discussion also covers modern scams in the crypto space and emphasizes the importance of critical thinking and awareness in navigating a world filled with misinformation and exploitation. It's made known that even the smartest scientists can be fooled by charlatans. 

Takeaways

  • People are gullible because they care deeply about their beliefs.
  • Charlatans exploit emotional connections to manipulate individuals.
  • Astrology remains popular despite its lack of scientific basis.
  • Baba Ramdev exemplifies a modern charlatan with a yoga empire.
  • Mega churches can exploit vulnerable populations for profit.
  • The crypto space has seen significant charlatanry and scams.
  • Identifying red flags is crucial in protecting oneself from charlatans.
  • The internet allows charlatans to target niche audiences more effectively.
  • Critical thinking is essential in the digital age to avoid exploitation.
  • Understanding one's beliefs can help in recognizing manipulation.

Chapters

  • 00:00 Introduction and the Nature of Gullibility
  • 04:25 Understanding Charlatans and Their Tactics
  • 07:29 Case Studies: Astrology and Blood Type Beliefs
  • 09:46 Exploring Notable Charlatans: Baba Ramdev and Others
  • 11:11 The Role of Mega Churches in Exploitation
  • 14:18 Medical Charlatans: Dr. Oz and Dr. Mercola
  • 16:40 The Crypto Grift and Its Impact
  • 21:55 The Legacy of Charlatans: From Alchemy to Crypto
  • 25:07 Identifying Vulnerabilities: The Psychology of Belief
  • 28:53 Case Study: The Rise and Fall of Abraaj
  • 32:05 Future Trends: The Evolution of Charlatanry
  • 34:51 The Impact of Technology on Deception
  • 37:37 Navigating a World of Misinformation

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Published 2025-09-30

Economica with Victoria Bateman

64 min
Open

In this conversation, economist Dr. Victoria Bateman discusses the critical role of women in shaping economic prosperity throughout history. She argues that women's choices, independence, and labor have been overlooked in traditional economic narratives. The discussion covers various themes, including the impact of women's marriage decisions on population control, the relationship between women's independence and technological advancements, and the historical marginalization of women in economic history. Bateman emphasizes the importance of recognizing women's contributions to economic growth and the need for policies that support women's rights and independence.

Takeaways

  • Women's choices have historically shaped economic prosperity.
  • Independence in marriage decisions leads to smaller families and economic stability.
  • Women's labor is crucial for technological advancements and economic growth.
  • Democracy is sustained by empowering women and encouraging their participation.
  • The historical narrative often overlooks women's contributions to the economy.
  • Property rights for women are essential for their economic independence.
  • The blend of market and state influences leads to successful societies.
  • The cult of female modesty restricts women's economic participation.

Chapters

  • 00:00 The Hidden Role of Women in Economic History
  • 08:03 Impact of Women's Economic Freedom on Society
  • 14:41 Democracy and Women's Independence
  • 21:31 The Gender Gap in Economics
  • 27:50 Household Dynamics and Unpaid Labor
  • 35:03 Property Rights and Women's Economic Roles
  • 38:24 Empowering Women: The Role of Economic Freedom
  • 42:11 The Interplay of Markets and States
  • 44:43 The Cult of Female Modesty: Historical Context
  • 55:58 Modern Parallels: Women’s Freedom and Economic Prosperity
  • 59:24 Lessons from History: Women as Economic Drivers
  • 01:04:04 Revisiting Historical Narratives
  • 01:04:29 Conclusion and Call to Action

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Published 2025-09-09

Blueprints with Marcus du Sautoy

59 min
Open

In this conversation, Marcus Du Sautoy explores the intricate relationship between mathematics and various forms of art, including music, literature, and visual arts. He discusses how mathematical concepts such as prime numbers, symmetry, and randomness influence creative processes and artistic expressions. Through examples from renowned artists like Shakespeare and Dali, Du Sautoy illustrates how mathematics serves as a blueprint for understanding and creating art, while also emphasizing the emotional and aesthetic dimensions of both fields.

Takeaways

  • Mathematics and art are deeply interconnected.
  • The circle is fundamental to both mathematics and nature.
  • Prime numbers are essential building blocks in mathematics.
  • Music often employs mathematical structures for creativity.
  • Shakespeare used prime numbers to disrupt rhythm.
  • Symmetry plays a crucial role in both art and mathematics.
  • Dali's work reflects his fascination with scientific ideas.
  • Theatre allows for abstract exploration of mathematical concepts.
  • Ambiguity is embraced in art but avoided in mathematics.
  • Randomness can lead to unexpected creative outcomes.

Chapters

  • 00:00 Blueprints of Mathematics and Art
  • 02:35 Defining Creativity and Its Interplay
  • 04:24 Mathematicians as Collaborators with Artists
  • 07:17 The Fractal Nature of Jackson Pollock's Art
  • 12:54 The Significance of Circles in Mathematics
  • 16:31 Exploring the Mystery of Prime Numbers
  • 19:52 The Role of Primes in Music Composition
  • 28:01 Mathematics and the Structure of Music
  • 29:00 The Mathematical Foundations of Music
  • 31:50 Art and Mathematics: Dali's Exploration
  • 38:56 Theatrical Structures and Mathematical Concepts
  • 43:46 The Distinct Narratives of Numbers and Art
  • 48:07 Symmetry and Randomness: Blueprints of Creativity
  • 58:49 Exploring Creativity Through Mathematics

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Published 2025-09-05

Unequal with Eugenia Cheng

46 min
Open

In this conversation, Eugenia Cheng discusses the importance of making math accessible and engaging for everyone, particularly those who have been discouraged by traditional education methods. She emphasizes the intersection of math and art, the dangers of oversimplifying complex issues with numbers, and the need for a more nuanced understanding of equality and fairness in society. Cheng also highlights the significance of mentorship and the impact of gender dynamics in mathematics, advocating for a more inclusive approach to learning and appreciating math as a creative and thoughtful discipline.

Takeaways

  • Many people are put off math due to early education experiences.
  • Math and art should not be pitted against each other.
  • Creativity is essential in STEM fields.
  • Numbers can oversimplify complex realities.
  • Understanding inequality requires recognizing its nuances.
  • Context matters in mathematical reasoning.
  • We often forget important details in data interpretation.
  • Math can be appreciated without full understanding.
  • Building confidence in math is crucial for everyone.
  • Mentorship plays a vital role in academic success.

Chapters

  • 00:00 Introduction to Mathematical Laziness
  • 04:21 The Journey of a Mathematician
  • 06:57 Creativity in Math and Art
  • 09:33 Understanding Inequality through Math
  • 11:57 The Dangers of Simplifying with Numbers
  • 15:07 Political Debates and Mathematical Perspectives
  • 17:15 The Importance of Context in Math
  • 17:44 Category Theory and Abstraction in Math
  • 20:29 Neutrality and the Gray Areas of Equality
  • 24:02 Exploring Equality and Its Nuances
  • 25:17 Mathematics in Real-World Contexts
  • 28:49 The Intersection of Math and Marginalized Voices
  • 32:39 Overcoming Gender Bias in Mathematics
  • 35:28 The Role of Gut Instinct in Math
  • 37:54 The Surprising Aspects of Writing a Book
  • 42:51 Building Confidence in Math for Everyone
  • 46:15 Rethinking Fairness and Structural Challenges

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Published 2025-08-28

Breaking Math: When Math Meets a Technology Glitch

4 min
Open

This week’s episode isn’t our usual deep dive—it’s a behind-the-scenes update. On Monday, Breaking Math vanished from Spotify, Apple, YouTube, and more without warning. After digging in, we discovered a strange RSS glitch that merged our feed with another podcast.

In this quick update, Autumn shares:

  • What happened behind the scenes when the show disappeared
  • Which platforms are already fixed (and which we’re still waiting on)
  • How you can make sure you never lose track of Breaking Math again
  • What to expect from upcoming guest episodes

Follow Breaking Math online:
Website: https://www.breakingmath.io/
YouTube: youtube.com/@breakingmathpod
Twitter/X: @breakingmathpod
Bluesky: breakingmath.bsky.social
Instagram: @breakingmathmedia
Facebook: Breaking Math Community

Thanks for sticking with us—we’ll be back with a brand-new episode on Tuesday.

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Published 2025-08-19

Hate the Game

34 min
Open

In this conversation, Dr. Daryl Fairweather, chief economist at Redfin, discusses her book “Hate the Game,” that frames life and career decisions as strategic games. She emphasizes the importance of understanding economic principles to navigate personal and professional challenges, negotiate effectively, and reclaim agency in various aspects of life. Fairweather shares insights on overcoming barriers related to race and gender, the impact of information asymmetry, and the significance of designing one's own path in a competitive environment. The conversation highlights the necessity of introspection, strategic thinking, and the ability to adapt in a world that often feels rigged against certain individuals.

Takeaways

  • Life can be viewed as a game where strategic decisions matter.
  • Negotiation requires awareness of both your and your employer's options.
  • Workplace bullying can be addressed with strategic approaches.
  • Information asymmetry can hinder career advancement; awareness is key.
  • Barriers in academia can be overcome with strategy and support.
  • Race and gender dynamics play a significant role in economic opportunities.
  • Balancing strategic thinking with empathy is crucial for long-term success.
  • You can still achieve your goals despite systemic unfairness.

Chapters

  • 00:00 Introduction to Economic Principles
  • 03:57 Understanding Economic Cheat Codes
  • 07:08 Navigating Career Options and Negotiations
  • 09:39 Dealing with Workplace Dynamics
  • 11:33 Information Asymmetry in Decision Making
  • 14:02 Designing Your Own Game
  • 15:06 Identity and Power in Economics
  • 17:21 Overcoming Barriers in Economics
  • 25:51 The Impact of Housing on Economic Understanding
  • 30:38 Applying Economic Theory to Relationships
  • 33:02 Winning in a Rigged Game
  • 34:01 Life as a Game: Making Informed Decisions.

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Published 2025-08-12

Dots and Lines: Hidden Networks

37 min
Open

In this conversation, Autumn and Dr. Anthony Bonato explore the fascinating world of networks, discussing their significance in various fields, including mathematics, social interactions, and even the spread of diseases like COVID-19 in his new book Dots and Lines. Anthony shares his journey into network science, the importance of understanding networks in everyday life, and how they can reveal hidden connections. The discussion also touches on popular culture references, such as Game of Thrones and Survivor, to illustrate the practical applications of network theory. Ultimately, the conversation emphasizes the need to embrace mathematics and recognize the pervasive role of networks in our lives.

Takeaways

  • Networks are fundamental to understanding complex systems.
  • The COVID-19 pandemic highlighted the importance of network science.
  • Mathematics encompasses more than just numbers and shapes.
  • Personal experiences can lead to profound realizations about networks.
  • Everyday life is filled with examples of networks in action.
  • Game of Thrones and Survivor serve as engaging examples of network analysis.
  • The Bacon number illustrates connections in Hollywood.
  • Erdős number connects mathematicians through collaboration.

Chapters

  • 00:00 The Inspiration Behind the Book
  • 03:38 Understanding Networks: A New Perspective
  • 06:13 Networks in Everyday Life
  • 08:28 The Power of Networks in Society
  • 11:03 Real-World Applications of Network Science
  • 13:32 Pop Culture and Network Analysis
  • 15:38 The Bacon Number and Network Connections
  • 21:53 The Bacon Number and Small World Phenomenon
  • 26:34 Network Embeddings and Their Applications
  • 31:04 Graph Theory: Patterns and Connections
  • 35:11 The Importance of Mathematics in Everyday Life
  • 36:57 Introduction and Curiosity in Connections

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Published 2025-08-05

Robin Hood Math

32 min
Open

In this episode of Breaking Math, Dr. Noah Giansiracusa discusses his book 'Robin Hood Math', emphasizing the importance of mathematical literacy in navigating an algorithm-driven world. He explores how math can empower everyday people, the writing process behind his book, and practical applications of math in daily life, including social media algorithms and financial decisions. The conversation highlights the simplicity of the math that truly matters and encourages listeners to reclaim agency through understanding mathematics.

Takeaways

  • Math is a powerful tool that can empower individuals.
  • The concept of Robin Hood Math aims to redistribute mathematical knowledge.
  • Mathematical literacy is becoming as essential as reading.
  • Algorithms are deeply embedded in our daily lives, influencing decisions.
  • Understanding expected value can improve decision-making.
  • Averaging guesses can lead to better predictions.
  • Social media algorithms prioritize engagement, affecting content visibility.
  • Credit scores are calculated using weighted sums of various factors.
  • Many important mathematical concepts are simpler than they appear.
  • Mathematical literacy can help close equity gaps in society.

Chapters

  • 00:00 Monetizing Social Media for Educators
  • 02:25 The Birth of Robin Hood Math
  • 05:18 Empowering the Everyday Person with Math
  • 08:01 The Writing Process and Surprising Discoveries
  • 10:37 Practical Math Lessons for Everyday Life
  • 13:22 Understanding Algorithms in Social Media
  • 21:56 Understanding Engagement Algorithms
  • 24:28 The Impact of Mathematics on Financial Decisions
  • 29:54 Empowering Through Mathematical Literacy
  • 32:23 Exploring Key Themes in Mathematics

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Published 2025-07-29

What are Swim Training Patterns?

45 min
Open

In this conversation, Dr. Christoph Bartneck discusses the intersection of swimming and computer science, exploring how mathematical patterns can enhance swim training. He introduces the concept of a formal swim markup language to improve data exchange and training efficiency. The discussion also delves into the visualization of swimming techniques, the importance of mental engagement in training, and the aesthetic appeal of mathematics. Christoph shares insights on the challenges of writing his book and his vision for creating a global community around swimming and mathematics.

Takeaways

  • Programming languages can optimize swim training.
  • There's a gap in literature between math and sports science.
  • Data exchange in swimming training is challenging.
  • Visualizing swimming techniques aids in understanding.
  • Mathematical patterns can enhance training routines.
  • Repetitive tasks in swimming can be likened to repetitive songs.
  • Engagement in training is crucial for success.

Chapters

  • 00:00 The Motivation Behind Swim Training Patterns
  • 02:32 Intersection of Swimming and Computer Science
  • 05:56 Challenges in Measuring and Documenting Swim Performance
  • 09:32 The Role of Patterns in Swim Training
  • 11:54 Mathematical Patterns and Their Application in Swimming
  • 15:14 Exploring Repetitiveness in Music and Swim Training
  • 18:08 Art Projects and Mathematical Patterns
  • 21:13 Fermat's Theorem and Impossible Squares
  • 23:14 Making Math Accessible in Swim Training
  • 26:40 The Importance of a Shared Language in Coaching
  • 27:35 Applying Pattern-Based Approaches to Sports
  • 29:17 The Role of Structure in Training Across Sports
  • 30:02 Current Use of Frameworks in Elite Swimming
  • 30:10 Innovative Training Philosophies in Swimming
  • 32:30 Programming Languages and Their Applications in Sports Science
  • 34:56 The Joy of Writing and Creating
  • 38:59 Challenges in Writing and Communicating Mathematical Concepts
  • 41:37 The Journey of a Book and Community Engagement

Follow Christoph on his YouTube Channel and on bartneck.de.
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Published 2025-07-22

AI Ethics: Algorithms Go To College

11 min
Open

In this episode of Breaking Math, Autumn explores the complex world of AI ethics, focusing on its implications in education, the accuracy of AI systems, the biases inherent in algorithms, and the challenges of data privacy. The discussion emphasizes the importance of ethical considerations in mathematics and computer science, advocating for transparency and accountability in AI systems. Autumn also highlights the role of mathematicians in addressing these ethical dilemmas and the need for society to engage critically with AI technologies.

Takeaways

  • AI systems can misinterpret student behavior, leading to false accusations.
  • Bias in AI reflects historical prejudices encoded in data.
  • Predictive analytics can help identify at-risk students but may alter their outcomes.
  • Anonymization of data is often ineffective in protecting privacy.
  • Differential privacy offers a way to share data while safeguarding individual identities.
  • Ethics should be a core component of algorithm design.
  • The impact of biased algorithms can accumulate over time.
  • Mathematicians must understand both technical and human aspects of AI.
  • Society must question the values embedded in AI systems.
  • Small changes in initial conditions can lead to vastly different outcomes.

Chapters

  • 00:00 Introduction to AI Ethics
  • 02:14 The Accuracy and Implications of AI in Education
  • 04:14 Bias in AI and Its Consequences
  • 05:45 Data Privacy Challenges in AI
  • 06:37 Mathematical Solutions for Ethical AI
  • 08:04 The Role of Mathematicians in AI Ethics
  • 09:42 The Future of AI and Ethical Considerations

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Published 2025-07-08

Random Shuffle Isn't Random At All

8 min
Open

In this episode, we explore the intricate mathematics behind Sp0tify's (ok... and other's) shuffle feature, revealing how it is designed to feel random while actually being carefully curated. We discuss the psychological implications of randomness, the Fisher-Yates shuffle algorithm, and how engineers have created a system that respects human perception of randomness. The conversation delves into the philosophical aspects of curated randomness and the broader implications of mathematical principles in technology and human experience.

Takeaways

  • The shuffle feature is not truly random.
  • Humans struggle to recognize true randomness due to cognitive biases.
  • The Fisher-Yates shuffle algorithm is a standard for randomization.
  • Uses psychological techniques to enhance user satisfaction with shuffle.
  • Dithering is a method used to create a perception of randomness.
  • Shuffle feature analyzes multiple dimensions to optimize song selection.
  • The algorithm incorporates noise to maintain unpredictability.
  • Curated randomness is prevalent in various technologies beyond music.
  • Humans prefer sequences with fewer clusters to feel more random.
  • Mathematics can reveal insights into human behavior and preferences.

Chapters

00:00 The Hidden Mathematics of Spotify Shuffle

05:56 The Art of Psychological Randomness

07:58 Philosophical Implications of Curated Randomness

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Published 2025-07-01

Algorithms & AI Simplified - The Not So Mathy Version

9 min
Open

This conversation explores the intricate relationship between mathematics and artificial intelligence (AI) for people who don't want to get too math heavy and want things simplified as much as possible. It delves into how algorithms, machine learning, and various mathematical tools like linear algebra, calculus, and statistics form the backbone of AI technologies. The discussion highlights real-world applications of AI, the ethical implications of its use, and the importance of mathematical literacy in an increasingly AI-driven world. Ultimately, it emphasizes that understanding the mathematical foundations of AI empowers individuals to engage meaningfully with technology and its impact on society.

Takeaways:

  • Mathematics powers seemingly magical technologies like AI.
  • Algorithms are sets of instructions that guide AI processes.
  • Machine learning finds patterns in data through trial and error.
  • Linear algebra organizes data into vectors and matrices.
  • Calculus helps AI find optimal solutions to problems.
  • Probability theory allows AI to express uncertainty in predictions.
  • AI applications include medical diagnostics and financial algorithms.
  • Self-driving cars use mathematics to navigate and make decisions.
  • Mathematical literacy is crucial in an AI-driven world.
  • Understanding AI's math gives individuals agency in technology.


Chapters: 

00:00 The Mathematical Heart of AI

03:28 Mathematics in Action: Real-World Applications

05:33 Empowerment Through Understanding Mathematics

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Published 2025-06-24

What is Cryptography?

40 min
Open

This conversation delves into the intersection of quantum computing and cryptography, focusing on the implications of quantum computers for current encryption methods and the necessity for post-quantum cryptography. Dr. Dustin Moody from NIST discusses the threats posed by quantum computing, particularly through Shor's algorithm, and the ongoing efforts to develop new cryptographic standards that can withstand these threats. The discussion also covers the role of NIST in standardizing post-quantum algorithms, the mathematical challenges involved, and the importance of preparing businesses for the transition to these new systems.

All opinions are of the individual scientist and do not reflect the opinions of NIST or the federal Government.

Takeaways

  • Quantum computers harness principles of quantum physics for computation.
  • Shor's algorithm can efficiently factor large numbers, threatening RSA encryption.
  • Post-quantum cryptography aims to develop algorithms resistant to quantum attacks.
  • NIST is leading the effort to standardize post-quantum cryptographic algorithms.
  • Lattice-based algorithms are promising for post-quantum cryptography due to their efficiency.
  • Businesses must be proactive in transitioning to post-quantum cryptography.
  • The Harvest Now, Decrypt Later threat highlights the urgency of transitioning.
  • Quantum key distribution offers theoretically perfect security.
  • Different cryptographic algorithms are needed for various applications and devices.
  • The future of cryptography will rely on new mathematical challenges to ensure security.

Keywords

quantum computing, cryptography, post-quantum cryptography, NIST, cybersecurity, Shor's algorithm, digital signatures, lattice-based algorithms, encryption, quantum threats

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Published 2025-06-17

We Live in a Radioactive World: What is Dosimetry?

32 min
Open

In this episode,  Autumn interviews Dr. Ileana Pazos, an expert in dosimetry, discussing the critical role of radiation measurement in various industries, including healthcare and food safety. They explore the science behind dosimetry, the applications of radiation, the challenges faced in accurate measurements, and the misconceptions surrounding food irradiation. Ileana emphasizes the importance of public education and the need for global standards in radiation measurement, while also sharing her personal connection to the field and the future of radiation technologies.

All opinions are of the individual scientist and do not reflect the opinions of NIST or the federal Government.

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Published 2025-06-10

What is Life?

41 min
Open

In this conversation, Dr. Elizabeth Strychalski discusses the fascinating field of synthetic biology, particularly focusing on synthetic cells. She shares her journey into this research area, the challenges of defining life, and the ethical considerations surrounding synthetic biology. The conversation also explores the potential applications of synthetic cells in environmental science and medicine, as well as the importance of engineering standards and biomanufacturing for sustainability. Dr. Strychalski emphasizes the need for collaboration and communication in the scientific community to advance this field responsibly and effectively.

All opinions are of the individual scientist and do not reflect the opinions of NIST or the federal Government.

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Published 2025-06-03

Fire Science: What are Photoacoustic Measurements?

49 min
Open

In this episode of Breaking Math, hosts Autumn and Gabriel explore the innovative intersections of fire science and technology with experts Amy Mensch and Ryan Falkenstein-Smith who work at NIST. They discuss the groundbreaking photoacoustic technique for measuring soot deposition, its applications in fire safety and forensic investigations, and the broader implications for fire research. The conversation highlights the importance of integrating advanced technologies into firefighting and the potential for future developments in the field.

You can learn more about Time at time.gov and NIST at nist.gov.

All opinions are of the individual scientist and do not reflect the opinions of  NIST or the federal Government.

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Published 2025-02-26

What is Time?

71 min
Open

In this episode of Breaking Math, Autumn and Andrew Novick delve into the intricate world of timekeeping, exploring the significance of precise time measurement in modern technology. They discuss the evolution from traditional atomic clocks to cutting-edge optical clocks, the critical role of time in various industries, and the implications of time on fundamental physics, including Einstein's theories. The conversation also touches on the quirky concept of leap seconds and the future advancements in timekeeping technology, emphasizing the relative nature of time and its perception.

You can learn more about Time at time.gov and NIST at nist.gov.

All opinions are of the individual scientist and do not reflect the opinions of  NIST or the federal Government.

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Published 2025-02-18

What is Measurement?

7 min
Open

Summary

This episode of Breaking Math explores the fundamental concept of measurement, its importance in daily life, and the necessity for standardized units. The discussion highlights the role of the International System of Units (SI) and the National Institute of Standards and Technology (NIST) in maintaining measurement accuracy. It also touches on historical measurement failures and the evolution of measurement definitions, emphasizing the future of measurement in technology and science.

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Published 2024-11-19

How Analytics Can Revolutionize Affordable Energy

41 min
Open

In this episode, Dr. Destine Nock, CEO of Peoples Energy Analytics and a Professor at Carnegie Mellon University, joins Autumn to dive deep into the world of energy equity. They explore how cutting-edge data analytics are revolutionizing the landscape of affordable energy access. As the global demand for sustainable energy solutions continues to grow, the need to ensure fair and inclusive energy distribution becomes more critical than ever. Together, our hosts break down how data-driven insights are being leveraged to develop and implement policies that make energy more accessible to underserved communities, tearing down socioeconomic barriers and paving the way for a more equitable future.

Dr. Nock and Autumn discuss the powerful role that advanced analytics play in everything from analyzing consumption patterns to optimizing renewable energy distribution. They explore real-world case studies, highlight key initiatives, and speak with experts who are at the forefront of these transformative efforts. By the end of this episode, you’ll understand how strategic use of data can drive lasting change and help us build a world where energy is not a privilege but a right accessible to all.

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Published 2024-11-12

What is Chaos Theory?

13 min
Open

In this captivating episode of Breaking Math, hosts Gabriel and Autumn dive deep into chaos theory—a fascinating branch of mathematics that explores the behavior of complex systems highly sensitive to initial conditions. They break down the butterfly effect, revealing how tiny variations can lead to major consequences and discuss the inherent unpredictability in weather forecasting and the financial markets. The episode also uncovers chaos theory’s influence on human physiology, such as heart rate variability, and the mathematical beauty of fractals. Additionally, the hosts explore philosophical viewpoints, emphasizing how accepting life’s uncertainties can foster adaptability and resilience.

Key Takeaways:

Chaos Theory: Small actions can trigger significant outcomes, impacting everything from nature to human-made systems.

Butterfly Effect: Demonstrates how tiny differences in initial conditions can lead to vastly different outcomes.

Weather Forecasting: An excellent real-world illustration of chaos theory, showing how unpredictable weather can be.

Financial Markets: A reminder of the chaotic, complex forces that drive economic shifts and unpredictability.

Human Physiology: Chaos theory sheds light on natural processes, like the variability of heart rhythms.

Fractals: These intricate patterns showcase self-similarity and are visually striking examples of chaos in nature.

Philosophical Implications: Embracing chaos and uncertainty equips us to be more adaptable and creative.

Life's Unpredictability: A reflection of chaotic systems, reminding us to value flexibility.   Interconnectedness: Understanding chaos theory enhances our appreciation of how interwoven our world truly is.

Keywords: Chaos Theory, Butterfly Effect, Weather Forecasting, Economics, Fractals, Unpredictability, Complex Systems, Human Physiology, Philosophical Implications, Adaptability.

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Published 2024-11-05

AI in the Lab: How GPT-4 is Changing Molecules and Models

12 min
Open

In this episode of Breaking Math, we dive deep into the transformative power of large language models (LLMs) like GPT-4 in the fields of chemistry and materials science, based on the article "14 examples of how LLMs can transform materials science and chemistry: a reflection on a large language model hackathon" by Jablonka et al. from the Digital Discovery Journal. Discover how AI is revolutionizing scientific research with predictive modeling, lab automation, natural language interfaces, and data extraction from research papers. We explore how these models are streamlining workflows, accelerating discovery, and even reshaping education with personalized AI tutors.

Tune in to learn about real-world examples from a hackathon where scientists used LLMs to tackle some of the most pressing challenges in materials science and chemistry—and what this means for the future of scientific innovation.

Keywords: GPT-4, large language models, AI in chemistry, AI in materials science, predictive modeling, lab automation, AI in education, natural language processing, LLM hackathon, scientific research, molecular properties, Digital Discovery Journal, Jablonka

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Published 2024-10-29

The Fluid Dynamics of Sheep

15 min
Open

In this episode of Breaking Math, we explore the unexpected link between sheep herding and fluid dynamics!  Did you know that the way sheep move in a herd is governed by the same mathematical principles as water flowing in a river? By following simple rules of alignment, cohesion, and separation, sheep create a coordinated, fluid-like movement that scientists can model to predict behavior.

Join us as we break down how these principles apply not only to animal herds but also to real-world applications like robotics, autonomous vehicles, and crowd management. Whether you're a math lover, curious about animal behavior, or fascinated by the science behind traffic flow, this episode reveals the incredible power of mathematics in nature. Don’t forget to subscribe for more insights into the surprising connections between math and the world around us!

Timestamps:
00:00 - Introduction to Sheep Herding and Fluid Dynamics
02:15 - What is Fluid Dynamics?
06:30 - How Sheep Behave Like Particles in a Fluid
10:45 - Mathematical Models of Herding Behavior
16:20 - Real-world Applications: From Farming to Robotics
20:55 - Conclusion & Key Takeaways

Tags: #BreakingMath #FluidDynamics #AnimalBehavior #MathInNature #SheepHerding #Robotics #ScienceExplained #EmergentBehavior

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Published 2024-10-22

The Discovery of the Largest Prime Number: M136279841

8 min
Open

In this exciting episode of Breaking Math, we explore the groundbreaking discovery of the largest prime number ever found—M136279841, a Mersenne prime with over 41 million digits! Join us as we dive deep into the story behind this astonishing mathematical achievement, led by Luke Durant, a volunteer from the Great Internet Mersenne Prime Search (GIMPS) project.

Discover how Mersenne primes work, why they’re so important to the world of mathematics, and how cutting-edge technology like GPUs has revolutionized the search for these massive numbers. We also discuss the critical role that prime numbers play in cryptography and online security, making this discovery relevant far beyond just the realm of theoretical mathematics.

Learn about the global collaborative effort that made this record-breaking discovery possible, and find out how you can join the hunt for the next giant prime! Whether you're a math enthusiast, a tech geek, or just curious about the wonders of numbers, this episode is packed with insights that will inspire you to think about prime numbers in a whole new way.

Key Takeaways:
  • The discovery of M136279841, a prime number with 41,024,320 digits.
  • The role of Luke Durant and the GIMPS project in pushing the boundaries of prime number research.
  • How GPUs are transforming the way we discover massive primes.
  • The importance of prime numbers in modern cryptography and technology.
  • The connection between Mersenne primes and perfect numbers.
Links Mentioned:

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Published 2024-10-22

Exploring GFlowNets and AI-Driven Material Discovery for Carbon Capture

10 min
Open

In this episode of Breaking Math, hosts Gabriel Hesch and Autumn Phaneuf dive into the cutting-edge world of Generative Flow Networks (GFlowNets) and their role in artificial intelligence and material science. The discussion centers on how GFlowNets are revolutionizing the discovery of new materials for carbon capture, offering a powerful alternative to traditional AI models. Learn about the mechanics of GFlowNets, their advantages, and the groundbreaking results in developing materials with enhanced CO2 absorption capabilities. The episode also explores the future potential of GFlowNets in AI-driven material discovery and beyond, emphasizing their transformative impact on carbon capture technology and sustainable innovation.

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You can find the paper “Discovery of novel reticular materials for carbon dioxide capture using GFlowNets” by Cipcigan et al in Digital Discovery Journal by the Royal Society of Chemistry.

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Published 2024-10-15

Victorian Era Spooky Scientists & Paranormal Activity

23 min
Open

Explore the intriguing intersection of science and spiritualism in the Victorian era. This episode uncovers how prominent scientists like Michael Faraday, William James, and Marie & Pierre Curie engaged with supernatural phenomena and the rise of spiritualism. Discover the scientific efforts to debunk or understand paranormal activities, and how these investigations shaped modern science. Dive into the fascinating legacy of this 19th-century movement and its lasting impact on today's scientific inquiries into the unknown. Perfect for fans of history, science, and the supernatural.

Keywords: Victorian era, spiritualism, science, supernatural, Michael Faraday, William James, Alfred Russell Wallace, Curies, Eleanor Sidgwick, idiomotor effect

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Published 2024-10-08

Is AI Conscious?

11 min
Open

AI & Consciousness: Philosophical Debates, Ethical Implications & the Future of Conscious Machines
In this episode of Breaking Math, hosts Autumn and Gabriel explore the intricate relationship between artificial intelligence (AI) and consciousness. Delve into historical perspectives, philosophical debates, and the ethical questions surrounding the creation of conscious machines. Key topics include the evolution of AI, challenges in defining and testing consciousness, and the potential rights of AI beings. We also examine the Turing Test, the debate between strong AI vs. weak AI, and concepts like personhood and integrated information theory. Perfect for anyone interested in AI ethics, the nature of consciousness, and the responsibilities of advanced AI technology.

Keywords: AI, consciousness, Turing test, strong AI, weak AI, ethics, philosophy, personhood, integrated information theory, neural networks

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Published 2024-10-01

Molecular dynamics simulation with GFlowNets: machine learning the importance of energy estimators in computational chemistry and drug discovery

9 min
Open

In this episode of Breaking Math, hosts Autumn and Gabriel take a deep dive into the paper “Towards Equilibrium Molecular Conformation Generation with GFlowNets” by Volokova et al., published in the Digital Discovery Journal by the Royal Society of Chemistry. They explore the cutting-edge intersection of molecular conformations and machine learning, comparing traditional methods like molecular dynamics and cheminformatics with the innovative approach of Generative Flow Networks (GFlowNets) for molecular conformation generation.

The episode covers empirical results that showcase the effectiveness of GFlowNets in computational chemistry, their scalability, and the role of energy estimators in advancing fields like drug discovery. Tune in to learn how machine learning is transforming the way we understand molecular structures and driving breakthroughs in chemistry and pharmaceuticals.

Keywords: molecular conformations, machine learning, GFlowNets, computational chemistry, drug discovery, molecular dynamics, cheminformatics, energy estimators, empirical results, scalability, math, mathematics, physics, AI

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You can find the paper  “Towards equilibrium molecular conformation generation with GFlowNets” by Volokova et al in Digital Discovery Journal by the Royal Society of Chemistry.

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Published 2024-09-24

Do Plants Know Math?

56 min
Open

Mathematical Patterns in Plants: Fibonacci, Golden Ratio & Nature's Hidden Math with Christophe Gole & Nancy Pick
In this episode of Breaking Math, host Autumn interviews authors Christophe Gole and Nancy Pick about the captivating world of mathematical patterns in plants, inspired by their book Do Plants Know Math?. Explore the intersection of mathematics and biology as they discuss the Fibonacci sequence, the golden ratio, and spiral formations that reveal nature's mathematical beauty. Learn about the optimization of plant structures, the role of women in mathematics, and get recommendations for further reading. Topics include phyllotaxis, fractals, and their connections to AI, physics, and topology.

Keywords: mathematics, biology, plant math, Fibonacci, phylotaxis, spirals, golden ratio, fractals, nature, science, women in math,topology, ai, physics, math, plants, gardening

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Published 2024-09-17

Mapmatics: A Mathematician's Guide to Navigating the World with Maps with Paulina Rowinska

57 min
Open

Math & Cartography: Dr. Paula Rowinska on Map Projections, Gerrymandering & Real-World Math
In this episode of Breaking Math, host Autumn interviews Dr. Paula Rowinska about her unique journey from earning a PhD in mathematics to writing about math and cartography. They discuss the fascinating connection between map-making and mathematics, debunking misconceptions about map projections and exploring key topics like the coastline paradox, gerrymandering, and the traveling salesman problem. Learn how these mathematical concepts play a crucial role in areas like crime analysis, geopolitics, and more. Perfect for enthusiasts of math, cartography, and real-world problem-solving.

The conversation also celebrates the contributions of underrepresented women in mathematics and underscores the importance of math in everyday life. Tune in to discover how mathematics shapes our understanding of the world through cartography, topology, and even AI.

Keywords: mathematics, cartography, map projections, coastline paradox, gerrymandering, women in math, traveling salesman problem, crime analysis, topology, metric map, ai, physics, math

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Published 2024-09-10

The Intentional Engineer (with Jeff Perry)

55 min
Open

In this conversation, Gabriel and Autumn interview Jeff Perry, a career coach and author of the book 'The Intentional Engineer'. They discuss the importance of being intentional in one's career, understanding one's passions and skills, and building a strong professional network. Jeff shares his journey from being an engineer to becoming an engineer coach and offers advice on how to navigate career transitions. They also explore the concept of 'genius zones' and how to identify and leverage one's unique strengths and talents. In this conversation, Jeff discusses the concept of the zone of incompetence, competence, excellence, and genius. They share personal anecdotes and examples to illustrate these zones and emphasize the importance of self-awareness and collaboration. They also touch on the role of mindset in driving behavior and results, particularly in the context of engineering and tech careers. Jeff offers coaching and resources for individuals looking to make intentional career shifts or upgrades.

Keywords: career, intentionality, engineering, skills, passions, network, genius zones, strengths, talents, zone of incompetence, zone of competence, zone of excellence, zone of genius, self-awareness, collaboration, mindset, engineering, tech careers, intentional career shifts

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Published 2024-09-03

Math for English Majors with Ben Orlin

58 min
Open

Math & Language: Creativity, Quantification, and Making Math Accessible with Ben Orlin
In this episode of Breaking Math, hosts sit down with Ben Orlin, author of Math for English Majors and Math with Bad Drawings, to explore the intersection of math and language. Discover the unique skill sets required for mathematics and creativity, how math education can be made more accessible, and the role of quantification in empowering individuals across various fields, including literature and the arts. The conversation highlights the historical contributions of women in math, including the impact of Einstein’s wife on his work. Ben also shares insights into his writing process and the challenges of making math relatable to a broad audience. Learn how mathematical thinking can enhance one's appreciation for literature and the world.

Keywords: math, language, skill sets, math education, accessibility, quantification, power of math, women in math, Einstein's wife, math, literature, book, writing, perspective, abstraction, relationships

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Follow Ben Orlin on Twitter, and on his websites mathwithbaddrawings.com and mathgameswithbaddrawings.com  and find his book “Math for English Majors” on Amazon

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Published 2024-08-27

What is Data Visualization? From the Expert Behind PolicyViz

53 min
Open

In this episode Autumn and Dr. Jonathan Schwabish discuss the importance of strategic thinking in data visualization and the key elements of good data. He emphasizes the need to understand the data and how it was collected, as well as the importance of starting bar charts at zero. He also highlights common mistakes in data visualization, such as distorting or lying with visuals, and the potential impact of data visualization on policy decisions. Looking to the future, he discusses the role of AI in data visualization, the integration of AI into visualization tools, and the potential of augmented reality and virtual reality in data visualization. Jon Schwabish discusses the different data visualization tools he uses, including Excel, R, Tableau, Datawrapper, and Flourish. He emphasizes the importance of choosing the right tool for the specific use case and audience. He also highlights the need for policymakers and individuals to be trained in interpreting and using data visualizations effectively. Schwabish discusses the ethical considerations in data visualization, such as using inclusive language and considering accessibility.

Keywords: data visualization, strategic thinking, good data, common mistakes, impact on policy decisions, AI, augmented reality, virtual reality, data visualization tools, Excel, R, Tableau, Datawrapper, Flourish, policymakers, data interpretation, ethical considerations, inclusive language, accessibility

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Published 2024-08-20

Love Triangle and Other Maths (with Matt Parker)

59 min
Open

In this episode, Gabriel and Autumn interview mathematician, comedian, and author Matt Parker about his latest book, "Love Triangle." They discuss the unique page numbering system in the book, which is based on the sine function, and how it adds an extra layer of discovery for readers. They also explore the use of triangles and quads in 3D modeling, the concept of Perlin noise, and the perception of randomness. The conversation touches on the intersection of mathematics and creativity, as well as the practical applications of mathematical concepts in various fields. The conversation explores various topics related to mathematics, including the analysis of the Mona Lisa, the use of math in playing pool, the discovery of new shapes, and the application of math in various fields. The speakers discuss the motivation behind exploring these topics and the interplay between math and art. They also provide advice for science and math content creators on YouTube.

Keywords: mathematics, book, Love Triangle, page numbering, sine function, triangles, quads, 3D modeling, Perlin noise, randomness, creativity, practical applications, mathematics, Mona Lisa, parallax, pool, shapes, Fourier analysis, YouTube, physics, AI, machine learning

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Published 2024-08-16

The Black Hole Heist

12 min
Open

Surprise! It's a Friday episode for you! Yes, yes it is a rerun, but we wanted to share it anyways.  We can't wait for our fall lineup because it's packed with surprises. See you back on Tuesday. 

Keywords: Black holes, gravity, universe, physics, ai, machine learning, education, statistics, engineering, humanity

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Published 2024-08-13

Black Holes: The Abyss Part 3

77 min
Open

It's the last week of our summer break and we have 2 episodes this week for you as a little treat. So check out our show on Friday too for a little bit more fun. We can't wait for our fall lineup because it's packed with surprises. If you have not listened to the last two episodes, then we'd highly recommend going back and listening to those. We're choosing to present this information this way because otherwise we'd waste most of your time re-explaining concepts we've already covered.

Black holes are so bizarre when we measured against the yardstick of the mundanity of our day to day lives that they inspire fear, awe, and controversy. In this last episode of the Abyss series, we will look at some more cutting-edge problems and paradoxes surrounding black holes. So how are black holes and entanglement related? What is the holographic principle? And what is the future of black holes?

Keywords: Black holes, gravity, universe, physics, ai, machine learning, education, statistics, engineering, humanity

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Published 2024-08-06

Black Holes: The Abyss Part 2

56 min
Open

Happy Summer! We have another week of our summer break after this episode from 2018. We will be back shortly with more content and surprises!

Black holes are objects that seem exotic to us because they have properties that boggle our comparatively mild-mannered minds. These are objects that light cannot escape from, yet glow with the energy they have captured until they evaporate out all of their mass. They thus have temperature, but Einstein's general theory of relativity predicts a paradoxically smooth form. And perhaps most mind-boggling of all, it seems at first glance that they have the ability to erase information. So what is black hole thermodynamics? How does it interact with the fabric of space? And what are virtual particles?

Keywords: Black holes, gravity, universe, physics, ai, machine learning, education, statistics, engineering, humanity

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Published 2024-07-30

Black Holes: The Abyss Part 1

52 min
Open

Happy Summer! Check out part one of our three part series on black holes from 2018. Enjoy!

The idea of something that is inescapable, at first glance, seems to violate our sense of freedom. This sense of freedom, for many, seems so intrinsic to our way of seeing the universe that it seems as though such an idea would only beget horror in the human mind. And black holes, being objects from which not even light can escape, for many do beget that same existential horror. But these objects are not exotic: they form regularly in our universe, and their role in the intricate web of existence that is our universe is as valid as the laws that result in our own humanity. So what are black holes? How can they have information? And how does this relate to the edge of the universe?


Keywords: Black holes, gravity, universe, physics, ai, machine learning, education, statistics, engineering, humanity

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Published 2024-07-23

What are Journal Rankings? The basics: a minisode.

12 min
Open

In this minisode, Autumn explores the basics in the world of journal rankings and metrics. She discusses the importance of journal rankings and how they are determined, focusing on metrics like impact factor, mathematical citation quotient (MCQ), and publication power approach (PPA). She explains how these metrics provide insights into a journal's influence and performance, but also emphasizes the need for a comprehensive evaluation of research beyond just metrics.

Keywords: journal rankings, journal metrics, impact factor, mathematical citation quotient, publication power approach, research evaluation, math, physics, ai, machine learning, education, publishing, academic journals

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Published 2024-07-16

Why Machines Learn: The Math Behind AI

40 min
Open

In this episode Autumn and Anil Ananthaswamy discuss the inspiration behind his book “Why Machines Learn” and the importance of understanding the math behind machine learning. He explains that the book aims to convey the beauty and essential concepts of machine learning through storytelling, history, sociology, and mathematics. Anil emphasizes the need for society to become gatekeepers of AI by understanding the mathematical basis of machine learning. He also explores the history of machine learning, including the development of neural networks, support vector machines, and kernel methods. Anil highlights the significance of the backpropagation algorithm and the universal approximation theorem in the resurgence of neural networks.

Keywords: machine learning, math, inspiration, storytelling, history, sociology, gatekeepers, neural networks, support vector machines, kernel methods, backpropagation algorithm, universal approximation theorem, AI, ML, physics, mathematics, science

You can find Anil Ananthaswamy on Twitter @anilananth and his new book “Why Machines Learn”

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Published 2024-07-09

The Intersection of Mathematics and Democracy

62 min
Open

This discussion Autumn and Gabe delves into Ismar Volic's personal background and inspiration for writing the book, “Making Democracy Count” as well as the practical and theoretical aspects of voting systems. Additionally, the conversation explores the application of voting systems to everyday decision-making and the use of topological data analysis in understanding societal polarization. The conversation covers a wide range of topics, including data visualization, gerrymandering, electoral systems, and the intersection of mathematics and democracy. Volic, shares insights on the practical implications of implementing mathematical improvements in electoral systems and the legal and constitutional hurdles that may arise. He also discusses the importance of educating oneself about the quantitative underpinnings of democracy and the need for interdisciplinary discussions that bridge mathematics and politics.

Keywords: math podcast, creativity, mascot, background, Matlab, ranked choice voting, elections, author's background, inspiration, voting systems, topological data analysis, societal polarization, mathematics, democracy, data visualization, gerrymandering, electoral systems, interdisciplinary discussions, practical implications, legal hurdles, constitutional considerations

You can find Ismar Volic on Twitter and LinkedIn @ismarvolic. Please go check out the Institute for Mathematics and Democracy and Volic’s new book “Making Democracy Count”

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Published 2024-07-02

Math Lounge: Celebrating 101 Episodes

47 min
Open

In this conversation, Gabe and Autumn celebrate the 101st episode of Breaking Math and discuss the evolution of the podcast. They highlight the importance of creativity in teaching mathematics and share their plans to expand Breaking Math into Breaking Math Media. They also discuss the history of physics and the big questions that inform the podcast. The hosts express their desire to collaborate with listeners and explore practical applications of math in different fields. They also mention books like 'A Quantum Story' and 'Incomplete Nature' that delve into the mysteries of quantum mechanics and consciousness. The hosts highlight the unique and creative nature of their podcast, inviting listeners to join them in the Math Lounge, a metaphorical nightclub where math and creativity intersect.

Keywords: Breaking Math, podcast, creativity, mathematics, Breaking Math Media, physics, history, quantum mechanics, book discussion, double-slit experiment, quantum mechanics, interdisciplinary discussions, machine learning, neuroscience, gamification of math, collaboration, practical applications, consciousness, Math Lounge

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Published 2024-06-18

Minisode: Absolutely Nothing

19 min
Open

In this episode of Breaking Math, Autumn and Gabe explore the concept of nothingness and its significance in various fields. They discuss the philosophical, scientific, mathematical, and literary aspects of nothingness, highlighting its role in understanding reality and existence. They mention books like 'Incomplete Nature' by Terence Deacon and 'Zero: The Biography of a Dangerous Idea' by Charles Seife, which delve into the concept of absence and zero. The episode concludes by emphasizing the complexity and versatility of nothingness, inviting listeners to think deeper about its implications.

Keywords: nothingness, philosophy, science, mathematics, literature, reality, existence, absence, zero

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Published 2024-05-28

Can We Survive on Mars? Hot Tips with Zach Weinersmith (Part 2)

34 min
Open

In this conversation, Autumn Phaneuf interviews Zach Weinersmith, a cartoonist and writer, about the feasibility and implications of space settlement. They discuss the challenges and misconceptions surrounding space colonization, including the idea that it will make us rich, mitigate war, and make us wiser. They explore the potential of the moon and Mars as settlement options, as well as the concept of rotating space stations. They also touch on the physiological effects of space travel and the need for further research in areas such as reproduction and ecosystem design. The conversation explores the challenges and implications of human settlement in space. It discusses the lack of data on the long-term effects of space travel on the human body, particularly for women. The conversation also delves into the need for a closed-loop ecosystem for sustainable space settlement and the legal framework surrounding space exploration and resource extraction. The main takeaways include the importance of addressing reproductive and medical challenges, the need for a better legal regime, and the debunking of misconceptions about space settlement.

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email: breakingmathpodcast@gmail.com

A City on Mars, Keywords space settlement, feasibility, challenges, misconceptions, moon, Mars, rotating space stations, reproduction, ecosystem design, space settlement, human reproduction, closed-loop ecosystem, space law, resource extraction, logistics, math.

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Published 2024-05-21

Can We Survive on Mars? Hot Tips with Zach Weinersmith

32 min
Open

In this conversation, Autumn Phaneuf and Zach Weinersmith discusses his new book, A City on Mars, which takes a humorous look at the challenges of building a Martian society. He explores the misconceptions and myths surrounding space settlement and the feasibility of colonizing Mars. He argues that space is unlikely to make anyone rich and that the idea that space will mitigate war is unsupported. He also discusses the potential benefits and limitations of settling on the Moon and Mars, as well as the technical challenges involved.

Follow Zach Weinersmith on his website and Twitter

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email: breakingmathpodcast@gmail.com

A City on Mars, space settlement, Mars colonization, misconceptions, myths, feasibility, space myths, space economics, war, Moon settlement, technical challenges, logistics, math.

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Published 2024-05-14

What's the Use? Interview with Professor Ian Stewart

44 min
Open

Welcome to another engaging episode of the Breaking Math Podcast! Today's episode, titled "What is the Use?," features a fascinating conversation with the renowned mathematician and author, Professor Ian Stewart. As Professor Stewart discusses his latest book "What's the Use? How Mathematics Shapes Everyday Life," we dive deep into the real-world applications of mathematics that often go unnoticed in our daily technologies, like smartphones, and their unpredictable implications in various fields.

We'll explore the history of quaternions, invented by William Rowan Hamilton, which now play a critical role in computer graphics, gaming, and particle physics. Professor Stewart will also shed light on the non-commutative nature of quaternions, mirroring the complexities of spatial rotations, and how these mathematical principles find their correspondence in the natural world.

Furthermore, our discussion will encompass the interconnectivity within mathematics, touching upon how algebra, geometry, and trigonometry converge to paint a broader picture of this unified field. We also discuss the intriguing concept of "Fearful Symmetry" and how symmetrical and asymmetrical patterns govern everything from tiger stripes to sand dunes.

With references to his other works, including "Professor Stewart's Cabinet of Mathematical Curiosities" and "The Science of Discworld," Professor Stewart brings an element of surprise and entertainment to the profound impact of mathematics on our understanding of the world.

So stay tuned as we unlock the mysteries and the omnipresent nature of math in this thought-provoking episode with Professor Ian Stewart!

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Published 2024-05-07

Bayes' Theorem Explains It All: An Interview with Tom Chivers

49 min
Open

Tom Chivers discusses his book 'Everything is Predictable: How Bayesian Statistics Explain Our World' and the applications of Bayesian statistics in various fields. He explains how Bayesian reasoning can be used to make predictions and evaluate the likelihood of hypotheses. Chivers also touches on the intersection of AI and ethics, particularly in relation to AI-generated art. The conversation explores the history of Bayes' theorem and its role in science, law, and medicine. Overall, the discussion highlights the power and implications of Bayesian statistics in understanding and navigating the world.

The conversation explores the role of AI in prediction and the importance of Bayesian thinking. It discusses the progress of AI in image classification and the challenges it still faces, such as accurately depicting fine details like hands. The conversation also delves into the topic of predictions going wrong, particularly in the context of conspiracy theories. It highlights the Bayesian nature of human beliefs and the influence of prior probabilities on updating beliefs with new evidence. The conversation concludes with a discussion on the relevance of Bayesian statistics in various fields and the need for beliefs to have probabilities and predictions attached to them.

Takeaways

  • Bayesian statistics can be used to make predictions and evaluate the likelihood of hypotheses.
  • Bayes' theorem has applications in various fields, including science, law, and medicine.
  • The intersection of AI and ethics raises complex questions about AI-generated art and the predictability of human behavior.
  • Understanding Bayesian reasoning can enhance decision-making and critical thinking skills. AI has made significant progress in image classification, but still faces challenges in accurately depicting fine details.
  • Predictions can go wrong due to the influence of prior beliefs and the interpretation of new evidence.
  • Beliefs should have probabilities and predictions attached to them, allowing for updates with new information.
  • Bayesian thinking is crucial in various fields, including AI, pharmaceuticals, and decision-making.
  • The importance of defining predictions and probabilities when engaging in debates and discussions.

Subscribe to Breaking Math wherever you get your podcasts.

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email: breakingmathpodcast@gmail.com

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Published 2024-04-30

Interview with Steve Nadis, Co-author of 'Gravity of Math'

52 min
Open

Summary

**Tensor Poster - If you are interested in the Breaking Math Tensor Poster on the mathematics of General Relativity, email us at BreakingMathPodcast@gmail.com

In this episode, Gabriel Hesch and Autumn Phaneuf interview Steve Nadis, the author of the book 'The Gravity of Math.' They discuss the mathematics of gravity, including the work of Isaac Newton and Albert Einstein, gravitational waves, black holes, and recent developments in the field. Nadis shares his collaboration with Shing-Tung Yau and their journey in writing the book. They also talk about their shared experience at Hampshire College and the importance of independent thinking in education. In this conversation, Steve Nadis discusses the mathematical foundations of general relativity and the contributions of mathematicians to the theory. He explains how Einstein was introduced to the concept of gravity by Bernhard Riemann and learned about tensor calculus from Gregorio Ricci and Tullio Levi-Civita. Nadis also explores Einstein's discovery of the equivalence principle and his realization that a theory of gravity would require accelerated motion. He describes the development of the equations of general relativity and their significance in understanding the curvature of spacetime. Nadis highlights the ongoing research in general relativity, including the detection of gravitational waves and the exploration of higher dimensions and black holes. He also discusses the contributions of mathematician Emmy Noether to the conservation laws in physics. Finally, Nadis explains Einstein's cosmological constant and its connection to dark energy.

Chapters

00:00 Introduction and Book Overview

08:09 Collaboration and Writing Process

25:48 Interest in Black Holes and Recent Developments

35:30 The Mathematical Foundations of General Relativity

44:55 The Curvature of Spacetime and the Equations of General Relativity

56:06 Recent Discoveries in General Relativity

01:06:46 Emmy Noether's Contributions to Conservation Laws

01:13:48 Einstein's Cosmological Constant and Dark Energy

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email: breakingmathpodcast@gmail.com

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Published 2024-04-23

The 10,000 Year Problem (feat. David Gibson of Ray Kitty Creation Workship)

34 min
Open

Summary: The episode discusses the 10,000 year dilemma, which is a thought experiment on how to deal with nuclear waste in the future. Today's episode is hosted by guest host David Gibson, who is the founder of the Ray Kitty Creation Workshop. (Find out more about the Ray Kitty Creation Workshop by clicking here).

Gabriel and Autumn are out this week, but will be returning in short order with 3 separate interviews with authors of some fantastic popular science and math books including:

  • The Gravity of Math: How Geometry Rules the Universe by Dr. Shing-Tung Yau and Steve Nadis. This book is all about the history of our understanding of gravity from the theories of Isaac Newton to Albert Einstein and beyond, including gravitational waves, black holes, as well as some of the current uncertainties regarding a precise definition of mass. On sale now!
  • EVERYTHING IS PREDICTABLE: How Bayesian Statistics Explain Our World by Tom Chivers. Published by Simon and Schuster. This book explains the importance of Baye's Theorem in helping us to understand why highly accurate screening tests can lead to false positives, a phenomenon we saw during the Covid-19 pandemic; How a failure to account for Bayes’ Theorem has put innocent people in jail; How military strategists using the theorem can predict where an enemy will strike next, and how Baye's Theorem is helping us to understang machine learning processes - a critical skillset to have in the 21st century. Available 05/07/2024
  • A CITY ON MARS: Can we settle space, should we settle space, and have we really thought this through? by authors Dr. Kelly and Zach Weinersmith. Zach Weinersmith is the artist and creator of the famous cartoon strip Saturday Morning Breaking Cereal! We've got a lot of great episodes coming up! Stay tuned.

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Published 2024-04-16

The Mathematical Heart of Games Explored with Prof. du Sautoy

74 min
Open

An interview with Prof. Marcus du Sautoy about his book Around the Wold in Eighty Games . . . .a Mathematician Unlocks the Secrets of the World's Greatest Games. Topics covered in Today's Episode:

1. Introduction to Professor Marcus du Sautoy and the Role of Games

- Impact of games on culture, strategy, and learning

- The educational importance of games throughout history

2. Differences in gaming cultures across regions like India and China

3. Creative Aspects of Mathematics

4. The surprising historical elements and banned games by Buddha

5. Historical and geographical narratives of games rather than rules

6. Game Theory and Education

7. Unknowable questions like thermodynamics and universe's infinity

8. Professor du Sautoy's Former Books and Collections

9. A preview of his previous books and their themes

10. Gaming Cultures and NFTs in Blockchain

11. Gamification in Education

12. The Role of AI in Gaming

13. Testing machine learning in mastering games like Go

14. Alphago's surprising move and its impact on Go strategies

15 . The future of AI in developing video game characters, plots, and environments

16. Conclusion and Giveaway Announcement

*Free Book Giveaway of Around The World in 88 Games . . . by Professor Marcus Du Sautory! Follow us on our socials for details: Follow us on X: @BreakingMathPod

Follow us on Instagram: @Breaking Math Media

Email us: BreakingMathPodacst@gmail.com

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Published 2024-04-04

Brain Organelles, AI, and Other Scary Science - An Interview with GT (Part 2)

31 min
Open

Summary

Brain Organelles, A.I. and Defining Intelligence in Nature-

In this episode, we continue our fascinating interview with GT, a science content creator on TikTok and YouTube known for their captivating - and sometimes disturbing science content. GT can be found on the handle ‘@bearBaitOfficial’ on most social media channels. In this episode, we resume our discussion on Brain Organelles - which are grown from human stem cells - how they are being used to learn about disease, how they may be integrated in A.I. as well as eithical concerns with them. We also ponder what constitutes intelligence in nature, and even touch on the potential risks of AI behaving nefariously. You won't want to miss this thought-provoking and engaging discussion.30% Off ZenCastr Discount

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Published 2024-03-16

LEAN Theorem Provers used to model Physics and Chemistry

47 min
Open

This episode is inspired by a correspondence the Breaking Math Podcast had with the editors of Digital Discovery, a journal by the Royal Society of Chemistry. In this episode the hosts review a paper about how the Lean Interactive Theorem Prover, which is usually used as a tool in creating mathemtics proofs, can be used to create rigorous and robust models in physics and chemistry.

Also - we have a brand new member of the Breaking Math Team! This episode is the debut episode for Autumn, CEO of Cosmo Labs, occasional co-host / host of the Breaking Math Podcast, and overall contributor who has been working behind the scenes on the podcast on branding and content for the last several months. Welcome Autumn!

Autumn and Gabe discuss how the paper explores the use of interactive theorem provers to ensure the accuracy of scientific theories and make them machine-readable. The episode discusses the limitations and potential of interactive theorem provers and highlights the themes of precision and formal verification in scientific knowledge. This episode also provide resources (listed below) for listeners interested in learning more about working with the LEAN interactive theorem prover.

Takeaways

  • Interactive theorem provers can revolutionize the way scientific theories are formulated and verified, ensuring mathematical certainty and minimizing errors.
  • Interactive theorem provers require a high level of mathematical knowledge and may not be accessible to all scientists and engineers.
  • Formal verification using interactive theorem provers can eliminate human error and hidden assumptions, leading to more confident and reliable scientific findings.
  • Interactive theorem provers promote clear communication and collaboration across disciplines by forcing explicit definitions and minimizing ambiguities in scientific language. Lean Theorem Provers enable scientists to construct modular and reusable proofs, accelerating the pace of knowledge acquisition.
  • Formal verification presents challenges in terms of transforming informal proofs into a formal language and bridging the reality gap.
  • Integration of theorem provers and machine learning has the potential to enhance creativity, verification, and usefulness of machine learning models.
  • The limitations and variables in formal verification require rigorous validation against experimental data to ensure real-world accuracy.
  • Lean Theorem Provers have the potential to provide unwavering trust, accelerate innovation, and increase accessibility in scientific research.
  • AI as a scientific partner can automate the formalization of informal theories and suggest new conjectures, revolutionizing scientific exploration.
  • The impact of Lean Theorem Provers on humanity includes a shift in scientific validity, rapid scientific breakthroughs, and democratization of science.

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Published 2024-03-05

Brain Organelles, AI, and the Other Scary Science - An Interview with GT (Part 1)

30 min
Open

This conversation explores the topic of brain organoids and their integration with robots. The discussion covers the development and capabilities of brain organoids, the ethical implications of their use, and the differences between sentience and consciousness. The conversation also delves into the efficiency of human neural networks compared to artificial neural networks, the presence of sleep in brain organoids, and the potential for genetic memories in these structures. The episode concludes with an invitation to part two of the interview and a mention of the podcast's Patreon offering a commercial-free version of the episode.

Takeaways

  • Brain organoids are capable of firing neural signals and forming structures similar to those in the human brain during development.
  • The ethical implications of using brain organoids in research and integrating them with robots raise important questions about sentience and consciousness.
  • Human neural networks are more efficient than artificial neural networks, but the reasons for this efficiency are still unknown.
  • Brain organoids exhibit sleep-like patterns and can undergo dendrite growth, potentially indicating learning capabilities.
  • Collaboration between scientists with different thinking skill sets is crucial for advancing research in brain organoids and related fields.

Chapters

  1. 00:00 Introduction: Brain Organoids and Robots
  2. 00:39 Brain Organoids and Development
  3. 01:21 Ethical Implications of Brain Organoids
  4. 03:14 Summary and Introduction to Guest
  5. 03:41 Sentience and Consciousness in Brain Organoids
  6. 04:10 Neuron Count and Pain Receptors in Brain Organoids
  7. 05:00 Unanswered Questions and Discomfort
  8. 05:25 Psychological Discomfort in Brain Organoids
  9. 06:21 Early Videos and Brain Organoid Learning
  10. 07:20 Efficiency of Human Neural Networks
  11. 08:12 Sleep in Brain Organoids
  12. 09:13 Delta Brainwaves and Brain Organoids
  13. 10:11 Creating Brain Organoids with Specific Components
  14. 11:10 Genetic Memories in Brain Organoids
  15. 12:07 Efficiency and Learning in Human Brains
  16. 13:00 Sequential Memory and Chimpanzees
  17. 14:18 Different Thinking Skill Sets and Collaboration
  18. 16:13 ADHD and Hyperfocusing
  19. 18:01 Ethical Considerations in Brain Research
  20. 19:23 Understanding Genetic Mutations
  21. 20:51 Brain Organoids in Rat Bodies
  22. 22:14 Dendrite Growth in Brain Organoids
  23. 23:11 Duration of Dendrite Growth
  24. 24:26 Genetic Memory Transfer in Brain Organoids
  25. 25:19 Social Media Presence of Brain Organoid Companies
  26. 26:15 Brain Organoids Controlling Robot Spiders
  27. 27:14 Conclusion and Invitation to Part 2

References:

Muotri Labs (Brain Organelle piloting Spider Robot)

Cortical Labs (Brain Organelle's trained to play Pong)

*For a copy of the episode transcript, email us at breakingmathpodcast@gmail.com

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Summary:

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Published 2024-02-27

Can OpenAi's SORA learn and model real-world physics? (Part 1 of n)

34 min
Open

This is a follow up on our previous episode on OpenAi's SORA. We attempt to answer the question, "Can OpenAi's SORA model real-world physics?"

We go over the details of the technical report, we discuss some controversial opinoins by experts in the field at Nvdia and Google's Deep Mind.

The transcript for episode is avialable below upon request.

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Published 2024-02-20

OpenAi SORA, Physics-Informed ML, and a.i. Fraud- Oh My!

36 min
Open

OpenAI's Sora, a text-to-video model, has the ability to generate realistic and imaginative scenes based on text prompts. This conversation explores the capabilities, limitations, and safety concerns of Sora. It showcases various examples of videos generated by Sora, including pirate ships battling in a cup of coffee, woolly mammoths in a snowy meadow, and golden retriever puppies playing in the snow. The conversation also discusses the technical details of Sora, such as its use of diffusion and transformer models. Additionally, it highlights the potential risks of AI fraud and impersonation. The episode concludes with a look at the future of physics-informed modeling and a call to action for listeners to engage with Breaking Math content.

Takeaways

  • OpenAI's Sora is a groundbreaking text-to-video model that can generate realistic and imaginative scenes based on text prompts.
  • Sora has the potential to revolutionize various industries, including entertainment, advertising, and education.
  • While Sora's capabilities are impressive, there are limitations and safety concerns, such as the potential for misuse and the need for robust verification methods.
  • The conversation highlights the importance of understanding the ethical implications of AI and the need for ongoing research and development in the field.

Chapters

00:00 Introduction to OpenAI's Sora

04:22 Overview of Sora's Capabilities

07:08 Exploring Prompts and Generated Videos

12:20 Technical Details of Sora

16:33 Limitations and Safety Concerns

23:10 Examples of Glitches in Generated Videos

26:04 Impressive Videos Generated by Sora

29:09 AI Fraud and Impersonation

35:41 Future of Physics-Informed Modeling

36:25 Conclusion and Call to Action

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Contact us at breakingmathpodcast@gmail.com

Summary

#OpenAiSora #

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Published 2024-02-18

Math, Music, and Artificial Intelligence - Levi McClain Interview (Final Part)

28 min
Open

Help Support The Podcast by clicking on the links below:

Transcripts are available upon request. Email us at BreakingMathPodcast@gmail.com

Follow us on X (Twitter)

Follow us on Social Media Pages (Linktree)

Visit our guest Levi McClain's Pages:

youtube.com/@LeviMcClain

levimcclain.com/

Summary

Levi McClean discusses various topics related to music, sound, and artificial intelligence. He explores what makes a sound scary, the intersection of art and technology, sonifying data, microtonal tuning, and the impact of using 31 notes per octave. Levi also talks about creating instruments for microtonal music and using unconventional techniques to make music. The conversation concludes with a discussion on understanding consonance and dissonance and the challenges of programming artificial intelligence to perceive sound like humans do.

Takeaways:

  • The perception of scary sounds can be analyzed from different perspectives, including composition techniques, acoustic properties, neuroscience, and psychology.
  • Approaching art and music with a technical mind can lead to unique and innovative creations.
  • Sonifying data allows for the exploration of different ways to express information through sound.
  • Microtonal tuning expands the possibilities of harmony and offers new avenues for musical expression.
  • Creating instruments and using unconventional techniques can push the boundaries of traditional music-making.
  • Understanding consonance and dissonance is a complex topic that varies across cultures and musical traditions.
  • Programming artificial intelligence to understand consonance and dissonance requires a deeper understanding of human perception and cultural context.

Chapters

00:00 What Makes a Sound Scary

03:00 Approaching Art and Music with a Technical Mind

05:19 Sonifying Data and Turning it into Sound

08:39 Exploring Music with Microtonal Tuning

15:44 The Impact of Using 31 Notes per Octave

17:37 Why 31 Notes Instead of Any Other Arbitrary Number

19:53 Creating Instruments for Microtonal Music

21:25 Using Unconventional Techniques to Make Music

23:06 Closing Remarks and Questions

24:03 Understanding Consonance and Dissonance

25:25 Programming Artificial Intelligence to Understand Consonance and Dissonance

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Published 2024-02-13

Math, Music, Neuroscience, and Fear - an Interview with Musician Levi McClain

33 min
Open

We are joined today by content creator Levi McClain to discuss the mathematics behind music theory, neuroscience, and human experiences such as fear as they relate to audio processing.

For a copy of the episode transcript, email us at BreakingMathPodcast@gmail.com.

For more in depth discussions on these topics and more, check out Levi's channels at:

Patreon.com/LeviMcClain

youtube.com/@LeviMcClain

Tiktok.com/@levimcclain

Instagram.com/levimcclainmusic

Help Support The Podcast by clicking on the links below:

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Published 2024-02-06

Intelligence in Nature v. Machine Learning - an Interview with Brit Cruise(Part 2)

45 min
Open

Help Support The Podcast by clicking on the links below:

Part 2/2 of the interview with Brit Cruise, creator of the YouTube channel "Art of the Problem," about interesting mathematics,, electrical and computer engineering problems.

In Part 1, we explored what 'intelligence' may be defined as by looking for examples of brains and proto-brains found in nature (including mold, bacteria, fungus, insects, fish, reptiles, and mammals).

In Part 2, we discuss aritifical neural nets and how they are both similar different from human brains, as well as the ever decreasing gap between the two.

Brit's YoutTube Channel can be found here: Art of the Problem - Brit Cruise

Transcript will be made available soon! Stay tuned. You may receive a transcript by emailing us at breakingmathpodcast@gmail.com.

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Published 2024-01-30

Intelligence in Nature v. Machine Learning-An Interview with Brit Cruise - Part 1 of 2

36 min
Open

In this episode (part 1 of 2), I interview Brit Cruise, creator of the YouTube channel 'Art of the Problem.' On his channel, he recently released the video "ChatGPT: 30 Year History | How AI learned to talk." We discuss examples of intelligence in nature and what is required in order for a brain to evolve at the most basic level. We use these concepts to discuss what artificial intelligence - such as Chat GPT - both is and is not.

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Published 2024-01-21

A.I. and Materials Discovery - an Interview with Taylor Sparks

17 min
Open

Transcripts of this episode are avialable upon request. Email us at BreakingMathPodcast@gmail.com.

In this episode Gabriel Hesch interviews Taylor Sparks, a professor of material science and engineering, about his recent paper on the use of generative modeling a.i. for material disovery. The paper is published in the journal Digital Discovery and is titled 'Generative Adversarial Networks and Diffusion MOdels in Material Discovery. They discuss the purpose of the call, the process of generative modeling, creating a representation for materials, using image-based generative models, and a comparison with Google's approach. They also touch on the concept of conditional generation of materials, the importance of open-source resources and collaboration, and the exciting developments in materials and AI. The conversation concludes with a discussion on future collaboration opportunities.

Takeaways

  • Generative modeling is an exciting approach in materials science that allows for the prediction and creation of new materials.
  • Creating a representation for materials, such as using the crystallographic information file, enables the application of image-based generative models.
  • Google's approach to generative modeling received attention but also criticism for its lack of novelty and unconditioned generation of materials.
  • Open-source resources and collaboration are crucial in advancing materials informatics and machine learning in the field of materials science.

Help Support The Podcast by clicking on the links below:

  • Start YOUR podcast on ZenCastr! Use my special link ZenCastr Discount to save 30% off your first month of any Zencastr paid plan
  • Visit our PatreonHow is Machine Learning being used to further original scientific discoveries?

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Published 2024-01-11

In Memory of Sofia Baca, Cofounder and cohost of Breaking Math

48 min
Open
In October of 2023, Sofia Baca passed away unexpectedly from natural causes. Sofia was one of the founders and cohosts of the Breaking Math Podcast. In this episode, host Gabriel Hesch interviews Diane Baca, mother of Sofia Baca as we talk about her passions for creativity, mathematics, science, and discovering what it means to be human.


Sofia lived an exceptional life with explosive creativity, a voracious passion for mathematics, physics, computer science, and creativity. Sofia also struggled immensely with mental health issues which included substance abuse as well as struggling for a very long time understand the source of their discontent. Sofia found great happiness in connecting with other people through teaching, tutoring, and creative expression. The podcast will continue in honor of Sofia. There are many folders of ideas that Sofia left with ideas for the show or for other projects. We will continue this show with sharing some of these ideas, but also with sharing stories of Sofia - including her ideas and her struggles in hopes that others may find solace in that they are not alone in their struggles. But also in hopes that others may find inspiration in what Sofia had to offer.

We miss you dearly, Sofia.
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Published 2023-07-24

Correct. Now Try Again (Multiple Approaches to the Same Problem)

37 min
Open

Join Sofía Baca and her guests, the host and co-host of the Nerd Forensics podcast, Millicent Oriana and Jacob Urban, as they explore what it means to be able to solve one problem in multiple ways.

This episode is distributed under a Creative Commons Attribution-ShareAlike 4.0 International License. For full text, visit: https://creativecommons.org/licenses/by-sa/4.0/

[Featuring: Sofía Baca; Millicent Oriana, Jacob Urban[

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Published 2023-06-26

Physical Dimension (Dimensional Analysis)

35 min
Open

The history of mathematics, in many ways, begins with counting. Things that needed, initially, to be counted were, and often still are, just that; things. We can say we have twelve tomatoes, or five friends, or that eleven days have passed. As society got more complex, tools that had been used since time immemorial, such as string and scales, became essential tools for counting not only concrete things, like sheep and bison, but more abstract things, such as distance and weight based on agreed-upon multiples of physical artifacts that were copied. This development could not have taken place without the idea of a unit: a standard of measuring something that defines what it means to have one of something. These units can be treated not only as counting numbers, but can be manipulated using fractions, and divided into arbitrarily small divisions. They can even be multiplied and divided together to form new units. So where does the idea of a unit come from? What's the difference between a unit, a dimension, and a physical variable? And how does the idea of physical dimension allow us to simplify complex problems? All of this and more on this episode of Breaking Math.

Distributed under a CC BY-SA 4.0 International License. For full text, visit: https://creativecommons.org/licenses/by-sa/4.0/

[Featuring: Sofía Baca; Millicent Oriana, Jacob Urban]

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Published 2023-06-08

79: 1 2 3 (Counting)

47 min
Open


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Join Sofia Baca and Nerd Forensics co-host Jacob Urban as they discuss all things counting!

Counting is the first arithmetic concept we learn, and we typically learn to do so during early childhood. Counting is the basis of arithmetic. Before people could manipulate numbers, numbers had to exist. Counting was first done on the body, before it was done on apparatuses outside the body such as clay tablets and hard drives. However, counting has become an invaluable tool in mathematics itself, as became apparent when counting started to be examined analytically. How did counting begin? What is the study of combinatorics? And what can be counted? All of this and more, on this episode of Breaking Math.


This episode is distributed under a Creative Commons Attribution-ShareAlike 4.0 International License (full text: https://creativecommons.org/licenses/by-sa/4.0/)


[Featuring: Sofia Baca; Jacob Urban]

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Published 2023-05-09

78: Perpetual Notion (Entropy and Thermodynamics)

31 min
Open

As you listen to this episode, you'll be exerting mental effort, as well as maybe exerting effort doing other things. The energy allowing your neurons to continually charge and discharge, as well as exert mechanical energy in your muscles and chemical energy in places like your liver and kidneys, came from the food you ate. Specifically, it came from food you chewed, and then digested with acid and with the help of symbiotic bacteria. And even if that food you're eating is meat, you can trace its energy back to the sun and the formation of the earth. Much of this was established in the previous episode, but this time we're going to explore a fundamental property of all systems in which heat can be defined. All of these structures had a certain order to them; the cow that might have made your hamburger had all the same parts that you do: stomach, lips, teeth, and brain. The plants, such as the tomatoes and wheat, were also complex structures, complete with signaling mechanisms. As you chewed that food, you mixed it, and later, as the food digested, it became more and more disordered; that is to say, it became more and more "shuffled", so to speak, and at a certain point, it became so shuffled that you'd need all the original information to reconstruct it: reversing the flow of entropy would mean converting vomit back into the original food; you'd need all the pieces. The electrical energy bonding molecules were thus broken apart and made available to you. And, if you're cleaning your room while listening to this, you are creating order only at the cost of destroying order elsewhere, since you are using energy from the food you ate. Even in industrial agriculture where from 350 megajoules of human and machine energy, often 140 gigajoules of corn can be derived per acre, a ratio of more than 400:1, the order that the seeds seem to produce from nowhere is constructed from the energy of the chaotic explosion from a nearby star. So why are the concepts of heat, energy, and disorder so closely linked? Is there a general law of disorder? And why does the second law mean you can't freeze eggs in a hot pan? All of this and more on this episode of Breaking Math.

Distributed under a CC BY-SA 4.0 License (https://creativecommons.org/licenses/by-sa/4.0/)

[Featuring: Sofia Baca; Millicent Oriana, Jacob Urban]

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Published 2023-02-28

77: An Interview with Christopher Roblesz of MathNMore

55 min
Open

Christopher Roblesz is a math educator who, until the pandemic, worked as a teacher. It was his experiences during the pandemic, and his unwavering passion for preparing disadvantaged youth for STEM careers, that eventually led him to developing mathnmore, a company focused on providing an enriched educational experience for sstudents who are preparing for these careers.More on energy and entropy next time!All of this and more on this interview episode of Breaking Math!


[Featuring: Sofia Baca; Christopher Roblesz]

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Published 2023-01-15

76: Joule Pay for This! (Energy)

66 min
Open

Join Sofia Baca and her guests Millicent Oriana from Nerd Forensics and Arianna Lunarosa as they discuss energy.


The sound that you're listening to, the device that you're listening on, and the cells in both the ear you're using to listen and the brain that understands these words have at least one thing in common: they represent the consumption or transference of energy. The same goes for your eyes if you're reading a transcript of this. The waves in the ears are pressure waves, while eyes receive information in the form of radiant energy, but they both are still called "energy". But what is energy? Energy is a scalar quantity measured in dimensions of force times distance, and the role that energy plays depends on the dynamics of the system. So what is the difference between potential and kinetic energy? How can understanding energy simplify problems? And how do we design a roller coaster in frictionless physics land?[Featuring: Sofia Baca; Millicent Oriana, Arianna Lunarosa]


This episode is distributed under a Creative Commons Attribution-ShareAlike 4.0 International License. Full text here: https://creativecommons.org/licenses/by-sa/4.0/

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Published 2022-06-18

74: Lights, Camera, Action! (3D Computer Graphics: Part I)

42 min
Open

The world around us is a four-dimensional world; there are three spatial dimensions, and one temporal dimension. Many of these objects emit an almost unfathomable number of photons. As we developed as creatures on this planet, we gathered the ability to sense the world around us; and given the amount of information represented as photons, it is no surprise that we developed an organ for sensing photons. But because of the amount of photons that are involved, and our relatively limited computational resources, it is necessary to develop shortcuts if we want to simulate an environment in silico. So what is raytracing? How is that different from what happens in games? And what does Ptolemy have to do with 3D graphics? All of this and more on this episode of Breaking Math.

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Published 2022-05-28

73: Materialism: a Material Science Podcast Podcast Episode (Interview with Taylor Sparks)

55 min
Open

Physical objects are everywhere, and they're all made out of molecules, and atoms. However, the arrangement and refinement of these atoms can be the difference between a computer and sand, or between a tree and paper. For a species as reliant on tool use, the ability to conceieve of, design, create, and produce these materials is an ongoing concern. Since we've been around as humans, and even before, we have been material scientists in some regard, searching for new materials to make things out of, including the tools we use to make things. So what is the difference between iron and steel? How do we think up new things to make things out of? And what are time crystals? All of this and more on this episode of Breaking Math.


This episode is released under a Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) license. More information here: https://creativecommons.org/licenses/by-nc/4.0/


[Featuring: Sofía Baca, Gabriel Hesch; Taylor Sparks]

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Published 2022-05-15

72: The Lifestyles of the Mathematical and Famous (an Interview with Author Robert Black)

50 min
Open

Robert Black is an author who has written a six-book series about seven influential mathematicians, their lives, and their work. We interview him and his books, and take a peek into the lives of these influential mathematicians.


Addendum: Hey Breaking Math fans, I just wanted to let y'all know that the second material science podcast is delayed.


[Featuring: Sofía Baca; Robert Black]

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Published 2022-04-12

71: What's the Matter? An Interview with Chris Cogswell of the Mad Scientist Podcast (Material Science)

55 min
Open
Matter is that which takes up space, and has mass. It is what we interact with, and what we are. Imagining a world without matter is to imagine light particles drifting aimlessly in space. Gasses, liquids, solids, and plasmas are all states of matter. Material science studies all of these, and their combinations and intricacies, found in examining foams, gels, meshes, and other materials and metamaterials. Chris Cogswell is a material scientist, and host of The Mad Scientist Podcast, a podcast that takes a critical look at things ranging from technological fads, to pseudoscience, and topics that deserve a critical eye. On the first of a pair of two episodes about material science, we interview Chris about his experience with studying material science, and ask questions about the subject in general.
Links referenced by Chris Cogswell:
- https://www.youtube.com/watch?v=bUvi5eQhPTc is about nanomagnetism and cool demonstration of ferrofluid
- https://www.youtube.com/watch?v=4Dlt63N-Uuk goes over nanomagnetic applications in medicine
- http://yaghi.berkeley.edu/pdfPublications/04MOFs.pdf Great review paper on new class of materials known as MOFs which are going to be very important in coming years
- https://www.youtube.com/watch?v=IkYimZBzguw Crash course engineering on nanomaterials, really good introduction to the field
- https://www.youtube.com/watch?v=t7EYQLOlwDM Oak Ridge national lab paper on using nano materials for carbon dioxide conversion to other carbon molecules
- https://www.youtube.com/watch?v=cxVFopLpIQY Really good paper on carbon capture technology challenges and economics
[Featuring: Sofía Baca, Gabriel Hesch, Meryl Flaherty; Chris Cogswell]

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Published 2022-03-20

70.1: Episode 70.1 of Breaking Math Podcast (Self-Reference)

46 min
Open

Seldom do we think about self-reference, but it is a huge part of the world we live in. Every time that we say 'myself', for instance, we are engaging in self-reference. Long ago, the Liar Paradox and the Golden Ratio were among the first formal examples of self-reference. Freedom to refer to the self has given us fruitful results in mathematics and technology. Recursion, for example, is used in algorithms such as PageRank, which is one of the primary algorithms in Google's search engine. Elements of self-reference can also be found in foundational shifts in the way we understand mathematics, and has propelled our understanding of mathematics forward. Forming modern set theory was only possible due to a paradox called Russel's paradox, for example. Even humor uses self-reference. Realizing this, can we find harmony in self-reference? Even in a podcast intro, are there elements of self-reference? Nobody knows, but I'd check if I were you. Catch all of this, and more, on this episode of Breaking Math. Episode 70.1: Episode Seventy Point One of Breaking Math Podcast


[Featuring: Sofía Baca, Gabriel Hesch; Millicent Oriana]


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Published 2022-03-19

70: This Episode Intentionally Left Blank

46 min
Open

This episode description intentionally left blank!   As in completely on purpose.   Fun Fact!  The creators of the Breaking Math Podcast, Sofia and Gabriel always thought it was funny that many books that we've read - even going back to our childhood - had a page in it with the sentence printed, "This Page Intentionally Left Blank."   Like-  okay; what does this 'intentionally left blank page' add to the reading experience?  Does anyone know?  Oh look here!  There is a wikipedia page on it. Huh.  Now I know.  Now we know.   And knowing is half the battle!  

 Sofia would frequently leave post-it notes on Gabe's laptop saying, "This Post-it note intentionally left blank."  Because . . . . why?   Sofia would often leave a twitter or facebook post that declared "This post intentionally left blank."   

And now - we release an entire podcast episode that is intentionally left blank.  Are we trolls?  NO!  We prefer to think of ourselves as artists in the style of Banksy making a statement! 

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Published 2022-01-23

69: An Interview with Michael Brooks, Author of "The Art of More: How Mathematics Created Civilization"

62 min
Open

Michael Brooks is a science writer who specializes in making difficult concepts easier to grasp. In his latest book, Brooks goes through several mathematical concepts and discusses their motivation, history, and discovery. So how do stories make it easier to learn? What are some of the challenges associated with conveying difficult concepts to the general public? And who, historically, has been a mathematician? All of this and more on this episode of Breaking Math.  Songs were Breaking Math Intro and Outro by Elliot Smith of Albuquerque.  This episode is published under a Creative Commons 4.0 Attribute-ShareAlike-NonCommercial license. For more information, visit CreativeCommons.org  [Featuring: Sofía Baca, Gabriel Hesch, Meryl Flaherty; Michael Brooks]

t

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Published 2022-01-04

P12: O My God (Big O Notation)

22 min
Open

There are times in mathematics when we are generalizing the behavior of many different, but similar, entities. One such time that this happens is the use cases of Big O notation, which include describing the long-term behavior of functions, and talking about how accurate numerical calculations are. On this problem episode, we are going to discuss Big O notation and how to use it.


This episode is licensed by Sofia Baca under a Creative Commons Attribution-ShareAlike-NonCommercial 4.0 International License. For more information, visit CreativeCommons.org.

[Featuring: Sofía Baca]


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Published 2021-12-23

68: LOL!!! SO RANDOM (Random Variables)

34 min
Open

The world is often uncertain, but it has only been in the last half millennium that we've found ways to interact mathematically with that concept. From its roots in death statistics, insurance, and gambling to modern Bayesian networks and machine learning, we've seen immense productivity in this field. Every way of looking at probability has something in common: the use of random variables. Random variables let us talk about events with uncertain outcomes in a concrete way. So what are random variables? How are they defined? And how do they interact? All of this, and more, on this episode of Breaking Math.


Interact with the hosts:

@SciPodSofia

@TechPodGabe


Or the guest:

@KampPodMillie


Patreon here: patreon.com/breakingmathpodcast


Featuring music by Elliot Smith. For info about music used in ads, which are inserted dynamically, contact us at breakingmathpodcast@gmail.com


[Featuring: Sofía Baca, Gabriel Hesch; Millicent Oriana]



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Published 2021-12-09

67: Wrath of Math (Mathematics Used Unwisely)

23 min
Open
Mathematics is a subject that has been used for great things over time: it has helped people grow food, design shelter, and in every part of life. It should be, then, no surprise that sometimes mathematics is used for evil; that is to say, there are times where mathematics is used to either implement or justify regressive things like greed, racism, classism, and even genocide. So when has math been used for destructive purposes? What makes us mis-apply mathematics? And why can oversimplification lead to devastation? All of this, and more, on this episode of Breaking Math.

Theme song is Breaking Math Theme by Elliot Smith of Albuquerque.

This episode is distributed under a Creative Commons Attribution-ShareAlike-NonCommercial 4.0 International License. For more information, go to CreativeCommons.org

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Published 2021-11-30

P11: Feeling Lucky? (Probability and Intuition)

30 min
Open

Join Sofía Baca with her guest Millicent Oriana from the newly launched Nerd Forensics podcast as they discuss some apparent paradoxes in probability and Russian roulette.


Intro is "Breaking Math Theme" by Elliot Smith. Ads feature "Ding Dong" by Simon Panrucker


[Featuring: Sofía Baca; Millicent Oriana]


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This episode is sponsored by 

· Anchor: The easiest way to make a podcast.  https://anchor.fm/app


Support this podcast: https://anchor.fm/breakingmathpodcast/support

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Published 2021-11-20

66: Hayhoe, Let's Go! (An Interview With Climate Scientist Katharine Hayhoe)

71 min
Open

Katharine Hayhoe was the lead author on the 2018 US Climate Assessment report, and has spent her time since then spreading the word about climate change. She was always faced with the difficult task of convincing people who had stakes in things that would be affected by acknowledging the information in her report. In her newest book, “Saving Us: A Climate Scientist’s Case for Hope and Healing in a Divided World”, she discusses the challenges associated with these conversations, at both the micro and macro level. So who is Katherine Heyhoe? How has she learned to get people to acknowledge the reality of climate science? And is she the best, or worst, person to strike up a discussion about how the weather’s been? All of this, and more, on this episode of Breaking Math. Papers Cited: -“99.94 percent of papers agree with the scientific consensus.”

More info: https://journals.sagepub.com/doi/10.1177/0270467617707079

This episode is distributed under a CC BY-NC 4.0 International License. For more information, visit creativecommons.org.

Intro is "Breaking Math Theme" by Elliot Smith. Ads feature "Ding Dong" by Simon Panrucker

[Featuring: Sofía Baca, Gabriel Hesch, Meryl Flaherty; Katherine Heyhoe, Elliot Smith]


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Published 2021-11-14

P10: Chivalry is Dead (Knights and Knaves #1)

18 min
Open

One tells a lie, the other the truth! Have fun with Sofía and Meryl as they investigate knight, knave, and spy problems!


Intro is "Breaking Math Theme" by Elliot Smith. Music in the ads were Plug Me In by Steve Combs and "Ding Dong" by Simon Panrucker. You can access their work at freemusicarchive.org.


[Featuring: Sofia Baca; Meryl Flaherty]


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Published 2021-10-24

65: An Interview with Author Ian Stewart (Book About Everyday Math)

44 min
Open

Welcome to another engaging episode of the Breaking Math Podcast! Today's episode, titled "What is the Use?," features a fascinating conversation with the renowned mathematician and author, Professor Ian Stewart. As Professor Stewart discusses his latest book "What's the Use? How Mathematics Shapes Everyday Life," we dive deep into the real-world applications of mathematics that often go unnoticed in our daily technologies, like smartphones, and their unpredictable implications in various fields.

We'll explore the history of quaternions, invented by William Rowan Hamilton, which now play a critical role in computer graphics, gaming, and particle physics. Professor Stewart will also shed light on the non-commutative nature of quaternions, mirroring the complexities of spatial rotations, and how these mathematical principles find their correspondence in the natural world.

Furthermore, our discussion will encompass the interconnectivity within mathematics, touching upon how algebra, geometry, and trigonometry converge to paint a broader picture of this unified field. We also discuss the intriguing concept of "Fearful Symmetry" and how symmetrical and asymmetrical patterns govern everything from tiger stripes to sand dunes.

With references to his other works, including "Professor Stewart's Cabinet of Mathematical Curiosities" and "The Science of Discworld," Professor Stewart brings an element of surprise and entertainment to the profound impact of mathematics on our understanding of the world.

So stay tuned as we unlock the mysteries and the omnipresent nature of math in this thought-provoking episode with Professor Ian Stewart!

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Published 2021-09-29

64: What Projection Is This? (Map Projections)

47 min
Open

The world is a big place with a lot of wonderful things in it. The world also happens to be spherical, which can make getting to those things a challenge if you don't have many landmarks. This is the case when people are navigating by sea. For this reason, map projections, which take a sphere and attempt to flatten it onto a sheet, were born. So what is a map projection? Why are there so many? And why is Gall-Peters the worst? All of this, and more, on this episode of Breaking Math.

Theme was written by Elliot Smith.

This episode is distributed under a Creative Commons 4.0 Attribution-ShareAlike-NonCommercial International License. For more information, visit CreativeCommons.org.


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Published 2021-09-19

RR36: The Most Boring Episode Ever (Rerun: Math Games)

49 min
Open

This is a rerun of one of our favorite episodes! We hope that you enjoy it if you haven't listened to it yet. We'll be back next week with new content! Thank you so much for listening to Breaking Math!


Math is a gravely serious topic which has been traditionally been done by stodgy people behind closed doors, and it cannot ever be taken lightly. Those who have fun with mathematics mock science, medicine, and the foundation of engineering. That is why on today's podcast, we're going to have absolutely no fun with mathematics. There will not be a single point at which you consider yourself charmed, there will not be a single thing you will want to tell anyone for the sake of enjoyment, and there will be no tolerance for your specific brand of foolishness, and that means you too, Kevin.


Theme by Elliot Smith.


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Published 2021-09-05

63: Broken Voting Systems (Voting Systems and Paradoxes)

33 min
Open

Voting systems are, in modern times, essential to the way that large-scale decisions are made. The concept of voicing an opinion to be, hopefully, considered fairly is as ancient and well-established as the human concept of society in general. But, as time goes on, the recent massive influx of voting systems in the last 150 years have shown us that there are as many ways to vote as there are flaws in the way that the vote is tallied. So what problems exist with voting? Are there any intrinsic weaknesses in group decision-making systems? And what can we learn by examining these systems? All of this, and more, on this episode of Breaking Math.


Licensed under Creative Commons Attribution-ShareAlike-NonCommercial 4.0 International License. For more information, visit CreativeCommons.org.


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Published 2021-08-22

62: The Atom Bomb of Information Operations (An Interview with John Fuisz of Veriphix)

45 min
Open

Forecasting is a constantly evolving science, and has been applied to complex systems; everything from the weather, to determining what customers might like to buy, and even what governments might rise and fall. John Fuisz is someone who works with this science, and has experience improving the accuracy of forecasting. So how can forecasting be analyzed? What type of events are predictable? And why might Russia think a Missouri senator's race hinges upon North Korea? All of this and more on this episode of Breaking Math.

The theme for this episode was written by Elliot Smith.

[Featuring: Sofía Baca, Gabriel Hesch; John Fuisz]


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Published 2021-04-25

61: Look at this Graph! (Graph Theory)

29 min
Open

In mathematics, nature is a constant driving inspiration; mathematicians are part of nature, so this is natural. A huge part of nature is the idea of things like networks. These are represented by mathematical objects called 'graphs'. Graphs allow us to describe a huge variety of things, such as: the food chain, lineage, plumbing networks, electrical grids, and even friendships. So where did this concept come from? What tools can we use to analyze graphs? And how can you use graph theory to minimize highway tolls? All of this and more on this episode of Breaking Math.

Episode distributed under an Creative Commons Attribution-ShareAlike-NonCommercial 4.0 International License. For more information, visit CreativeCommons.org

[Featuring: Sofía Baca, Meryl Flaherty]


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This episode is sponsored by 

· Anchor: The easiest way to make a podcast.  https://anchor.fm/app


Support this podcast: https://anchor.fm/breakingmathpodcast/support

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Published 2021-04-19

P9: Give or Take (Back-of-the-Envelope Estimates / Fermi Problems)

31 min
Open

How many piano tuners are there in New York City? How much cheese is there in Delaware? And how can you find out? All of this and more on this problem-episode of Breaking Math.

This episode distributed under a Creative Commons Attribution-ShareAlike-Noncommercial 4.0 International License. For more information, visit creativecommons.org

Featuring theme song and outro by Elliot Smith of Albuquerque.


[Featuring: Sofía Baca, Meryl Flaherty]

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Published 2021-04-03

60: HAMILTON! [But Not the Musical] (Quaternions)

29 min
Open

i^2 = j^2 = k^2 = ijk = -1. This deceptively simple formula, discovered by Irish mathematician William Rowan Hamilton in 1843, led to a revolution in the way 19th century mathematicians and scientists thought about vectors and rotation. This formula, which extends the complex numbers, allows us to talk about certain three-dimensional problems with more ease. So what are quaternions? Where are they still used? And what is inscribed on Broom Bridge? All of this and more on this episode of Breaking Math.


This episode is distributed under a CC BY-SA 4.0 license. For more information, visit CreativeCommons.org.

The theme for this episode was written by Elliot Smith.

[Featuring: Sofía Baca, Meryl Flaherty]

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Published 2021-03-21

59: A Good Source of Fibers (Fiber Bundles)

42 min
Open

Mathematics is full of all sorts of objects that can be difficult to comprehend. For example, if we take a slip of paper and glue it to itself, we can get a ring. If we turn it a half turn before gluing it to itself, we get what's called a Möbius strip, which has only one side twice the length of the paper. If we glue the edges of the Möbius strip to each other, and make a tube, you'll run into trouble in three dimensions, because the object that this would make is called a Klein flask, and can only exist in four dimensions. So what is a fiber? What can fiber bundles teach us about higher dimensional objects?


All of this, and more, on this episode of Breaking Math.


[Featuring: Sofía Baca, Meryl Flaherty]

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Published 2021-03-03

58: Bringing Curvy Back (Gaussian Curvature)

42 min
Open

In introductory geometry classes, many of the objects dealt with can be considered 'elementary' in nature; things like tetrahedrons, spheres, cylinders, planes, triangles, lines, and other such concepts are common in these classes. However, we often have the need to describe more complex objects. These objects can often be quite organic, or even abstract in shape, and include things like spirals, flowery shapes, and other curved surfaces. These are often described better by differential geometry as opposed to the more elementary classical geometry. One helpful metric in describing these objects is how they are curved around a certain point. So how is curvature defined mathematically? What is the difference between negative and positive curvature? And what can Gauss' Theorema Egregium teach us about eating pizza?

This episode distributed under a Creative Commons Attribution ShareAlike 4.0 International License. For more information, go to creativecommons.org

Visit our sponsor today at Brilliant.org/BreakingMath for 20% off their annual membership! Learn hands-on with Brilliant.

[Featuring: Sofía Baca, Meryl Flaherty]


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Published 2021-02-24

P8: Tangent Tango (Morikawa's Recently Solved Problem)

19 min
Open

Join Sofía and Gabriel as they talk about Morikawa's recently solved problem, first proposed in 1821 and not solved until last year!


Also, if you haven't yet, check out our sponsor The Great Courses at thegreatcoursesplus.com/breakingmath for a free month! Learn basically anything there.


The paper featured in this episode can be found at https://arxiv.org/abs/2008.00922


This episode is distributed under a Creative Commons Attribution-ShareAlike 4.0 International License. For more information, visit CreativeCommons.org!


[Featuring: Sofía Baca, Gabriel Hesch]


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Published 2021-02-07

P7: Root for Squares (Irrationality of the Square Root of Two)

14 min
Open

Join Sofía and Gabriel as they discuss an old but great proof of the irrationality of the square root of two.


[Featuring: Sofía Baca, Gabriel Hesch]

Patreon-Become a monthly supporter at patreon.com/breakingmath

Merchandise

Ad contained music track "Buffering" from Quiet Music for Tiny Robots.

Distributed under a Creative Commons Attribution-ShareAlike 4.0 International License. For more information, visit creativecommons.org.

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Published 2021-02-01

57: You Said How Much?! (Measure Theory)

30 min
Open

If you are there, and I am here, we can measure the distance between us. If we are standing in a room, we can calculate the area of where we're standing; and, if we want, the volume. These are all examples of measures; which, essentially, tell us how much 'stuff' we have. So what is a measure? How are distance, area, and volume related? And how big is the Sierpinski triangle? All of this and more on this episode of Breaking Math.

Ways to support the show:

Patreon-Become a monthly supporter at patreon.com/breakingmath

The theme for this episode was written by Elliot Smith.

Episode used in the ad was Buffering by Quiet Music for Tiny Robots.


[Featuring: Sofía Baca; Meryl Flaherty]

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Published 2021-01-28

P6: How Many Angles in a Circle? (Curvature; Euclidean Geometry)

28 min
Open

Sofía and Gabriel discuss the question of "how many angles are there in a circle", and visit theorems from Euclid, as well as differential calculus.

This episode is distributed under a CC BY-SA 4.0 license. For more information, visit CreativeCommons.org.

Ways to support the show:

Patreon-Become a monthly supporter at patreon.com/breakingmath

The theme for this episode was written by Elliot Smith.

Music in the ad was Tiny Robot Armies by Quiet Music for Tiny Robots.

[Featuring: Sofía Baca, Gabriel Hesch]

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Published 2021-01-24

56: More Sheep than You Can Count (Transfinite Cardinal Numbers)

34 min
Open

Look at all you phonies out there.

You poseurs.

All of you sheep. Counting 'til infinity. Counting sheep.

*pff*

What if I told you there were more there? Like, ... more than you can count?

But what would a sheeple like you know about more than infinity that you can count?

heh. *pff*

So, like, what does it mean to count til infinity? What does it mean to count more? And, like, where do dimensions fall in all of this?


Ways to support the show:

Patreon-Become a monthly supporter at patreon.com/breakingmath

(Correction: at 12:00, the paradox is actually due to Galileo Galilei)

Distributed under a Creative Commons Attribution-ShareAlike 4.0 International License. For more information, visit CreativeCommons.org

Music used in the The Great Courses ad was Portal by Evan Shaeffer


[Featuring: Sofía Baca, Gabriel Hesch]


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Published 2021-01-14

55: Order in the Court (Transfinite Ordinal Numbers)

31 min
Open

As a child, did you ever have a conversation that went as follows:

"When I grow up, I want to have a million cats"

"Well I'm gonna have a billion billion cats"

"Oh yeah? I'm gonna have infinity cats"

"Then I'm gonna have infinity plus one cats"

"That's nothing. I'm gonna have infinity infinity cats"

"I'm gonna have infinity infinity infinity infinity *gasp* infinity so many infinities that there are infinity infinities plus one cats"

What if I told you that you were dabbling in the transfinite ordinal numbers? So what are ordinal numbers? What does "transfinite" mean? And what does it mean to have a number one larger than another infinite number?


[Featuring: Sofía Baca; Diane Baca]

Ways to support the show:

Patreon

Become a monthly supporter at patreon.com/breakingmath

This episode is released under a Creative Commons attribution sharealike 4.0 international license. For more information, go to CreativeCommoms.org

This episode features the song "Buffering" by "Quiet Music for Tiny Robots"


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Published 2020-12-21

54: Oodles (Large Numbers)

27 min
Open

There are a lot of things in the universe, but no matter how you break them down, you will still have far fewer particles than even some of the smaller of what we're calling the 'very large numbers'. Many people have a fascination with these numbers, and perhaps it is because their sheer scale can boggle the mind. So what numbers can be called 'large'? When are they useful? And what is the Ackermann function? All of this and more on this episode of Breaking Math


[Featuring: Sofía Baca; Diane Baca]


Ways to support the show:

Patreon

Become a monthly supporter at patreon.com/breakingmath

Merchandise

Purchase a Math Poster on Tensor Calculus at our facebook store at facebook.com/breakingmathpodcast


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Published 2020-12-11

53: Big Brain Time (An Interview with Peter Zeidman from the UCL Institute of Neurology)

43 min
Open

Neuroscience is a topic that, in many ways, is in its infancy. The tools that are being used in this field are constantly being honed and reevaluated as our understanding of the brain and mind increase. And it's no surprise: the brain is responsible for the way we interact with the world, and the idea that ideas hone one another is not new to anyone who possesses a mind. But how can the tools that we use to study the brain and the mind be linked? How do the mind and the brain encode one another? And what does Bayes have to do with this? All of this and more on this episode of Breaking Math.


[Featuring: Sofía Baca, Gabriel Hesch; Peter Zeidman]

Patreon

Become a monthly supporter at patreon.com/breakingmath

This episode is distributed under a CC BY-SA 4.0 license. For more information, visit CreativeCommons.org.


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Published 2020-12-05

52: Round (Circles and Spheres)

30 min
Open

Spheres and circles are simple objects. They are objects that are uniformly curved throughout in some way or another. They can also be defined as objects which have a boundary that is uniformly distant from some point, using some definition of distance. Circles and spheres were integral to the study of mathematics at least from the days of Euclid, being the objects generated by tracing the ends of idealized compasses. However, these objects have many wonderful and often surprising mathematical properties. To this point, a circle's circumference divided by its diameter is the mathematical constant pi, which has been a topic of fascination for mathematicians for as long as circles have been considered.


[Featuring Sofía Baca; Meryl Flaherty]

Patreon 

Become a monthly supporter at patreon.com/breakingmath


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Published 2020-11-15

51: Episode "-2,0,1" (Bases; Exotic Bases)

34 min
Open

A numerical base is a system of representing numbers using a sequence of symbols. However, like any mathematical concept, it can be extended and re-imagined in many different forms. A term used occasionally in mathematics is the term 'exotic', which just means 'different than usual in an odd or quirky way'. In this episode we are covering exotic bases. We will start with something very familiar (viz., decimal points) as a continuation of our previous episode, and then progress to the more odd, such as non-integer and complex bases. So how can the base systems we covered last time be extended to represent fractional numbers? How can fractional numbers be used as a base for integers? And what is pi plus e times i in base i + 1?

This episode is distributed under a CC BY-SA 4.0 license. For more information, visit CreativeCommons.org.

[Featuring: Sofía Baca; Merryl Flaherty]

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Published 2020-08-31

50: Episode "101" (Bases)

54 min
Open

Numbering was originally done with tally marks: the number of tally marks indicated the number of items being counted, and they were grouped together by fives. A little later, people wrote numbers down by chunking the number in a similar way into larger numbers: there were symbols for ten, ten times that, and so forth, for example, in ancient Egypt; and we are all familiar with the Is, Vs, Xs, Ls, Cs, and Ds, at least, of Roman numerals. However, over time, several peoples, including the Inuit, Indians, Sumerians, and Mayans, had figured out how to chunk numbers indefinitely, and make numbers to count seemingly uncountable quantities using the mind, and write them down in a few easily mastered motions. These are known as place-value systems, and the study of bases has its root in them: talking about bases helps us talk about what is happening when we use these magical symbols.

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Published 2020-05-26

49: Thinking Machines II (Techniques in Artificial Intelligence)

57 min
Open
Machines have been used to simplify labor since time immemorial, and simplify thought in the last few hundred years. We are at a point now where we have the electronic computer to aid us in our endeavor, which allows us to build hypothetical thinking machines by simply writing their blueprints — namely, the code that represents their function — in a general way that can be easily reproduced by others. This has given rise to an astonishing array of techniques used to process data, and in recent years, much focus has been given to methods that are used to answer questions where the question or answer is not always black and white. So what is machine learning? What problems can it be used to solve? And what strategies are used in developing novel approaches to machine learning problems? This episode is distributed under a CC BY-SA 4.0 license. For more information, visit CreativeCommons.org. For more Breaking Math info, visit BreakingMathPodcast.app [Featuring: Sofía Baca, Gabriel Hesch] References: https://spectrum.ieee.org/tag/history+of+natural+language+processing

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Published 2020-05-17

48: Thinking Machines (Philosophical Basis of Artificial Intelligence)

54 min
Open

Machines, during the lifetime of anyone who is listening to this, have advanced and revolutionized the way that we live our lives. Many listening to this, for example, have lived through the rise of smart phones, 3d printing, massive advancements in lithium ion batteries, the Internet, robotics, and some have even lived through the introduction of cable TV, color television, and computers as an appliance. All advances in machinery, however, since the beginning of time have one thing in common: they make what we want to do easier. One of the great tragedies of being imperfect entities, however, is that we make mistakes. Sometimes those mistakes can lead to war, famine, blood feuds, miscalculation, the punishment of the innocent, and other terrible things. It has, thus, been the goal of many, for a very long time, to come up with a system for not making these mistakes in the first place: a thinking machine, which would help eliminate bias in situations. Such a fantastic machine is looking like it's becoming closer and closer to reality, especially with the advancements in artificial intelligence. But what are the origins of this fantasy? What attempts have people made over time to encapsulate reason? And what is ultimately possible with the automated manipulation of meaning? All of this and more on this episode of Breaking Math. Episode 48: Thinking Machines References: * https://publicdomainreview.org/essay/let-us-calculate-leibniz-llull-and-the-computational-imagination * https://spectrum.ieee.org/tag/history+of+natural+language+processing https://en.wikipedia.org/wiki/Characteristica_universalis https://ourworldindata.org/coronavirus-source-data This episode is distributed under a CC BY-SA 4.0 license. For more information, visit CreativeCommons.org. [Featuring: Sofía Baca, Gabriel Hesch]

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Published 2020-02-29

47: Blast to the Past (Retrocausality)

29 min
Open

Time is something that everyone has an idea of, but is hard to describe. Roughly, the arrow of time is the same as the arrow of causality. However, what happens when that is not the case? It is so often the case in our experience that this possibility brings not only scientific and mathematic, but ontological difficulties. So what is retrocausality? What are closed timelike curves? And how does this all relate to entanglement?

This episode is distributed under a CC BY-SA 4.0 license. For more information, visit CreativeCommons.org.


[Featuring: Sofía Baca, Gabriel Hesch]

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Published 2020-02-03

P3: Radiativeforcenado (Radiative Forcing)

39 min
Open

Learn more about radiative forcing, the environment, and how global temperature changes with atmospheric absorption with this Problem Episode about you walking your (perhaps fictional?) dog around a park.  This episode is distributed under a CC BY-SA license. For more information, visit CreativeCommons.org.


[Featuring: Sofía Baca, Gabriel Hesch]


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Published 2020-01-20

46: Earth Irradiated (the Greenhouse Effect)

41 min
Open

Since time immemorial, blacksmiths have known that the hotter metal gets, the more it glows: it starts out red, then gets yellower, and then eventually white. In 1900, Max Planck discovered the relationship between an ideal object's radiation of light and its temperature. A hundred and twenty years later, we're using the consequences of this discovery for many things, including (indirectly) LED TVs, but perhaps one of the most dangerously neglected (or at least ignored) applications of this theory is in climate science. So what is the greenhouse effect? How does blackbody radiation help us design factories? And what are the problems with this model?

This episode is distributed under a CC BY-SA license. For more information, visit CreativeCommons.org.

[Featuring: Sofía Baca, Gabriel Hesch]


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Published 2019-12-10

45: Climate Denialism and Cranky Uncles (Interview with John Cook of Skeptical Science)

25 min
Open

Climate change is an issue that has become frighteningly more relevant in recent years, and because of special interests, the field has become muddied with climate change deniers who use dishonest tactics to try to get their message across. The website SkepticalScience.com is one line of defense against these messengers, and it was created and maintained by a research assistant professor at the Center for Climate Change Communication at George Mason University, and both authored and co-authored two books about climate science with an emphasis on climate change. He also lead-authored a 2013 award-winning paper on the scientific consensus on climate change, and in 2015, he developed an open online course on climate change denial with the Global Change Institute at the University of Queensland. This person is John Cook.


This episode is distributed under a CC BY-SA license. For more information, visit CreativeCommons.org.


[Featuring: Sofía Baca, Gabriel Hesch; John Cook]


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Published 2019-11-03

44: Vestigial Math (Math That Is Not Used like It Used to Be)

36 min
Open

Mathematics, like any intellectual pursuit, is a constantly-evolving field; and, like any evolving field, there are both new beginnings and sudden unexpected twists, and things take on both new forms and new responsibilities. Today on the show, we're going to cover a few mathematical topics whose nature has changed over the centuries. So what does it mean for math to be extinct? How does this happen? And will it continue forever?

This episode is distributed under a CC BY-SA license. For more information, visit CreativeCommons.org.

[Featuring: Sofía Baca, Gabriel Hesch]


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Published 2019-10-30

P2: Walk the Dog (Calculus: Chain Rule)

18 min
Open

Learn more about calculus, derivatives, and the chain rule with this Problem Episode about you walking your (perhaps fictional?) dog around a park.


This episode is distributed under a CC BY-SA license. For more information, visit CreativeCommons.org.

[Featuring: Sofía Baca, Gabriel Hesch]


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Published 2019-10-23

43: Interview II with Author Ben Orlin (Change is the Only Constant: the Wisdom of Calculus in a Madcap World)

42 min
Open

Ben Orlin has been a guest on the show before. He got famous with a blog called 'Math With Bad Drawings", which is what it says on the tin: he teaches mathematics using his humble drawing skills. His last book was a smorgasbord of different mathematical topics, but he recently came out with a new book 'Change is the Only Constant: the Wisdom of Calculus in a Madcap World', which focuses more on calculus itself.

This episode is distributed under a CC BY-SA license. For more info, visit creativecommons.org

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Published 2019-09-29

P1: Peano Addition

37 min
Open
On this problem episode, join Sofía and guest Diane Baca to learn about what an early attempt to formalize the natural numbers has to say about whether or not m+n equals n+m.

This episode is distributed under a CC BY-SA 4.0 license (https://creativecommons.org/licenses/by-sa/4.0/)

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Published 2019-08-15

42: Maybe? (Probability and Statistics)

32 min
Open

Statistics is a field that is considered boring by a lot of people, including a huge amount of mathematicians. This may be because the history of statistics starts in a sort of humdrum way: collecting information on the population for use by the state. However, it has blossomed into a beautiful field with its fundamental roots in measure theory, and with some very interesting properties. So what is statistics? What is Bayes' theorem? And what are the differences between the frequentist and Bayesian approaches to a problem?


Distributed under a Creative Commons Attribution-ShareAlike 4.0 International License (creativecommons.org)


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Published 2019-07-29

41: Reality Is More Than Complex (Group Theory and Physics)

54 min
Open

Children who are being taught mathematics often balk at the idea of negative numbers, thinking them to be fictional entities, and often only learn later that they are useful for expressing opposite extremes of things, such as considering a debt an amount of money with a negative sum. Similarly, students of mathematics often are puzzled by the idea of complex numbers, saying that it makes no sense to be able to take the square root of something negative, and only realizing later that these can have the meaning of two-dimensional direction and magnitude, or that they are essential to our modern understanding of electrical engineering. Our discussion today will be much more abstract than that. Much like in our discussion in episode five, "Language of the Universe", we will be discussing how math and physics draw inspiration from one another; we're going to talk about what different fields (such as the real, complex, and quaternion fields) seem to predict about our universe. So how are real numbers related to classical mechanics? What does this mean complex numbers and quaternions are related to? And what possible physicses exist?


Update:  Dr. Alex Alaniz and the Breaking Math Podcast have teamed up to create a new youtube show called the "Turing Rabbit Holes Podcast."  We discuss science, math, and society with spectacular visuals.    Available at youtube.com/TuringRabbitHolesPodcast and on all other podcast platforms.  


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License is Creative Commons Attribution-ShareAlike 4.0 (See https://creativecommons.org/licenses/by-sa/4.0/)


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Published 2019-05-28

39: Syntax Matters: Syntax... Matters? (Formal Grammar)

33 min
Open

We communicate every day through languages; not only human languages, but other things that could be classified as languages such as internet protocols, or even the structure of business transactions. The structure of words or sentences, or their metaphorical equivalents, in that language is known as their syntax. There is a way to describe certain syntaxes mathematically through what are known as formal grammars. So how is a grammar defined mathematically? What model of language is often used in math? And what are the fundamental limits of grammar?

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Published 2019-04-23

38: The Great Stratagem Heist (Game Theory: Iterated Elimination of Dominated Strategies)

32 min
Open

Game theory is all about decision-making and how it is impacted by choice of strategy, and a strategy is a decision that is influenced not only by the choice of the decision-maker, but one or more similar decision makers. This episode will give an idea of the type of problem-solving that is used in game theory. So what is strict dominance? How can it help us solve some games? And why are The Obnoxious Seven wanted by the police?

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Published 2019-02-25

37: The One Where They Parody Saw [audio fixed again] (Game Theory)

39 min
Open

Hello listeners. You don't know me, but I know you. I want to play a game. In your ears are two earbuds. Connected to the earbuds are a podcast playing an episode about game theory. Hosting that podcast are two knuckleheads. And you're locked into this episode. The key is at the end of the episode. What is game theory? Why did we parody the Saw franchise? And what twisted lessons will you learn?


-See our New Youtube Show "Turing Rabbit Holes Podcast" at youtube.com/TuringRabbitHolesPodcast.   Also available on all podcast players.  


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Published 2018-11-23

36: The Most Boring Episode Ever. (Math Games)

46 min
Open

Math is a gravely serious topic which has been traditionally been done by stodgy people behind closed doors, and it cannot ever be taken lightly. Those who have fun with mathematics mock science, medicine, and the foundation of engineering. That is why on today's podcast, we're going to have absolutely no fun with mathematics. There will not be a single point at which you consider yourself charmed, there will not be a single thing you will want to tell anyone for the sake of enjoyment, and there will be no tolerance for your specific brand of foolishness, and that means you too, Kevin.

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Published 2018-11-05

35: Please Be Discrete (Discrete Math)

34 min
Open

Centuries ago, there began something of a curiosity between mathematicians that didn't really amount to much but some interesting thoughts and cool mathematical theorems. This form of math had to do with strictly integer quantities; theorems about whole numbers. Things started to change in the 19th century with some breakthroughs in decrypting intelligence through examining the frequency of letters. In the fervor that followed to increase the security of existing avenues of communication, and to speed up the newfound media of telegraphy, came a field of mathematics called discrete math. It is now an essential part of our world today, with technologies such as online banking being essentially impossible without it. So what have we learned from discrete math? What are some essential methods used within it? And how is it applied today?

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Published 2018-09-23

32: Gaze into the Abyss (Part Three; Black Holes)

77 min
Open

A lot of the information in this episode of Breaking Math depends on episodes 30 and 31 entitled "The Abyss" and "Into the Abyss" respectively. If you have not listened to those episodes, then we'd highly recommend going back and listening to those. We're choosing to present this information this way because otherwise we'd waste most of your time re-explaining concepts we've already covered.


Black holes are so bizarre when we measured against the yardstick of the mundanity of our day to day lives that they inspire fear, awe, and controversy. In this last episode of the Abyss series, we will look at some more cutting-edge problems and paradoxes surrounding black holes. So how are black holes and entanglement related? What is the holographic principle? And what is the future of black holes?


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Published 2018-08-22

31: Into the Abyss (Part Two; Black Holes)

56 min
Open

Black holes are objects that seem exotic to us because they have properties that boggle our comparatively mild-mannered minds. These are objects that light cannot escape from, yet glow with the energy they have captured until they evaporate out all of their mass. They thus have temperature, but Einstein's general theory of relativity predicts a paradoxically smooth form. And perhaps most mind-boggling of all, it seems at first glance that they have the ability to erase information. So what is black hole thermodynamics? How does it interact with the fabric of space? And what are virtual particles?

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Published 2018-08-02

30: The Abyss (Part One; Black Holes)

51 min
Open

The idea of something that is inescapable, at first glance, seems to violate our sense of freedom. This sense of freedom, for many, seems so intrinsic to our way of seeing the universe that it seems as though such an idea would only beget horror in the human mind. And black holes, being objects from which not even light can escape, for many do beget that same existential horror. But these objects are not exotic: they form regularly in our universe, and their role in the intricate web of existence that is our universe is as valid as the laws that result in our own humanity. So what are black holes? How can they have information? And how does this relate to the edge of the universe?


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Published 2018-07-13

29: War

34 min
Open

In the United States, the fourth of July is celebrated as a national holiday, where the focus of that holiday is the war that had the end effect of ending England’s colonial influence over the American colonies. To that end, we are here to talk about war, and how it has been influenced by mathematics and mathematicians. The brutality of war and the ingenuity of war seem to stand at stark odds to one another, as one begets temporary chaos and the other represents lasting accomplishment in the sciences. Leonardo da Vinci, one of the greatest western minds, thought war was an illness, but worked on war machines. Feynman and Von Neumann held similar views, as have many over time; part of being human is being intrigued and disgusted by war, which is something we have to be aware of as a species. So what is warfare? What have we learned from refining its practice? And why do we find it necessary?


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Published 2018-06-19

28: Bell's Infamous Theorem (Bell's Theorem)

34 min
Open

The history of physics as a natural science is filled with examples of when an experiment will demonstrate something or another, but what is often forgotten is the fact that the experiment had to be thought up in the first place by someone who was aware of more than one plausible value for a property of the universe, and realized that there was a way to word a question in such a way that the universe could understand. Such a property was debated during the quantum revolution, and involved Einstein, Polodsky, Rosen, and Schrödinger. The question was 'do particles which are entangled "know" the state of one another from far away, or do they have a sort of "DNA" which infuses them with their properties?' The question was thought for a while to be purely philosophical one until John Stewart Bell found the right way to word a question, and proved it in a laboratory of thought. It was demonstrated to be valid in a laboratory of the universe. So how do particles speak to each other from far away? What do we mean when we say we observe something? And how is a pair of gloves like and unlike a pair of walkie talkies?

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Published 2018-05-14

27: Peer Pressure (Cellular Automata)

51 min
Open

The fabric of the natural world is an issue of no small contention: philosophers and truth-seekers universally debate about and study the nature of reality, and exist as long as there are observers in that reality. One topic that has grown from a curiosity to a branch of mathematics within the last century is the topic of cellular automata. Cellular automata are named as such for the simple reason that they involve discrete cells (which hold a (usually finite and countable) range of values) and the cells, over some field we designate as "time", propagate to simple automatic rules. So what can cellular automata do? What have we learned from them? And how could they be involved in the future of the way we view the world?

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Published 2018-04-26

26: Infinity Shades of Grey (Paradox)

48 min
Open

A paradox is characterized either by a logical problem that does not have a single dominant expert solution, or by a set of logical steps that seem to lead somehow from sanity to insanity. This happens when a problem is either ill-defined, or challenges the status quo. The thing that all paradoxes, however, have in common is that they increase our understanding of the phenomena which bore them. So what are some examples of paradox? How does one go about resolving it? And what have we learned from paradox?


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Published 2018-04-13

25: Pandemic Panic (Epidemiology)

44 min
Open

The spectre of disease causes untold mayhem, anguish, and desolation. The extent to which this spectre has yielded its power, however, has been massively curtailed in the past century. To understand how this has been accomplished, we must understand the science and mathematics of epidemiology. Epidemiology is the field of study related to how disease unfolds in a population. So how has epidemiology improved our lives? What have we learned from it? And what can we do to learn more from it?



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Published 2018-03-07

24: Language and Entropy (Information Theory in Language)

44 min
Open

Information theory was founded in 1948 by Claude Shannon, and is a way of both qualitatively and quantitatively describing the limits and processes involved in communication. Roughly speaking, when two entities communicate, they have a message, a medium, confusion, encoding, and decoding; and when two entities communicate, they transfer information between them. The amount of information that is possible to be transmitted can be increased or decreased by manipulating any of the aforementioned variables. One of the practical, and original, applications of information theory is to models of language. So what is entropy? How can we say language has it? And what structures within language with respect to information theory reveal deep insights about the nature of language itself?


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Published 2018-01-15

23: Don't Touch My Circles! (Geometry)

52 min
Open

In the study of mathematics, there are many abstractions that we deal with. For example, we deal with the notion of a real number with infinitesimal granularity and infinite range, even though we have no evidence for this existing in nature besides the generally noted demi-rules 'smaller things keep getting discovered' and 'larger things keep getting discovered'. In a similar fashion, we define things like circles, squares, lines, planes, and so on. Many of the concepts that were just mentioned have to do with geometry; and perhaps it is because our brains developed to deal with geometric information, or perhaps it is because geometry is the language of nature, but there's no doubt denying that geometry is one of the original forms of mathematics. So what defines geometry? Can we make progress indefinitely with it? And where is the line between geometry and analysis?


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Published 2017-12-23

22: Incomplet (Gödel, Escher, Bach: an Eternal Golden Braid: Chapter IV Discussion)

56 min
Open

Gödel, Escher, Bach is a book about everything from formal logic to the intricacies underlying the mechanisms of reasoning. For that reason, we've decided to make a tribute episode; specifically, about episode IV. There is a Sanskrit word "maya" which describes the difference between a symbol and that which it symbolizes. This episode is going to be all about the math of maya. So what is a string? How are formal systems useful? And why do we study them with such vigor?


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Published 2017-12-04

21: Einstein's Biggest Idea (General Relativity)

40 min
Open

Some see the world of thought divided into two types of ideas: evolutionary and revolutionary ideas. However, the truth can be more nuanced than that; evolutionary ideas can spur revolutions, and revolutionary ideas may be necessary to create incremental advancements. General relativity is an idea that was evolutionary mathematically, revolutionary physically, and necessary for our modern understanding of the cosmos. Devised in its full form first by Einstein, and later proven correct by experiment, general relativity gives us a framework for understanding not only the relationship between mass and energy and space and time, but topology and destiny. So why is relativity such an important concept? How do special and general relativity differ? And what is meant by the equation G=8πT?


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Published 2017-11-18

20: Rational (Ratios)

40 min
Open

From MC²’s statement of mass energy equivalence and Newton’s theory of gravitation to the sex ratio of bees and the golden ratio, our world is characterized by the ratios which can be found within it. In nature as well as in mathematics, there are some quantities which equal one another: every action has its equal and opposite reaction, buoyancy is characterized by the displaced water being equal to the weight of that which has displaced it, and so on. These are characterized by a qualitative difference in what is on each side of the equality operator; that is to say: the action is equal but opposite, and the weight of water is being measured versus the weight of the buoyant object. However, there are some formulas in which the equality between two quantities is related by a constant. This is the essence of the ratio. So what can be measured with ratios? Why is this topic of importance in science? And what can we learn from the mathematics of ratios?


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Published 2017-11-07

19: Tune of the Hickory Stick (Beginning to Intermediate Math Education)

39 min
Open

The art of mathematics has proven, over the millennia, to be a practical as well as beautiful pursuit. This has required us to use results from math in our daily lives, and there's one thing that has always been true of humanity: we like to do things as easily as possible. Therefore, some very peculiar and interesting mental connections have been developed for the proliferation of this sort of paramathematical skill. What we're talking about when we say "mental connections"  is the cerebral process of doing arithmetic and algebra. So who invented arithmetic? How are algebra and arithmetic related? And how have they changed over the years? 


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Published 2017-10-11

18: Frequency (Fourier and Related Analyses)

44 min
Open

Duration and proximity are, as demonstrated by Fourier and later Einstein and Heisenberg, very closely related properties. These properties are related by a fundamental concept: frequency. A high frequency describes something which changes many times in a short amount of space or time, and a lower frequency describes something which changes few times in the same time. It is even true that, in a sense, you can ‘rotate’ space into time. So what have we learned from frequencies? How have they been studied? And how do they relate to the rest of mathematics?


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Published 2017-10-05

17: Navier Stoked (Vector Calculus and Navier-Stokes Equations)

60 min
Open
From our first breath of the day to brushing our teeth to washing our faces to our first sip of coffee, and even in the waters of the rivers we have built cities upon since antiquity, we find ourselves surrounded by fluids. Fluids, in this context, mean anything that can take the shape of its container. Physically, that means anything that has molecules that can move past one another, but mathematics has, as always, a slightly different view. This view is seen by some as more nuanced, others as more statistical, but by all as a challenge. This definition cannot fit into an introduction, and I’ll be picking away at it for the remainder of this episode. So what is a fluid? What can we learn from it? And how could learning from it be worth a million dollars?

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Published 2017-09-19

BFNB2: Thought for Food (Discussion about Learning)

71 min
Open
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What you're about to hear is part two of an episode recorded by the podcasting network ___forNon___ (Blank for Non-Blank), of which Breaking Math, along with several other podcasts, is a part. To check out more ___forNon___ content, you can click on the link in this description. And of course, for more info and interactive widgets you can go to breakingmathpodcast.com, you can support us at patreon.com/breakingmathpodcast, and you can contact us directly at breakingmathpodcast@gmail.com. We hope you enjoy the second part of the first ___forNon___ group episode. You can also support ___forNon___ by donating at patreon.com/blankfornonblank.

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Published 2017-09-16

BFNB1: Food for Thought (Discussion about Learning)

35 min
Open
This is the first group podcast for the podcasting network ___forNon___ (pronounced "Blank for Non-Blank"), a podcasting network which strives to present expert-level subject matter to non-experts in a way which is simultaneously engaging, interesting, and simple. The episode today delves into the problem of learning. We hope you enjoy this episode.

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Published 2017-07-30

15: Consciousness

60 min
Open

What does it mean to be a good person? What does it mean to make a mistake? These are questions which we are not going to attempt to answer, but they are essential to the topic of study of today’s episode: consciousness. Conscious is the nebulous thing that lends a certain air of importance to experience, but as we’ve seen from 500 centuries of fascination with this topic, it is difficult to describe in languages which we’re used to. But with the advent of neuroscience and psychology, we seem to be closer than ever to revealing aspects of consciousness that we’ve never beheld. So what does it mean to feel? What are qualia? And how do we know that we ourselves are conscious?


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Published 2017-07-10

14: Artificial Thought (Neural Networks)

65 min
Open

Go to www.brilliant.org/breakingmathpodcast to learn neural networks, everyday physics, computer science fundamentals, the joy of problem solving, and many related topics in science, technology, engineering, and math. 


Mathematics takes inspiration from all forms with which life interacts. Perhaps that is why, recently, mathematics has taken inspiration from that which itself perceives the world around it; the brain itself. What we’re talking about are neural networks. Neural networks have their origins around the time of automated computing, and with advances in hardware, have advanced in turn. So what is a neuron? How do multitudes of them contribute to structured thought? And what is in their future?


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Published 2017-06-26

13: Math and Prison Riots (Interview with Frank Salas)

49 min
Open

Frank Salas is an statistical exception, but far from an irreplicable result. Busted on the streets of Albuquerque for selling crack cocaine at 17, an age where many of us are busy honing the skills that we've chosen to master, and promply incarcerated in one of the myriad concrete boxes that comprise the United States penal system. There, he struggled, as most would in his position, to better himself spiritually or ethically, once even participating in a prison riot. After two stints in solitary confinement, he did the unthinkable: he imagined a better world for himself. One where it was not all him versus the world. With newfound vigor, he discovered what was there all along: a passion for mathematics and the sciences. After nine years of hard time he graduated to a halfway house. From there, we attended classes at community college, honing his skills using his second lease on life. That took him on a trajectory which developed into him working on a PhD in electrical engineering from the University of Michegan. We're talking, of course, about Frank Salas; a man who is living proof that condition and destiny are not forced to correlate, and who uses this proof as inspiration for many in the halway house that he once roamed. So who is he? What is his mission? And who is part of that mission? And what does this have to do with Maxwell's equations of electromagnetism?


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Published 2017-06-12

12: Math Factory (Algorithms)

53 min
Open

In a universe where everything is representable by information, what does it mean to interact with that world? When you follow a series of steps to accomplish a goal, what you're doing is taking part in a mathematical tradition as old as math itself: algorithms. From time immemorial, we've accelerated the growth of this means of transformation, and whether we're modeling neurons, recognizing faces, designing trusses on a bridge, or coloring a map, we're involving ourselves heavily in a fantastic world, where everything is connected to everything else through a massive network of mathematical factories. So does it mean to do something? What does it mean for something to end? And what is time relative to these questions?


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Published 2017-05-31

11: A Culture of Hacking (Hacker Culture)

62 min
Open
The culture of mathematics is a strange topic. It is almost as important to the history of mathematics as the theorems that have come from it, yet it is rarely commented upon, and it is almost never taught in schools. One form of mathematical inquiry that has cropped up in the last two centuries has been the algorithm. While not exclusive to this time period, it has achieved a renaissance, and with the algorithm has come what has come to be known as "hacker culture". From Lord Byron to Richard Stallman, from scratches on paper to masses of wire, hacker culture has influenced the way in which we interact with conveniences that algorithms have endowed upon our society. So what are these advances? How have they been affected by the culture which birthed them? And what can we learn from this fragile yet pervasive relationship?

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Published 2017-05-16

10: Cryptomath (Cryptography)

76 min
Open
Language and communication is a huge part of what it means to be a person, and a large part of this importance is the ability to direct the flow of that information; this is a practice known as cryptography. There are as many ways to encrypt data as there are ways to use them, ranging from cryptoquips solvable by children in an afternoon to four kilobit RSA taking eons of time. So why are there so many forms of encryption? What can they be used for? And what are the differences in their methodology, if not philosophy?

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Published 2017-05-02

9: Humanity 2.0 (Transhumanism)

52 min
Open

Humanity, since its inception, has been nebulously defined. Every technological advancement has changed what it means to be a person, and every person has changed what it means to advance. In this same vein, there is a concept called “transhumanism”, which refers to what it will mean to be a person. This can range from everything from genetic engineering, to artificial intelligence, to technology which is beyond our current physical understanding. So what does it mean to be a person? And is transhumanism compatible with our natural understanding, if it exists, of being?


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Published 2017-04-18

8: Evolution and Engineering (Genetic Algorithms)

57 min
Open

Computation is a nascent science, and as such, looks towards the other sciences for inspiration. Whether it be physics, as in simulated annealing, or, as now is popular, biology, as in neural networks, computer science has shown repeatedly that it can learn great things from other sciences. Genetic algorithms are one such method that is inspired, of course, by biological evolution. So what are genetic algorithms used for? What have they taught us about the natural process of evolution? And how can we use them to improve our world?


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Published 2017-04-04

7: QED? Prove it. (Proofs)

44 min
Open

Proofs are sometimes seen as an exercise in tedium, other times as a pure form of beauty, and often as both. But from time immemorial, people have been using mathematics to demonstrate new theorems, and advance the state of the art of mathematics. However, it is only relatively recently, within the last 3,000 years, that the art of mathematical proof has been considered essential to the study of mathematics. Mathematicians constantly fight over what constitutes a proof, and even what makes a proof valid, partially because proof requires delicate insight. So what is the art of mathematical proof? How has it changed? And who can do it?


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Published 2017-03-21

6: Word (Linguistics)

49 min
Open

Mathematics has a lot in common with language. Both have been used since the dawn of time to shape and define our world, both have sets of rules which one must master before bending, both are natural consequences of the way humans are raised, and both are as omnipresent as they are seemingly intangible. Language has thrived for almost, or as long as humans have possessed the ability to use it. But what can we say that language is? Is it a living breathing organism, a set of rigid ideals, somewhere in between, or something else altogether?


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Published 2017-03-07

5: Language of the Universe (Relationship Between Physics and Math)

48 min
Open

1948. A flash, followed by an explosion. Made possible by months of mathematical computation, the splitting of the atom was hailed as a triumph of both science and mathematics. Mathematics is seen by many as a way of quantifying experiments. But is that always the case? There are cases where it seems as though mathematics itself has made predictions about the universe and vice versa. So how are these predictions made? And what can we learn about both physics and math by examining the way in which these topics intermingle?


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Published 2017-02-21

4: Digital Evolution (Digital Computing)

52 min
Open

We live in an era of unprecedented change, and the tip of the spear of this era of change is currently the digital revolution. In fact, in the last decade we’ve gone from an analog to a digitally dominated society, and the amount of information has recently been increasing exponentially. Or at least it seems like it’s recent; in fact, however, the digital revolution has been going on for hundreds of centuries. From numerals inscribed in“We live in an era of unprecedented change, and the tip of the spear of this era of change is currently the digital revolution. In fact, in the last decade we’ve gone from an analog to a digitally dominated society, and the amount of information has recently been increasing exponentially. Or at least it seems like it’s recent; in fact, however, the digital revolution has been going on for hundreds of centuries. From numerals inscribed in bone to signals zipping by at almost the speed of light, our endeavors as humans, and some argue, our existence in the universe, is ruled by the concept of digital information. So how did we discover digital information? And what has it been used for?


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Published 2017-02-07

3: TMI (Information Theory)

48 min
Open
“ABABABABABABABAB”. How much information was that? You may say “sixteen letters worth”, but is that the true answer? You could describe what you just read as “AB 8 times”, and save a bunch of characters, and yet have the same information. But what is information in the context of mathematics? The answer is nothing short of miraculous; information theory has applications in telephony, human language, and even physics. So what is information theory, and what can we learn from it?

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Published 2017-02-07

2: Wreaking Chaos (Chaos Theory)

51 min
Open

The void has always intrigued mankind; the concept of no concept defies the laws of human reasoning to such a degree that we have no choice but to pursue it. But ancient Assyrian, Norse, Judeo-Christian creation stories, and even our own scientific inquiries have one thing in common: creation from “nothingness”. But is it really nothingness? The ancients used the term “chaos”, and, although to some “chaos” has become synonymous with “bedlam” or “randomness”, it has much more to do with the timeless myths of creation of form from the formless. So how does chaos take form? And is there meaning to be found in the apparent arbitrariness of chaos, or is it a void that defines what we think it means to be?

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Published 2017-02-07

1: Forbidden Formulas (Elitism in Math)

59 min
Open

From Pythagoras to Einstein, from the banks of the Nile to the streamlined curves of the Large Hadron Collider, math has shown itself again and again to be fundamental to the way that humans interact with the world. Then why is math such a pain for so many people? Our answer is simple: math is, and always has been, in one way or another, guarded as an elite skill. We visit the worlds that were shaped by math, the secrets people died for, the false gods created through this noble science, and the gradual chipping away of this knowledge by a people who have always yearned for this magical skill. So what is it? And how can we make it better?

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[Featuring: Sofía Baca, Gabriel Hesch; Amy Lynn, Ian McLaughlin]


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