Breaking Math Podcast

Mathematician, mental-math performer, and backgammon grandmaster Arthur Benjamin joins Noah and Autumn to talk about his book How to Win. Together they explore what mathematics knows about winning that human intuition gets wrong: coincidences, the birthday paradox, gambler's ruin, and why the house wins even when you reach your goal more than half the time.

Timeline:

00:00 Can math ruin the fun of games?

00:38 Why people play for the challenge, not the answer

02:35 Mental arithmetic and the human element

03:30 Calculators, AI, and the future of coding

05:47 What does math know about winning that intuition gets wrong?

06:02 Coincidences and the birthday paradox

10:16 Why games are a microcosm for pattern-seeking

16:40 What games teach that the classroom doesn't

16:52 Gambler's ruin: how to get to the concert

20:30 The paradox: why casinos aren't afraid

22:30 What does "winning" really mean?

23:29 Wordle streaks vs. average guesses

27:07 Rubik's Cube, blackjack, and why some games never get old

35:38 Does math take the mystery out of games?

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(https://www.arthurbenjamin.info/)

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"I'm just not a math person." If you've ever said that about yourself, this episode is for you.

Dr. Geillan Aly, author of Compassionate Math, joins Breaking Math to break down the real difference between math anxiety and math trauma — and why mathematics, more than almost any other subject, is uniquely built to make one bad experience feel like permanent proof of failure.

In this episode we cover:

00:00 – What is math trauma, and why is it different from anxiety?

02:35 – Why math specifically (vs. history, reading, or other subjects)?

07:28 – Teaching concepts vs. teaching procedures

13:32 – The "sixes" story: a failing student's transformative breakthrough

20:15 – Math anxiety vs. math trauma, explained

28:56 – Whose fault is math trauma — students, teachers, or society?

36:21 – How compassionate math scales beyond the classroom

39:21 – One piece of advice for students, and one for teachers

Follow Geillan Aly on her website:

(https://www.compassionatemath.com/)

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Professional forecaster Molly Hickman breaks down what it really means to assign a probability to the future — and why she believes generalists often out-forecast subject-matter experts. This episode explores the art and science of forecasting, from techniques to ethical considerations, and how AI and prediction markets are shaping our understanding of the future.

Key Topics

The definition of forecasting and its importance

Techniques for starting in forecasting

The role of AI and large language models in forecasting

How to interpret probabilities and conditional forecasts

Forecasting in complex systems like climate and geopolitics

Ethical boundaries and red lines in prediction markets

The impact of AI bots on forecasting accuracy and decision making

Chapters

03:06 Getting Started with Forecasting: Tools and Techniques

06:15 Beginning Forecasting as a Beginner

07:31 Gut Feelings vs Market Wisdom

08:33 The Delphi Loop and Group Forecasting

09:39 Measuring Forecast Accuracy and Skill

11:17 Forecasting Long-Term and Uncertain Events

12:40 Extrapolating Trends and Model Limitations

14:19 AI Bots in Forecasting and Their Performance

18:16 Prediction Markets as Collective Wisdom

19:19 The Future of Prediction Markets and Society

24:06 The Meaning of Probabilities and Risk Assessment

27:20 Dealing with Chaos and Unpredictability

32:52 Combining Models and Expert Opinions

36:31 Forecasting and Expertise in Science and Policy

39:01 Forecasting AI Risks and Ethical Boundaries

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What does it mean to be alive? In this episode of Breaking Math, Autumn and Noah speak with Melanie Challenger, author of Alive, about one of the most profound questions in science and philosophy: how do we define life?

Challenger argues that life is not simply a machine-like process or a bundle of genetic instructions. Living beings are embodied, purposeful agents. From single-celled organisms to sequoia seeds, from animals to human beings, life is marked by an astonishing capacity to work to keep itself alive.

Chapters

08:12 The concept of purpose in living beings

09:14 The scientific view of purpose and agency

11:52 The importance of purpose and meaning in life

13:19 The danger of ignoring organism agency in science

14:34 Living beings as purposeful agents

15:35 Comparing purpose in a Roomba and a single-celled organism

18:03 Autopoetic vs allopoetic systems

20:03 Free will, agency, and the universe

23:24 The physical basis of life and energy

28:38 Aristotle's concept of psyche and purpose

33:46 The importance of understanding what life truly is

37:56 Material integration and the difference between machines and living beings

38:15 The concept of self and embodiment in life

41:09 The whole body as the agent, not just the brain

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Neuroscientist Stuart Firestein (Columbia University) joins Breaking Math to make an extravagant claim: uncertainty isn't a weakness in science — it's the defining feature that makes progress possible. In this episode, we break down why the "one right answer" myth is one of the most damaging ideas in science, why real experts are often the most uncertain people in the room, and why authority and expertise pull in opposite directions, covering two fundamentally different kinds of probability, why Darwin never erased a 300-year-old classification system built on an assumption he disproved, why AI is exceptional at prediction but not built for causation, and why pseudoscience always has a confident answer while real science rarely does — plus the philosophical difference between hope and optimism, and why Voltaire had to invent the word "optimism" in 1759 to describe it.

Chapters

03:00 Predictability and the sea of uncertainties

04:08 Science as a search for probabilities and multiple solutions

06:16 Biological classification and the dynamic nature of species

09:10 The optimistic view of a branching universe

12:41 Probability as the language of optimism

16:48 Two types of probability and their roles

17:50 AI, probabilistic models, and the future of certainty

21:40 Science and the creation of better ignorance

23:21 The importance of asking questions over giving answers

27:21 Authority versus knowledge in science

30:04 Pluralism and multiple solutions in science

32:46 Science in the gray area of uncertainty

35:39 The brain and randomness in thought

39:44 Science as a source of hope and optimism

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Neuroscientist, entrepreneur, and author Dr. Vivienne Ming joins Autumn and Noah to make the case that if we want better AI, we need to build better people first. We get into why AI tutors that hand students answers make learning worse, not better; what her research on "hybrid intelligence" reveals about the human traits — not the AI model — that predict elite human-AI collaboration; a wild experiment running Dungeons & Dragons with Claude and Gemini as dungeon masters to expose the gap between knowing and understanding; her case for "fiduciary AI," legal duty-of-care standards for tutors, hiring tools, and diagnostic models; and the real story of a hiring algorithm that learned to discriminate against women after every explicit gender marker was stripped out.

Chapters

02:20 Why build this book now? The importance of human qualities

04:16 AI in education and the concept of robot-proofing

06:37 The median student and AI personalization

09:31 The limitations of AI understanding and theory of mind

11:30 Building better people with AI and human interaction

14:23 Hybrid intelligence and the role of human-AI collaboration

23:56 Case study: AI in Dungeons & Dragons

30:42 AI's strengths and limitations in understanding and cognition

37:34 The science of purpose and its impact on life and society

44:44 The collective intelligence of humans versus AI

46:54 Key takeaway: Build better people for better

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In this episode, Historian and author Marc Dunkelman to explain why the 19th-century fight over railroad power is the exact fight we're about to have over algorithms and AI. Drawing on his acclaimed book Why Nothing Works: Who Killed Progress — and How to Bring It Back (a Best Book of the Year in the Financial Times and The Economist), Marc unpacks the two competing tools America has always used against concentrated power — antitrust vs. regulation — and why our government's "endemic diffusion of authority" now means nobody can decide anything, from congestion pricing to clean-energy transmission lines to AI safety.

CHAPTERS

04:52 — When private projects come back to the public: Warp Speed, DARPA, CHIPS

08:55 — Two ways to fight concentrated power: break them up vs. regulate

10:52 — Railroads, island communities & the birth of regulation

12:29 — The railroad = algorithm parallel

20:33 — Why nothing gets built: the diffusion of authority

27:30 — "A voice without a veto" and the AI moment

32:53 — Where should government draw the line on new tech?

37:20 — Dunkelman the pragmatist: there is no simple answer

38:21 — Where math and AI can genuinely help public policy

40:46 — The lesson we keep overlooking

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In this conversation we chat with Julia Angwin — Pulitzer Prize-winning journalist, founder of Proof News, and former Wall Street Journal and ProPublica reporter — to make the case that journalism should function more like mathematical proof than anecdote.

We cover how Angwin's team at The Markup used a decision-tree model to prove Amazon was favoring its own products in search results by an 8-to-1 margin — a finding the House Antitrust Committee later cited when referring Amazon to the DOJ for possible perjury. We dig into her "ingredients label" approach to reporting at Proof News (hypothesis, sample size, techniques, limitations), the difference between mathematical proof and the scientific method, and why she thinks control over algorithmic media is now the central battleground for authoritarian power. She also unpacks her new book on resisting authoritarianism, built from interviews with dissidents worldwide, including the "Swiss cheese" model of personal security and why perfectionism is dangerous in a crisis.

Chapters

09:50 Proof News: A New Era in Journalism

19:56 Data-Driven Investigations: A Case Study

30:02 The Future of Journalism and AI

32:53 The Evolution of Search Rankings

35:06 The Role of Algorithms in Information Access

36:41 Fighting Authoritarianism Through Journalism

44:52 Community Resistance Against Authoritarianism

48:33 The Dangers of Perfectionism in Resistance

51:26 Declaring a Position in Journalism

56:25 The Importance of Math in Modern Society

Julia Angwin's book, “On Courage” (https://amzn.to/448G8kY)

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In this episode, Autumn and Noah talk with Kevin Hartnett about why mathematicians are willing to spend years reducing an idea to a level of detail a machine can check, whether formal verification can catch an AI that's technically correct but fundamentally misaligned, the cold-start problem that kept earlier theorem-provers niche, and what it means for the future of mathematical trust once AI can generate proofs faster than any human community can read them.

Timeline:

00:00 Introduction to Lean and Its Significance

03:18 The Journey of Writing the Book

05:13 Human Element in Mathematical Formalization

06:57 Understanding Formal Proofs in Mathematics

11:21 The Origins of Lean and Its Purpose

13:03 Misalignment in Software Specifications

14:39 Building Mathematical Libraries in Lean

17:23 Ensuring Accuracy in Mathematical Foundations

22:00 Overcoming the Cold Start Problem in Lean Adoption

24:36 The Future of Mathematical Proofs

30:26 AI's Role in Mathematics

38:29 Expanding Beyond Mathematics

41:40 The Long-Term Impact of Lean

The Proof in the Code is out now from Quanta Books. (https://amzn.to/3SuNlJm)

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What happens when the evidence of injustice is buried in messy, redacted, or inaccessible data? Mathematician and data scientist Chad Topaz joins Breaking Math to discuss his book Unlocking Justice. Together, we explore policing, sentencing, public records, Rikers Island, algorithmic risk, and the limits of quantifying human lives. This is a conversation about math, power, transparency, and the small acts of hope that can change systems.

Chapters

00:00 Introduction and Context of the Conversation

01:11 Chad's Journey from Mathematics to Social Justice

03:50 The Personal Nature of Chad's Book

04:40 Challenges in Data Collection and Access

08:03 The Impact of Data on Policing and Surveillance

09:51 Humorous Yet Tragic Data Collection Experiences

12:55 The Importance of Data Preparation and Cleaning

14:40 Navigating Imperfect Data and Its Consequences

17:48 The Balance Between Quantification and Human Stories

22:25 Incarceration and Public Health: The Rikers Island Case Study

31:36 Mathematics and Social Justice: Secrets of the Elite

39:03 Hope and Action: A Personal Journey in Data for Justice

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This conversation explores the profound impact of AI and automation on the future of work, economy, and society. Featuring Martin Ford, author of 'Rise of the Robots,' the discussion covers technological progress, economic implications, policy ideas like universal basic income, and the evolving nature of jobs in an AI-driven world.

Key Topics

Impact of AI on employment and economy

Potential of universal basic income as a solution

Differences between past technological revolutions and AI

The evolution from physical robots to AI software agents

Jobs most vulnerable to automation and AI

Chapters

04:14 The Impact of Technological Revolutions on Employment

10:40 The Shift from Physical to Intellectual Automation

12:16 The Debate: Replacement vs. Augmentation of Jobs

18:01 Economic Implications of Job Displacement

21:00 Exploring Solutions: Universal Basic Income and Beyond

24:08 The Awakening of Economists

25:12 Historical Perspectives on Automation

28:27 Navigating the Future Job Market

32:57 The Role of Skilled Trades in an AI World

38:13 The Alien Thought Experiment

42:17 The Future of AI and Its Implications

44:14 The Rise of Automation and Its Impact

45:14 AI as a Digital Workforce

45:38 The Shifting Landscape of Work

46:08 Questioning the Future of Automation and AI

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Dr. Emma Chapman explains radio astronomy using the fruit bowl metaphor, explores the emotional and scientific aspects of space exploration, and discusses future technologies like the Square Kilometre Array and lunar radio telescopes. The conversation highlights the poetic beauty of the universe, the importance of connection, and the role of math and AI in understanding the cosmos with her book the Echoing Universe.

Chapters

03:17 Understanding Radio Astronomy

08:12 The Intimacy of the Solar System

09:10 Tidal Locking and the Moon

13:36 The Emotional Lives of Astronauts' Families

17:53 The Shared Experience of Space Exploration

21:58 The Emotional Resonance of Celestial Events

26:41 Facing the Universe: Overcoming Fear through Cosmology

28:16 Cultural Perspectives: How Civilizations Understand the Cosmos

30:52 Astronomy's Historical Impact: Control and Awe in Civilizations

31:05 The Unlikely Scientist: James Stanley Hay's Discovery

40:31 AI in Astronomy: Harnessing Data for Discovery

45:14 The Next Frontier: Radio Telescopes on the Moon

47:38 A New Perspective: The Space Between Stars

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This episode explores how AI, specifically OpenAI's recent breakthrough in solving an 80-year-old math conjecture, is transforming the field of mathematics. Featuring insights from Professor Daniel Litt, the discussion covers the implications of AI in mathematical research, the value of human verification, and the future of mathematical practice.

Key topics

AI solving long-standing mathematical problems

The role of human verification in AI-generated proofs

Implications of AI breakthroughs in discrete geometry

The future of mathematical research with AI

Number theory and algebraic constructions in AI discoveries

Chapters

00:00 Introduction to the Conjecture and Its Significance

01:15 Understanding the Erdős Problem

04:34 The Role of AI in Solving Mathematical Problems

09:17 The Implications of AI in Mathematics

10:32 AI vs Human Mathematicians: A Comparative Analysis

17:20 Standards for AI-Generated Proofs

21:10 Corporate Interests in Mathematical Research

24:42 The Future of Mathematics and AI

27:50 Final Thoughts on AI and Mathematics

31:37 Revolutionizing Mathematics: AI's Breakthrough in Discrete Geometry

37:37 Exploring the Implications: AI and the Future of Mathematics

38:03 The Role of AI in Mathematics

39:23 Human Value in the Age of AI

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In this episode with award-winning journalist and author Maia Szalavitz challenges the idea that addiction is simply about pleasure or willpower. Instead, she explains addiction as compulsive behavior that continues despite negative consequences — and shows why withdrawal, dependence, and addiction are not the same thing.

The conversation explores “wanting” versus “liking,” why dopamine is misunderstood, how social media and AI can exploit reward systems, and why punishment often fails. Ultimately, Szalavitz argues that recovery depends less on tough love and more on connection, purpose, safety, and care.

Chapters

00:00 Understanding Addiction: Definitions and Mechanisms

10:43 The Role of Dopamine in Addiction

14:18 Addiction as a Learning Disorder

16:22 Substance vs. Experience: The Nature of Addiction

20:13 Evidence-Based Methods for Overcoming Addiction

25:20 Finding Meaning and Purpose Beyond Addiction

33:30 The Pursuit of Meaningful Experiences

34:15 Understanding Dopamine and Pleasure

39:10 The Complexity of Addiction

43:00 Social Media and Addiction Dynamics

50:42 Generational Perspectives on Technology and Addiction

57:53 Lessons Learned in Addiction Science

01:02:03 Rethinking Addiction: A New Perspective

01:03:54 The Compulsive Nature of Addiction

01:04:14 Understanding Addiction Beyond Pleasure

01:05:27 The Importance of Connection and Compassion

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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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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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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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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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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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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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