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.ioLinktree: https://linktr.ee/breakingmathmediaEmail: breakingmathpodcast@gmail.com

Episode List

$Why Uncertainty Is Science's Greatest Strength with Stuart Firestein$

Why Uncertainty Is Science's Greatest Strength with Stuart Firestein

Aug 6th, 2026 12:37 AM

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. Chapters03:00 Predictability and the sea of uncertainties04:08 Science as a search for probabilities and multiple solutions06:16 Biological classification and the dynamic nature of species09:10 The optimistic view of a branching universe12:41 Probability as the language of optimism16:48 Two types of probability and their roles17:50 AI, probabilistic models, and the future of certainty21:40 Science and the creation of better ignorance23:21 The importance of asking questions over giving answers27:21 Authority versus knowledge in science30:04 Pluralism and multiple solutions in science32:46 Science in the gray area of uncertainty35:39 The brain and randomness in thought39:44 Science as a source of hope and optimismFollow Breaking Math onSubstack (https://breakingmath.substack.com/)X (https://x.com/breakingmathpod)Instagram (https://www.instagram.com/breakingmathmedia/)Bluesky (https://bsky.app/profile/breakingmath.bsky.social)Website (https://www.breakingmath.io/)YouTube (https://www.youtube.com/@BreakingMathPod)Follow Noah onInstagram (https://www.instagram.com/profnoahgian/)X (https://x.com/ProfNoahGian)Bluesky (https://bsky.app/profile/profnoahgian.bsky.social)Follow Autumn onX (https://x.com/1autumn_leaf)Bluesky (https://bsky.app/profile/1autumnleaf.bsky.social)Instagram (https://www.instagram.com/1autumnleaf/)Substack (https://substack.com/@1autumnleaf)email: breakingmathpodcast@gmail.com

$Robot Proof: Why Better AI Starts With Better People with Vivienne Ming$

Robot Proof: Why Better AI Starts With Better People with Vivienne Ming

Jul 25th, 2026 2:10 AM

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.Chapters02:20 Why build this book now? The importance of human qualities04:16 AI in education and the concept of robot-proofing06:37 The median student and AI personalization09:31 The limitations of AI understanding and theory of mind11:30 Building better people with AI and human interaction14:23 Hybrid intelligence and the role of human-AI collaboration23:56 Case study: AI in Dungeons & Dragons30:42 AI's strengths and limitations in understanding and cognition37:34 The science of purpose and its impact on life and society44:44 The collective intelligence of humans versus AI46:54 Key takeaway: Build better people for better Follow Vivienne Ming on X (https://x.com/neuraltheory) Get Vivienne's book, Robot Proof: (https://amzn.to/3Tz21aP) Follow Breaking Math onSubstack (https://breakingmath.substack.com/)X (https://x.com/breakingmathpod)Instagram (https://www.instagram.com/breakingmathmedia/)Website (https://www.breakingmath.io/)YouTube (https://www.youtube.com/@BreakingMathPod)Follow Noah onInstagram (https://www.instagram.com/profnoahgian/)X (https://x.com/ProfNoahGian)Bluesky (https://bsky.app/profile/profnoahgian.bsky.social)Follow Autumn onX (https://x.com/1autumn_leaf)Bluesky (https://bsky.app/profile/1autumnleaf.bsky.social)Instagram (https://www.instagram.com/1autumnleaf/)Substack (https://substack.com/@1autumnleaf)email: breakingmathpodcast@gmail.com

$Why Nothing Works: Robber Barons, Algorithms & Governing AI$

Why Nothing Works: Robber Barons, Algorithms & Governing AI

Jul 10th, 2026 12:31 AM

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.CHAPTERS04:52 — When private projects come back to the public: Warp Speed, DARPA, CHIPS08:55 — Two ways to fight concentrated power: break them up vs. regulate10:52 — Railroads, island communities & the birth of regulation12:29 — The railroad = algorithm parallel20:33 — Why nothing gets built: the diffusion of authority27:30 — "A voice without a veto" and the AI moment32:53 — Where should government draw the line on new tech?37:20 — Dunkelman the pragmatist: there is no simple answer38:21 — Where math and AI can genuinely help public policy40:46 — The lesson we keep overlookingFollow Marc on X [https://x.com/MarcDunkelman]Get Marc's book, Why Nothing Works: https://amzn.to/4pbFvAB]Substack (https://breakingmath.substack.com/)X (https://x.com/breakingmathpod)Instagram (https://www.instagram.com/breakingmathmedia/)Bluesky (https://bsky.app/profile/breakingmath.bsky.social)Website (https://www.breakingmath.io/)YouTube (https://www.youtube.com/@BreakingMathPod)Follow Noah onInstagram (https://www.instagram.com/profnoahgian/)X (https://x.com/ProfNoahGian)Bluesky (https://bsky.app/profile/profnoahgian.bsky.social)Follow Autumn onX (https://x.com/1autumn_leaf)Bluesky (https://bsky.app/profile/1autumnleaf.bsky.social)Instagram (https://www.instagram.com/1autumnleaf/)Substack (https://substack.com/@1autumnleaf)email: breakingmathpodcast@gmail.com

$Can Math Save Journalism?: Julia Angwin on Proof, Power, and Amazon's Algorithm$

Can Math Save Journalism?: Julia Angwin on Proof, Power, and Amazon's Algorithm

Jul 2nd, 2026 9:56 PM

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. Chapters09:50 Proof News: A New Era in Journalism19:56 Data-Driven Investigations: A Case Study30:02 The Future of Journalism and AI32:53 The Evolution of Search Rankings35:06 The Role of Algorithms in Information Access36:41 Fighting Authoritarianism Through Journalism44:52 Community Resistance Against Authoritarianism48:33 The Dangers of Perfectionism in Resistance51:26 Declaring a Position in Journalism56:25 The Importance of Math in Modern Society Julia Angwin's book, “On Courage” (https://amzn.to/448G8kY)Follow Julia Angwin onX (https://x.com/JuliaAngwin/)Bluesky (https://bsky.app/profile/juliaangwin.com) Proof News (https://www.proofnews.org/)Follow Breaking Math onSubstack (https://breakingmath.substack.com/)X (https://x.com/breakingmathpod)Instagram (https://www.instagram.com/breakingmathmedia/)Bluesky (https://bsky.app/profile/breakingmath.bsky.social)Website (https://www.breakingmath.io/)YouTube (https://www.youtube.com/@BreakingMathPod)Follow Noah onInstagram (https://www.instagram.com/profnoahgian/)X (https://x.com/ProfNoahGian)Follow Autumn onX (https://x.com/1autumn_leaf)Instagram (https://www.instagram.com/1autumnleaf/)email: breakingmathpodcast@gmail.com

$The Proof in the Code: How Lean Is Quietly Rewriting Trust in Math (w/ Kevin Hartnett)$

The Proof in the Code: How Lean Is Quietly Rewriting Trust in Math (w/ Kevin Hartnett)

Jun 24th, 2026 2:09 PM

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 Significance03:18 The Journey of Writing the Book05:13 Human Element in Mathematical Formalization06:57 Understanding Formal Proofs in Mathematics11:21 The Origins of Lean and Its Purpose13:03 Misalignment in Software Specifications14:39 Building Mathematical Libraries in Lean17:23 Ensuring Accuracy in Mathematical Foundations22:00 Overcoming the Cold Start Problem in Lean Adoption24:36 The Future of Mathematical Proofs30:26 AI's Role in Mathematics38:29 Expanding Beyond Mathematics41:40 The Long-Term Impact of LeanThe Proof in the Code is out now from Quanta Books. (https://amzn.to/3SuNlJm)Follow Kevin Hartnett onX (https://x.com/KSHartnett) Bluesky (https://bsky.app/profile/kevinhartnett.bsky.social)Follow Breaking Math onSubstack (https://breakingmath.substack.com/)X (https://x.com/breakingmathpod)Instagram (https://www.instagram.com/breakingmathmedia/)Bluesky (https://bsky.app/profile/breakingmath.bsky.social)Website (https://www.breakingmath.io/)YouTube (https://www.youtube.com/@BreakingMathPod)Follow Noah onInstagram (https://www.instagram.com/profnoahgian/)X (https://x.com/ProfNoahGian)Bluesky (https://bsky.app/profile/profnoahgian.bsky.social)Follow Autumn onX (https://x.com/1autumn_leaf)Bluesky (https://bsky.app/profile/1autumnleaf.bsky.social)Instagram (https://www.instagram.com/1autumnleaf/)Substack (https://substack.com/@1autumnleaf)email: breakingmathpodcast@gmail.com

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