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    Mathematics

    Breaking Math Podcast

    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

    Advertise

    Copyright: © Copyright Breaking Math

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    Latest Episodes:
    Forecasting Explained: How Prediction Markets Beat Experts Sep 09, 2026
    Show notes

    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

    Follow Molly Hickman on X (https://x.com/celloMolly)

    Follow Breaking Math on

    Substack (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 on

    Instagram (https://www.instagram.com/profnoahgian/)

    X (https://x.com/ProfNoahGian)

    Bluesky (https://bsky.app/profile/profnoahgian.bsky.social)

    Follow Autumn on

    X (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


    What Actually Makes Something Alive? with Melanie Challenger Aug 19, 2026
    Show notes

    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

    Follow Melanie Challenger on her website:

    (https://www.melaniechallenger.com/) Subscribe for more on math, AI, technology, and the systems running the world. Follow Breaking Math on

    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 on

    Instagram (https://www.instagram.com/profnoahgian/)

    X (https://x.com/ProfNoahGian)

    Bluesky (https://bsky.app/profile/profnoahgian.bsky.social)

    Follow Autumn on

    X (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 Uncertainty Is Science's Greatest Strength with Stuart Firestein Aug 06, 2026
    Show notes

    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

    Follow Breaking Math on

    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 on

    Instagram (https://www.instagram.com/profnoahgian/)

    X (https://x.com/ProfNoahGian)

    Bluesky (https://bsky.app/profile/profnoahgian.bsky.social)

    Follow Autumn on

    X (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 Jul 25, 2026
    Show notes

    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

    Follow Vivienne Ming on X (https://x.com/neuraltheory) Get Vivienne's book, Robot Proof: (https://amzn.to/3Tz21aP)

    Follow Breaking Math on

    Substack (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 on

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    X (https://x.com/ProfNoahGian)

    Bluesky (https://bsky.app/profile/profnoahgian.bsky.social)

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    X (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 Jul 10, 2026
    Show notes

    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

    Follow 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 on

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    X (https://x.com/ProfNoahGian)

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    Follow Autumn on

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    Instagram (https://www.instagram.com/1autumnleaf/)

    Substack (https://substack.com/@1autumnleaf)

    email: breakingmathpodcast@gmail.com


    31: Into the Abyss (Part Two; Black Holes) Aug 23, 2018
    Show notes

    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?


    30: The Abyss (Part One; Black Holes) Aug 02, 2018
    Show notes

    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?



    29: War Jul 14, 2018
    Show notes

    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?



    27: Peer Pressure (Cellular Automata) May 14, 2018
    Show notes

    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?


    25: Pandemic Panic (Epidemiology) Apr 13, 2018
    Show notes

    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?




    1 2 3 21 Next

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