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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:
    24: Language and Entropy (Information Theory in Language) Mar 07, 2018
    Show notes

    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?


    ---


    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

    23: Don't Touch My Circles! (Geometry) Jan 15, 2018
    Show notes

    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?


    ---


    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

    22: Incomplet (Gödel, Escher, Bach: an Eternal Golden Braid: Chapter IV Discussion) Dec 23, 2017
    Show notes

    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?


    ---


    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

    21: Einstein's Biggest Idea (General Relativity) Dec 04, 2017
    Show notes

    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?


    ---


    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

    20: Rational (Ratios) Nov 18, 2017
    Show notes

    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?


    ---


    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

    19: Tune of the Hickory Stick (Beginning to Intermediate Math Education) Nov 07, 2017
    Show notes

    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?


    ---


    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

    18: Frequency (Fourier and Related Analyses) Oct 11, 2017
    Show notes

    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?


    ---


    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

    17: Navier Stoked (Vector Calculus and Navier-Stokes Equations) Oct 05, 2017
    Show notes

    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?
    ---
    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

    BFNB2: Thought for Food (Discussion about Learning) Sep 19, 2017
    Show notes

    Sponsored by www.brilliant.org/breakingmath, where you can take courses in calculus, computer science, chemistry, and other STEM subjects. All online; all at your own pace; and accessible anywhere with an internet connection, including your smartphone or tablet! Start learning today!
    Check out: https://blankfornonblank.podiant.co/e/357f09da787bac/
    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.
    ---
    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

    BFNB1: Food for Thought (Discussion about Learning) Sep 16, 2017
    Show notes

    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.
    ---
    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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