Breaking Math Podcast
Autumn Phaneuf
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 Gabriel Hesch, an electrical engineer (host from 2016-2024) with a passion for mathematical clarity, the show is dedicated to uncovering the mathematical structures behind science, engineering, technology, and the systems that shape 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—whether it’s into the strange beauty of chaos theory, the ethical dilemmas of AI, the deep structures of biological evolution, or the thermodynamics of black holes. Along the way, Autumn and Gabriel interview leading thinkers and working scientists from across the spectrum: computer scientists, quantum physicists, chemists, philosophers, neuroscientists, and more.But this isn’t just a podcast about equations—it’s a show about how mathematics influences the way we think, create, build, and understand. Breaking Math pushes back against the idea that STEM belongs behind a paywall or an academic podium. It’s for the curious, the critical, 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? How do we quantify uncertainty in climate models? Can consciousness be described in AI? Why does beauty matter in an equation?Then you’re in the right place.At its heart, Breaking Math is about building bridges—between disciplines, between experts and the public, and between the abstract world of mathematics and the messy, magnificent reality we live in. With humor, clarity, and deep respect for complexity, Autumn and Gabriel 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
Episodes
Mentioned books
Dec 23, 2017 • 57min
22: Incomplet (Gödel, Escher, Bach: an Eternal Golden Braid: Chapter IV Discussion)
Dive into the fascinating world of symbolism and mathematics inspired by Gödel, Escher, Bach. Explore the Sanskrit concept of 'maya' and its implications on formal logic. Engage with thought-provoking themes of self-reference and paradoxes that challenge our understanding of mathematical truth. Discover the essence of isomorphism through relatable examples and its significance in both art and technology. Enjoy a whimsical discussion on the relationship between music and philosophical concepts, all while navigating the quirks of formal systems.
Dec 4, 2017 • 40min
21: Einstein's Biggest Idea (General Relativity)
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/appSupport this podcast: https://anchor.fm/breakingmathpodcast/support
Nov 18, 2017 • 40min
20: Rational (Ratios)
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/appSupport this podcast: https://anchor.fm/breakingmathpodcast/support
Nov 7, 2017 • 40min
19: Tune of the Hickory Stick (Beginning to Intermediate Math Education)
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/appSupport this podcast: https://anchor.fm/breakingmathpodcast/support
Oct 11, 2017 • 44min
18: Frequency (Fourier and Related Analyses)
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/appSupport this podcast: https://anchor.fm/breakingmathpodcast/support
Oct 5, 2017 • 1h
17: Navier Stoked (Vector Calculus and Navier-Stokes Equations)
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/appSupport this podcast: https://anchor.fm/breakingmathpodcast/support
Sep 19, 2017 • 1h 12min
BFNB2: Thought for Food (Discussion about Learning)
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/appSupport this podcast: https://anchor.fm/breakingmathpodcast/support
Sep 16, 2017 • 36min
BFNB1: Food for Thought (Discussion about Learning)
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/appSupport this podcast: https://anchor.fm/breakingmathpodcast/support
Aug 18, 2017 • 26min
Minisode 0.6: Four Problems
Jonathan and Gabriel discuss four challenging problems.--- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/appSupport this podcast: https://anchor.fm/breakingmathpodcast/support
Jul 30, 2017 • 1h
15: Consciousness
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?--- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/appSupport this podcast: https://anchor.fm/breakingmathpodcast/support
