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
Feb 3, 2020 • 39min
P3: Radiativeforcenado (Radiative Forcing)
Learn more about radiative forcing, the environment, and how global temperature changes with atmospheric absorption with this Problem Episode about you walking your (perhaps fictional?) dog around a park. This episode is distributed under a CC BY-SA license. For more information, visit CreativeCommons.org.[Featuring: Sofía Baca, Gabriel Hesch]--- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/appSupport this podcast: https://anchor.fm/breakingmathpodcast/support
Jan 20, 2020 • 42min
46: Earth Irradiated (the Greenhouse Effect)
Since time immemorial, blacksmiths have known that the hotter metal gets, the more it glows: it starts out red, then gets yellower, and then eventually white. In 1900, Max Planck discovered the relationship between an ideal object's radiation of light and its temperature. A hundred and twenty years later, we're using the consequences of this discovery for many things, including (indirectly) LED TVs, but perhaps one of the most dangerously neglected (or at least ignored) applications of this theory is in climate science. So what is the greenhouse effect? How does blackbody radiation help us design factories? And what are the problems with this model?This episode is distributed under a CC BY-SA license. For more information, visit CreativeCommons.org.[Featuring: Sofía Baca, Gabriel Hesch]--- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/appSupport this podcast: https://anchor.fm/breakingmathpodcast/support
Dec 10, 2019 • 25min
45: Climate Denialism and Cranky Uncles (Interview with John Cook of Skeptical Science)
Climate change is an issue that has become frighteningly more relevant in recent years, and because of special interests, the field has become muddied with climate change deniers who use dishonest tactics to try to get their message across. The website SkepticalScience.com is one line of defense against these messengers, and it was created and maintained by a research assistant professor at the Center for Climate Change Communication at George Mason University, and both authored and co-authored two books about climate science with an emphasis on climate change. He also lead-authored a 2013 award-winning paper on the scientific consensus on climate change, and in 2015, he developed an open online course on climate change denial with the Global Change Institute at the University of Queensland. This person is John Cook.This episode is distributed under a CC BY-SA license. For more information, visit CreativeCommons.org.[Featuring: Sofía Baca, Gabriel Hesch; John Cook]--- 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 3, 2019 • 37min
44: Vestigial Math (Math That Is Not Used like It Used to Be)
Mathematics, like any intellectual pursuit, is a constantly-evolving field; and, like any evolving field, there are both new beginnings and sudden unexpected twists, and things take on both new forms and new responsibilities. Today on the show, we're going to cover a few mathematical topics whose nature has changed over the centuries. So what does it mean for math to be extinct? How does this happen? And will it continue forever?This episode is distributed under a CC BY-SA license. For more information, visit CreativeCommons.org.[Featuring: Sofía Baca, Gabriel Hesch]--- 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 30, 2019 • 19min
P2: Walk the Dog (Calculus: Chain Rule)
Learn more about calculus, derivatives, and the chain rule with this Problem Episode about you walking your (perhaps fictional?) dog around a park.This episode is distributed under a CC BY-SA license. For more information, visit CreativeCommons.org.[Featuring: Sofía Baca, Gabriel Hesch]--- 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 23, 2019 • 43min
43: Interview II with Author Ben Orlin (Change is the Only Constant: the Wisdom of Calculus in a Madcap World)
Ben Orlin has been a guest on the show before. He got famous with a blog called 'Math With Bad Drawings", which is what it says on the tin: he teaches mathematics using his humble drawing skills. His last book was a smorgasbord of different mathematical topics, but he recently came out with a new book 'Change is the Only Constant: the Wisdom of Calculus in a Madcap World', which focuses more on calculus itself.This episode is distributed under a CC BY-SA license. For more info, visit creativecommons.org
Sep 29, 2019 • 37min
P1: Peano Addition
On this problem episode, join Sofía and guest Diane Baca to learn about what an early attempt to formalize the natural numbers has to say about whether or not m+n equals n+m.This episode is distributed under a CC BY-SA 4.0 license (https://creativecommons.org/licenses/by-sa/4.0/)--- 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 15, 2019 • 33min
42: Maybe? (Probability and Statistics)
In this engaging discussion, guest Matt Barbato, a stats enthusiast and sports analyst, sheds light on the fascinating world of statistics. He unpacks the evolution of this oft-misunderstood field and explores crucial concepts like Bayes' theorem. Barbato dives into the differences between frequentist and Bayesian methods, sharing real-world examples from sports and fantasy leagues that make probability more relatable. The conversation reveals how understanding these principles can illuminate everyday decisions and perceptions of chance.
Jul 29, 2019 • 55min
41: Reality Is More Than Complex (Group Theory and Physics)
Children who are being taught mathematics often balk at the idea of negative numbers, thinking them to be fictional entities, and often only learn later that they are useful for expressing opposite extremes of things, such as considering a debt an amount of money with a negative sum. Similarly, students of mathematics often are puzzled by the idea of complex numbers, saying that it makes no sense to be able to take the square root of something negative, and only realizing later that these can have the meaning of two-dimensional direction and magnitude, or that they are essential to our modern understanding of electrical engineering. Our discussion today will be much more abstract than that. Much like in our discussion in episode five, "Language of the Universe", we will be discussing how math and physics draw inspiration from one another; we're going to talk about what different fields (such as the real, complex, and quaternion fields) seem to predict about our universe. So how are real numbers related to classical mechanics? What does this mean complex numbers and quaternions are related to? And what possible physicses exist?Update: Dr. Alex Alaniz and the Breaking Math Podcast have teamed up to create a new youtube show called the "Turing Rabbit Holes Podcast." We discuss science, math, and society with spectacular visuals. Available at youtube.com/TuringRabbitHolesPodcast and on all other podcast platforms. Ways to support the show:Patreon Become a monthly supporter at patreon.com/breakingmathLicense is Creative Commons Attribution-ShareAlike 4.0 (See https://creativecommons.org/licenses/by-sa/4.0/)
May 29, 2019 • 33min
39: Syntax Matters: Syntax... Matters? (Formal Grammar)
We communicate every day through languages; not only human languages, but other things that could be classified as languages such as internet protocols, or even the structure of business transactions. The structure of words or sentences, or their metaphorical equivalents, in that language is known as their syntax. There is a way to describe certain syntaxes mathematically through what are known as formal grammars. So how is a grammar defined mathematically? What model of language is often used in math? And what are the fundamental limits of grammar?
