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, 2021 • 34min
68: LOL!!! SO RANDOM (Random Variables)
The world is often uncertain, but it has only been in the last half millennium that we've found ways to interact mathematically with that concept. From its roots in death statistics, insurance, and gambling to modern Bayesian networks and machine learning, we've seen immense productivity in this field. Every way of looking at probability has something in common: the use of random variables. Random variables let us talk about events with uncertain outcomes in a concrete way. So what are random variables? How are they defined? And how do they interact? All of this, and more, on this episode of Breaking Math.Interact with the hosts:@SciPodSofia@TechPodGabeOr the guest:@KampPodMilliePatreon here: patreon.com/breakingmathpodcastFeaturing music by Elliot Smith. For info about music used in ads, which are inserted dynamically, contact us at breakingmathpodcast@gmail.com[Featuring: Sofía Baca, Gabriel Hesch; Millicent Oriana]
Dec 9, 2021 • 24min
67: Wrath of Math (Mathematics Used Unwisely)
Mathematics is a subject that has been used for great things over time: it has helped people grow food, design shelter, and in every part of life. It should be, then, no surprise that sometimes mathematics is used for evil; that is to say, there are times where mathematics is used to either implement or justify regressive things like greed, racism, classism, and even genocide. So when has math been used for destructive purposes? What makes us mis-apply mathematics? And why can oversimplification lead to devastation? All of this, and more, on this episode of Breaking Math.Theme song is Breaking Math Theme by Elliot Smith of Albuquerque.This episode is distributed under a Creative Commons Attribution-ShareAlike-NonCommercial 4.0 International License. For more information, go to CreativeCommons.org--- 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 30, 2021 • 30min
P11: Feeling Lucky? (Probability and Intuition)
Join Sofía Baca with her guest Millicent Oriana from the newly launched Nerd Forensics podcast as they discuss some apparent paradoxes in probability and Russian roulette.Intro is "Breaking Math Theme" by Elliot Smith. Ads feature "Ding Dong" by Simon Panrucker[Featuring: Sofía Baca; Millicent Oriana]--- 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 21, 2021 • 1h 12min
66: Hayhoe, Let's Go! (An Interview With Climate Scientist Katharine Hayhoe)
Katharine Hayhoe was the lead author on the 2018 US Climate Assessment report, and has spent her time since then spreading the word about climate change. She was always faced with the difficult task of convincing people who had stakes in things that would be affected by acknowledging the information in her report. In her newest book, “Saving Us: A Climate Scientist’s Case for Hope and Healing in a Divided World”, she discusses the challenges associated with these conversations, at both the micro and macro level. So who is Katherine Heyhoe? How has she learned to get people to acknowledge the reality of climate science? And is she the best, or worst, person to strike up a discussion about how the weather’s been? All of this, and more, on this episode of Breaking Math. Papers Cited: -“99.94 percent of papers agree with the scientific consensus.”More info: https://journals.sagepub.com/doi/10.1177/0270467617707079This episode is distributed under a CC BY-NC 4.0 International License. For more information, visit creativecommons.org.Intro is "Breaking Math Theme" by Elliot Smith. Ads feature "Ding Dong" by Simon Panrucker[Featuring: Sofía Baca, Gabriel Hesch, Meryl Flaherty; Katherine Heyhoe, Elliot Smith]
Nov 14, 2021 • 19min
P10: Chivalry is Dead (Knights and Knaves #1)
One tells a lie, the other the truth! Have fun with Sofía and Meryl as they investigate knight, knave, and spy problems!Intro is "Breaking Math Theme" by Elliot Smith. Music in the ads were Plug Me In by Steve Combs and "Ding Dong" by Simon Panrucker. You can access their work at freemusicarchive.org.[Featuring: Sofia Baca; Meryl Flaherty]
Oct 24, 2021 • 44min
65: An Interview with Author Ian Stewart (Book About Everyday Math)
Welcome to another engaging episode of the Breaking Math Podcast! Today's episode, titled "What is the Use?," features a fascinating conversation with the renowned mathematician and author, Professor Ian Stewart. As Professor Stewart discusses his latest book "What's the Use? How Mathematics Shapes Everyday Life," we dive deep into the real-world applications of mathematics that often go unnoticed in our daily technologies, like smartphones, and their unpredictable implications in various fields.We'll explore the history of quaternions, invented by William Rowan Hamilton, which now play a critical role in computer graphics, gaming, and particle physics. Professor Stewart will also shed light on the non-commutative nature of quaternions, mirroring the complexities of spatial rotations, and how these mathematical principles find their correspondence in the natural world.Furthermore, our discussion will encompass the interconnectivity within mathematics, touching upon how algebra, geometry, and trigonometry converge to paint a broader picture of this unified field. We also discuss the intriguing concept of "Fearful Symmetry" and how symmetrical and asymmetrical patterns govern everything from tiger stripes to sand dunes.With references to his other works, including "Professor Stewart's Cabinet of Mathematical Curiosities" and "The Science of Discworld," Professor Stewart brings an element of surprise and entertainment to the profound impact of mathematics on our understanding of the world.So stay tuned as we unlock the mysteries and the omnipresent nature of math in this thought-provoking episode with Professor Ian Stewart!
Sep 29, 2021 • 47min
64: What Projection Is This? (Map Projections)
The world is a big place with a lot of wonderful things in it. The world also happens to be spherical, which can make getting to those things a challenge if you don't have many landmarks. This is the case when people are navigating by sea. For this reason, map projections, which take a sphere and attempt to flatten it onto a sheet, were born. So what is a map projection? Why are there so many? And why is Gall-Peters the worst? All of this, and more, on this episode of Breaking Math.Theme was written by Elliot Smith.This episode is distributed under a Creative Commons 4.0 Attribution-ShareAlike-NonCommercial International License. For more information, visit CreativeCommons.org.--- 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, 2021 • 49min
RR36: The Most Boring Episode Ever (Rerun: Math Games)
This is a rerun of one of our favorite episodes! We hope that you enjoy it if you haven't listened to it yet. We'll be back next week with new content! Thank you so much for listening to Breaking Math!Math is a gravely serious topic which has been traditionally been done by stodgy people behind closed doors, and it cannot ever be taken lightly. Those who have fun with mathematics mock science, medicine, and the foundation of engineering. That is why on today's podcast, we're going to have absolutely no fun with mathematics. There will not be a single point at which you consider yourself charmed, there will not be a single thing you will want to tell anyone for the sake of enjoyment, and there will be no tolerance for your specific brand of foolishness, and that means you too, Kevin.Theme by Elliot Smith.
Sep 5, 2021 • 34min
63: Broken Voting Systems (Voting Systems and Paradoxes)
Voting systems are, in modern times, essential to the way that large-scale decisions are made. The concept of voicing an opinion to be, hopefully, considered fairly is as ancient and well-established as the human concept of society in general. But, as time goes on, the recent massive influx of voting systems in the last 150 years have shown us that there are as many ways to vote as there are flaws in the way that the vote is tallied. So what problems exist with voting? Are there any intrinsic weaknesses in group decision-making systems? And what can we learn by examining these systems? All of this, and more, on this episode of Breaking Math.Licensed under Creative Commons Attribution-ShareAlike-NonCommercial 4.0 International License. For more information, visit CreativeCommons.org.
Aug 22, 2021 • 45min
62: The Atom Bomb of Information Operations (An Interview with John Fuisz of Veriphix)
Forecasting is a constantly evolving science, and has been applied to complex systems; everything from the weather, to determining what customers might like to buy, and even what governments might rise and fall. John Fuisz is someone who works with this science, and has experience improving the accuracy of forecasting. So how can forecasting be analyzed? What type of events are predictable? And why might Russia think a Missouri senator's race hinges upon North Korea? All of this and more on this episode of Breaking Math.The theme for this episode was written by Elliot Smith.[Featuring: Sofía Baca, Gabriel Hesch; John Fuisz]
