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
Apr 25, 2021 • 30min
61: Look at this Graph! (Graph Theory)
In mathematics, nature is a constant driving inspiration; mathematicians are part of nature, so this is natural. A huge part of nature is the idea of things like networks. These are represented by mathematical objects called 'graphs'. Graphs allow us to describe a huge variety of things, such as: the food chain, lineage, plumbing networks, electrical grids, and even friendships. So where did this concept come from? What tools can we use to analyze graphs? And how can you use graph theory to minimize highway tolls? All of this and more on this episode of Breaking Math.Episode distributed under an Creative Commons Attribution-ShareAlike-NonCommercial 4.0 International License. For more information, visit CreativeCommons.org[Featuring: Sofía Baca, Meryl Flaherty]--- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/appSupport this podcast: https://anchor.fm/breakingmathpodcast/support
Apr 19, 2021 • 31min
P9: Give or Take (Back-of-the-Envelope Estimates / Fermi Problems)
How many piano tuners are there in New York City? How much cheese is there in Delaware? And how can you find out? All of this and more on this problem-episode of Breaking Math.This episode distributed under a Creative Commons Attribution-ShareAlike-Noncommercial 4.0 International License. For more information, visit creativecommons.orgFeaturing theme song and outro by Elliot Smith of Albuquerque.[Featuring: Sofía Baca, Meryl Flaherty]
Apr 3, 2021 • 29min
60: HAMILTON! [But Not the Musical] (Quaternions)
i^2 = j^2 = k^2 = ijk = -1. This deceptively simple formula, discovered by Irish mathematician William Rowan Hamilton in 1843, led to a revolution in the way 19th century mathematicians and scientists thought about vectors and rotation. This formula, which extends the complex numbers, allows us to talk about certain three-dimensional problems with more ease. So what are quaternions? Where are they still used? And what is inscribed on Broom Bridge? All of this and more on this episode of Breaking Math.This episode is distributed under a CC BY-SA 4.0 license. For more information, visit CreativeCommons.org.The theme for this episode was written by Elliot Smith.[Featuring: Sofía Baca, Meryl Flaherty]
Mar 21, 2021 • 42min
59: A Good Source of Fibers (Fiber Bundles)
Mathematics is full of all sorts of objects that can be difficult to comprehend. For example, if we take a slip of paper and glue it to itself, we can get a ring. If we turn it a half turn before gluing it to itself, we get what's called a Möbius strip, which has only one side twice the length of the paper. If we glue the edges of the Möbius strip to each other, and make a tube, you'll run into trouble in three dimensions, because the object that this would make is called a Klein flask, and can only exist in four dimensions. So what is a fiber? What can fiber bundles teach us about higher dimensional objects?All of this, and more, on this episode of Breaking Math.[Featuring: Sofía Baca, Meryl Flaherty]
Mar 3, 2021 • 43min
58: Bringing Curvy Back (Gaussian Curvature)
In introductory geometry classes, many of the objects dealt with can be considered 'elementary' in nature; things like tetrahedrons, spheres, cylinders, planes, triangles, lines, and other such concepts are common in these classes. However, we often have the need to describe more complex objects. These objects can often be quite organic, or even abstract in shape, and include things like spirals, flowery shapes, and other curved surfaces. These are often described better by differential geometry as opposed to the more elementary classical geometry. One helpful metric in describing these objects is how they are curved around a certain point. So how is curvature defined mathematically? What is the difference between negative and positive curvature? And what can Gauss' Theorema Egregium teach us about eating pizza?This episode distributed under a Creative Commons Attribution ShareAlike 4.0 International License. For more information, go to creativecommons.orgVisit our sponsor today at Brilliant.org/BreakingMath for 20% off their annual membership! Learn hands-on with Brilliant.[Featuring: Sofía Baca, Meryl Flaherty]
Feb 25, 2021 • 20min
P8: Tangent Tango (Morikawa's Recently Solved Problem)
Join Sofía and Gabriel as they talk about Morikawa's recently solved problem, first proposed in 1821 and not solved until last year!Also, if you haven't yet, check out our sponsor The Great Courses at thegreatcoursesplus.com/breakingmath for a free month! Learn basically anything there.The paper featured in this episode can be found at https://arxiv.org/abs/2008.00922This episode is distributed under a Creative Commons Attribution-ShareAlike 4.0 International License. For more information, visit CreativeCommons.org![Featuring: Sofía Baca, Gabriel Hesch]
Feb 7, 2021 • 14min
P7: Root for Squares (Irrationality of the Square Root of Two)
Join Sofía and Gabriel as they discuss an old but great proof of the irrationality of the square root of two.[Featuring: Sofía Baca, Gabriel Hesch]Patreon-Become a monthly supporter at patreon.com/breakingmathMerchandiseAd contained music track "Buffering" from Quiet Music for Tiny Robots.Distributed under a Creative Commons Attribution-ShareAlike 4.0 International License. For more information, visit creativecommons.org.
Feb 1, 2021 • 30min
57: You Said How Much?! (Measure Theory)
If you are there, and I am here, we can measure the distance between us. If we are standing in a room, we can calculate the area of where we're standing; and, if we want, the volume. These are all examples of measures; which, essentially, tell us how much 'stuff' we have. So what is a measure? How are distance, area, and volume related? And how big is the Sierpinski triangle? All of this and more on this episode of Breaking Math.Ways to support the show:Patreon-Become a monthly supporter at patreon.com/breakingmathThe theme for this episode was written by Elliot Smith.Episode used in the ad was Buffering by Quiet Music for Tiny Robots.[Featuring: Sofía Baca; Meryl Flaherty]
Jan 28, 2021 • 29min
P6: How Many Angles in a Circle? (Curvature; Euclidean Geometry)
Sofía and Gabriel discuss the question of "how many angles are there in a circle", and visit theorems from Euclid, as well as differential calculus.This episode is distributed under a CC BY-SA 4.0 license. For more information, visit CreativeCommons.org.Ways to support the show:Patreon-Become a monthly supporter at patreon.com/breakingmathThe theme for this episode was written by Elliot Smith.Music in the ad was Tiny Robot Armies by Quiet Music for Tiny Robots.[Featuring: Sofía Baca, Gabriel Hesch]
Jan 24, 2021 • 35min
56: More Sheep than You Can Count (Transfinite Cardinal Numbers)
Look at all you phonies out there.You poseurs.All of you sheep. Counting 'til infinity. Counting sheep.*pff*What if I told you there were more there? Like, ... more than you can count?But what would a sheeple like you know about more than infinity that you can count?heh. *pff*So, like, what does it mean to count til infinity? What does it mean to count more? And, like, where do dimensions fall in all of this?Ways to support the show:Patreon-Become a monthly supporter at patreon.com/breakingmath(Correction: at 12:00, the paradox is actually due to Galileo Galilei)Distributed under a Creative Commons Attribution-ShareAlike 4.0 International License. For more information, visit CreativeCommons.orgMusic used in the The Great Courses ad was Portal by Evan Shaeffer[Featuring: Sofía Baca, Gabriel Hesch]
