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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

    • Apple Podcasts
    • Google Play
    • Spotify

    Latest Episodes:
    Give or Take (Back-of-the-Envelope Estimates / Fermi Problems) Apr 19, 2021
    Show notes

    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.org

    Featuring theme song and outro by Elliot Smith of Albuquerque.

    [Featuring: Sofía Baca, Meryl Flaherty]


    HAMILTON! [But Not the Musical] (Quaternions) Apr 03, 2021
    Show notes

    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]


    A Good Source of Fibers (Fiber Bundles) Mar 21, 2021
    Show notes

    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]


    Bringing Curvy Back (Gaussian Curvature) Mar 03, 2021
    Show notes

    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.org

    Visit our sponsor today at Brilliant.org/BreakingMath for 20% off their annual membership! Learn hands-on with Brilliant.

    [Featuring: Sofía Baca, Meryl Flaherty]


    Tangent Tango (Morikawa's Recently Solved Problem) Feb 25, 2021
    Show notes

    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/2008.00922

    This episode is distributed under a Creative Commons Attribution-ShareAlike 4.0 International License. For more information, visit CreativeCommons.org!

    [Featuring: Sofía Baca, Gabriel Hesch]


    Root for Squares (Irrationality of the Square Root of Two) Feb 07, 2021
    Show notes

    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/breakingmath

    Merchandise

    Ad 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.


    You Said How Much?! (Measure Theory) Feb 01, 2021
    Show notes

    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/breakingmath

    The 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]


    How Many Angles in a Circle? (Curvature; Euclidean Geometry) Jan 28, 2021
    Show notes

    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/breakingmath

    The 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]


    More Sheep than You Can Count (Transfinite Cardinal Numbers) Jan 24, 2021
    Show notes

    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.org

    Music used in the The Great Courses ad was Portal by Evan Shaeffer

    [Featuring: Sofía Baca, Gabriel Hesch]


    55: Order in the Court (Transfinite Ordinal Numbers) Jan 14, 2021
    Show notes

    As a child, did you ever have a conversation that went as follows:

    "When I grow up, I want to have a million cats"

    "Well I'm gonna have a billion billion cats"

    "Oh yeah? I'm gonna have infinity cats"

    "Then I'm gonna have infinity plus one cats"

    "That's nothing. I'm gonna have infinity infinity cats"

    "I'm gonna have infinity infinity infinity infinity *gasp* infinity so many infinities that there are infinity infinities plus one cats"

    What if I told you that you were dabbling in the transfinite ordinal numbers? So what are ordinal numbers? What does "transfinite" mean? And what does it mean to have a number one larger than another infinite number?


    [Featuring: Sofía Baca; Diane Baca]

    Ways to support the show:

    Patreon

    Become a monthly supporter at patreon.com/breakingmath

    This episode is released under a Creative Commons attribution sharealike 4.0 international license. For more information, go to CreativeCommoms.org

    This episode features the song "Buffering" by "Quiet Music for Tiny Robots"



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