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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

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    Latest Episodes:
    Math, Music, Neuroscience, and Fear - an Interview with Musician Levi McClain Feb 13, 2024
    Show notes

    We are joined today by content creator Levi McClain to discuss the mathematics behind music theory, neuroscience, and human experiences such as fear as they relate to audio processing.

    For a copy of the episode transcript, email us at BreakingMathPodcast@gmail.com.

    For more in depth discussions on these topics and more, check out Levi's channels at:

    Patreon.com/LeviMcClain

    youtube.com/@LeviMcClain

    Tiktok.com/@levimcclain

    Instagram.com/levimcclainmusic

    Help Support The Podcast by clicking on the links below:

    • Start YOUR podcast on ZenCastr! Use my special link ZenCastr Discount to save 30% off your first month of any Zencastr paid plan
    • Visit our Patreon
    Intelligence in Nature v. Machine Learning - an Interview with Brit Cruise(Part 2) Feb 06, 2024
    Show notes

    Help Support The Podcast by clicking on the links below:

    • Start YOUR podcast on ZenCastr! Use my special link ZenCastr Discount to save 30% off your first month of any Zencastr paid plan
    • Visit our Patreon

    Part 2/2 of the interview with Brit Cruise, creator of the YouTube channel "Art of the Problem," about interesting mathematics,, electrical and computer engineering problems.

    In Part 1, we explored what 'intelligence' may be defined as by looking for examples of brains and proto-brains found in nature (including mold, bacteria, fungus, insects, fish, reptiles, and mammals).

    In Part 2, we discuss aritifical neural nets and how they are both similar different from human brains, as well as the ever decreasing gap between the two.

    Brit's YoutTube Channel can be found here: Art of the Problem - Brit Cruise

    Transcript will be made available soon! Stay tuned. You may receive a transcript by emailing us at breakingmathpodcast@gmail.com.

    Intelligence in Nature v. Machine Learning-An Interview with Brit Cruise - Part 1 of 2 Jan 30, 2024
    Show notes

    In this episode (part 1 of 2), I interview Brit Cruise, creator of the YouTube channel 'Art of the Problem.' On his channel, he recently released the video "ChatGPT: 30 Year History | How AI learned to talk." We discuss examples of intelligence in nature and what is required in order for a brain to evolve at the most basic level. We use these concepts to discuss what artificial intelligence - such as Chat GPT - both is and is not.

    Help Support The Podcast by clicking on the links below:

    • Start YOUR podcast on ZenCastr! Use my special link ZenCastr Discount to save 30% off your first month of any Zencastr paid plan
    • Visit our Patreon
    A.I. and Materials Discovery - an Interview with Taylor Sparks Jan 21, 2024
    Show notes

    Transcripts of this episode are avialable upon request. Email us at BreakingMathPodcast@gmail.com.

    In this episode Gabriel Hesch interviews Taylor Sparks, a professor of material science and engineering, about his recent paper on the use of generative modeling a.i. for material disovery. The paper is published in the journal Digital Discovery and is titled 'Generative Adversarial Networks and Diffusion MOdels in Material Discovery. They discuss the purpose of the call, the process of generative modeling, creating a representation for materials, using image-based generative models, and a comparison with Google's approach. They also touch on the concept of conditional generation of materials, the importance of open-source resources and collaboration, and the exciting developments in materials and AI. The conversation concludes with a discussion on future collaboration opportunities.

    Takeaways

    • Generative modeling is an exciting approach in materials science that allows for the prediction and creation of new materials.
    • Creating a representation for materials, such as using the crystallographic information file, enables the application of image-based generative models.
    • Google's approach to generative modeling received attention but also criticism for its lack of novelty and unconditioned generation of materials.
    • Open-source resources and collaboration are crucial in advancing materials informatics and machine learning in the field of materials science.

    Help Support The Podcast by clicking on the links below:

    • Start YOUR podcast on ZenCastr! Use my special link ZenCastr Discount to save 30% off your first month of any Zencastr paid plan
    • Visit our PatreonHow is Machine Learning being used to further original scientific discoveries?
    In Memory of Sofia Baca, Cofounder and cohost of Breaking Math Jan 11, 2024
    Show notes

    In October of 2023, Sofia Baca passed away unexpectedly from natural causes. Sofia was one of the founders and cohosts of the Breaking Math Podcast. In this episode, host Gabriel Hesch interviews Diane Baca, mother of Sofia Baca as we talk about her passions for creativity, mathematics, science, and discovering what it means to be human.
    Sofia lived an exceptional life with explosive creativity, a voracious passion for mathematics, physics, computer science, and creativity. Sofia also struggled immensely with mental health issues which included substance abuse as well as struggling for a very long time understand the source of their discontent. Sofia found great happiness in connecting with other people through teaching, tutoring, and creative expression. The podcast will continue in honor of Sofia. There are many folders of ideas that Sofia left with ideas for the show or for other projects. We will continue this show with sharing some of these ideas, but also with sharing stories of Sofia - including her ideas and her struggles in hopes that others may find solace in that they are not alone in their struggles. But also in hopes that others may find inspiration in what Sofia had to offer.
    We miss you dearly, Sofia.

    Correct. Now Try Again (Multiple Approaches to the Same Problem) Jul 24, 2023
    Show notes

    Join Sofía Baca and her guests, the host and co-host of the Nerd Forensics podcast, Millicent Oriana and Jacob Urban, as they explore what it means to be able to solve one problem in multiple ways.

    This episode is distributed under a Creative Commons Attribution-ShareAlike 4.0 International License. For full text, visit: https://creativecommons.org/licenses/by-sa/4.0/

    [Featuring: Sofía Baca; Millicent Oriana, Jacob Urban[

    Help Support The Podcast by clicking on the links below:

    • Try out ZenCastr w/ 30% DiscountUse my special link to save 30% off your first month of any Zencastr paid plan
    • Patreon
    • YouTube
    • Breaking Math WebsiteEmail us for copies of the transcript!
    Physical Dimension (Dimensional Analysis) Jun 26, 2023
    Show notes

    The history of mathematics, in many ways, begins with counting. Things that needed, initially, to be counted were, and often still are, just that; things. We can say we have twelve tomatoes, or five friends, or that eleven days have passed. As society got more complex, tools that had been used since time immemorial, such as string and scales, became essential tools for counting not only concrete things, like sheep and bison, but more abstract things, such as distance and weight based on agreed-upon multiples of physical artifacts that were copied. This development could not have taken place without the idea of a unit: a standard of measuring something that defines what it means to have one of something. These units can be treated not only as counting numbers, but can be manipulated using fractions, and divided into arbitrarily small divisions. They can even be multiplied and divided together to form new units. So where does the idea of a unit come from? What's the difference between a unit, a dimension, and a physical variable? And how does the idea of physical dimension allow us to simplify complex problems? All of this and more on this episode of Breaking Math.

    Distributed under a CC BY-SA 4.0 International License. For full text, visit: https://creativecommons.org/licenses/by-sa/4.0/

    [Featuring: Sofía Baca; Millicent Oriana, Jacob Urban]

    Help Support The Podcast by clicking on the links below:

    • Try out ZenCastr w/ 30% DiscountUse my special link to save 30% off your first month of any Zencastr paid plan
    • Patreon
    • YouTube
    • Breaking Math WebsiteEmail us for copies of the transcript!
    1 2 3 (Counting) Jun 08, 2023
    Show notes

    Help Support The Podcast by clicking on the links below:

    • Try out ZenCastr w/ 30% DiscountUse my special link to save 30% off your first month of any Zencastr paid plan
    • Patreon
    • YouTube
    • Breaking Math WebsiteEmail us for copies of the transcript!

    Join Sofia Baca and Nerd Forensics co-host Jacob Urban as they discuss all things counting!

    Counting is the first arithmetic concept we learn, and we typically learn to do so during early childhood. Counting is the basis of arithmetic. Before people could manipulate numbers, numbers had to exist. Counting was first done on the body, before it was done on apparatuses outside the body such as clay tablets and hard drives. However, counting has become an invaluable tool in mathematics itself, as became apparent when counting started to be examined analytically. How did counting begin? What is the study of combinatorics? And what can be counted? All of this and more, on this episode of Breaking Math.

    This episode is distributed under a Creative Commons Attribution-ShareAlike 4.0 International License (full text: https://creativecommons.org/licenses/by-sa/4.0/)

    [Featuring: Sofia Baca; Jacob Urban]

    Perpetual Notion (Entropy and Thermodynamics) May 09, 2023
    Show notes

    As you listen to this episode, you'll be exerting mental effort, as well as maybe exerting effort doing other things. The energy allowing your neurons to continually charge and discharge, as well as exert mechanical energy in your muscles and chemical energy in places like your liver and kidneys, came from the food you ate. Specifically, it came from food you chewed, and then digested with acid and with the help of symbiotic bacteria. And even if that food you're eating is meat, you can trace its energy back to the sun and the formation of the earth. Much of this was established in the previous episode, but this time we're going to explore a fundamental property of all systems in which heat can be defined. All of these structures had a certain order to them; the cow that might have made your hamburger had all the same parts that you do: stomach, lips, teeth, and brain. The plants, such as the tomatoes and wheat, were also complex structures, complete with signaling mechanisms. As you chewed that food, you mixed it, and later, as the food digested, it became more and more disordered; that is to say, it became more and more "shuffled", so to speak, and at a certain point, it became so shuffled that you'd need all the original information to reconstruct it: reversing the flow of entropy would mean converting vomit back into the original food; you'd need all the pieces. The electrical energy bonding molecules were thus broken apart and made available to you. And, if you're cleaning your room while listening to this, you are creating order only at the cost of destroying order elsewhere, since you are using energy from the food you ate. Even in industrial agriculture where from 350 megajoules of human and machine energy, often 140 gigajoules of corn can be derived per acre, a ratio of more than 400:1, the order that the seeds seem to produce from nowhere is constructed from the energy of the chaotic explosion from a nearby star. So why are the concepts of heat, energy, and disorder so closely linked? Is there a general law of disorder? And why does the second law mean you can't freeze eggs in a hot pan? All of this and more on this episode of Breaking Math.

    Distributed under a CC BY-SA 4.0 License (https://creativecommons.org/licenses/by-sa/4.0/)

    [Featuring: Sofia Baca; Millicent Oriana, Jacob Urban]

    Help Support The Podcast by clicking on the links below:

    • Try out ZenCastr w/ 30% DiscountUse my special link to save 30% off your first month of any Zencastr paid plan
    • Patreon
    • YouTube
    • Breaking Math WebsiteEmail us for copies of the transcript!
    An Interview with Christopher Roblesz of MathNMore Feb 28, 2023
    Show notes

    Christopher Roblesz is a math educator who, until the pandemic, worked as a teacher. It was his experiences during the pandemic, and his unwavering passion for preparing disadvantaged youth for STEM careers, that eventually led him to developing mathnmore, a company focused on providing an enriched educational experience for sstudents who are preparing for these careers.More on energy and entropy next time!All of this and more on this interview episode of Breaking Math!

    [Featuring: Sofia Baca; Christopher Roblesz]

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