Proofs are sometimes seen as an exercise in tedium, other times as a pure form of beauty, and often as both. But from time immemorial, people have been using mathematics to demonstrate new theorems, and advance the state of the art of mathematics. However, it is only relatively recently, within the last 3,000 years, that the art of mathematical proof has been considered essential to the study of mathematics. Mathematicians constantly fight over what constitutes a proof, and even what makes a proof valid, partially because proof requires delicate insight. So what is the art of mathematical proof? How has it changed? And who can do it? ---  Support this podcast: <a href="https://anchor.fm/breakingmathpodcast/support">https://anchor.fm/breakingmathpodcast/support</a>

Proofs are sometimes seen as an exercise in tedium, other times as a pure form of beauty, and often as both. But from time immemorial, people have been using mathematics to demonstrate new theorems, and advance the state of the art of mathematics. However, it is only relatively recently, within the last 3,000 years, that the art of mathematical proof has been considered essential to the study of mathematics. Mathematicians constantly fight over what constitutes a proof, and even what makes a proof valid, partially because proof requires delicate insight. So what is the art of mathematical proof? How has it changed? And who can do it? --- Support this podcast: https://anchor.fm/breakingmathpodcast/support

Proofs are sometimes seen as an exercise in tedium, other times as a pure form of beauty, and often as both. But from time immemorial, people have been using mathematics to demonstrate new theorems, and advance the state of the art of mathematics. However, it is only relatively recently, within the last 3,000 years, that the art of mathematical proof has been considered essential to the study of mathematics. Mathematicians constantly fight over what constitutes a proof, and even what makes a proof valid, partially because proof requires delicate insight. So what is the art of mathematical proof? How has it changed? And who can do it? ---&nbsp; Support this podcast: <a href="https://anchor.fm/breakingmathpodcast/support" rel="noopener noreferrer">https://anchor.fm/breakingmathpodcast/support</a>

7: QED? Prove it. (Proofs)

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:<ul> <li>What’s the math behind machine learning?</li> <li>How do we quantify uncertainty in climate models?</li> <li>Can consciousness be described in AI?</li> <li>Why does beauty matter in an equation?</li></ul>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: <a href="https://breakingmath.io/">https://breakingmath.io</a> Linktree: <a href="https://linktr.ee/breakingmathmedia">https://linktr.ee/breakingmathmedia</a> Email: breakingmathpodcast@gmail.com

Science

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Mathematics

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.io Linktree: https://linktr.ee/breakingmathmedia Email: breakingmathpodcast@gmail.com

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:<ul> <li>What’s the math behind machine learning?</li> <li>How do we quantify uncertainty in climate models?</li> <li>Can consciousness be described in AI?</li> <li>Why does beauty matter in an equation?</li></ul>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: <a href="https://breakingmath.io/" rel="noopener noreferrer">https://breakingmath.io</a> Linktree: <a href="https://linktr.ee/breakingmathmedia" rel="noopener noreferrer">https://linktr.ee/breakingmathmedia</a> Email: breakingmathpodcast@gmail.com

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7: QED? Prove it. (Proofs)

7: QED? Prove it. (Proofs)

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