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New Books in Mathematics

New Books in Mathematics

By: Marshall Poe
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 This podcast is a channel on the New Books Network. The New Books Network is an academic audio library dedicated to public education. In each episode you will hear scholars discuss their recently published research with another expert in their field. Discover our 150+ channels and browse our 28,000+ episodes on our website: newbooksnetwork.com Subscribe to our free weekly Substack newsletter to get informative, engaging content straight to your inbox: https://newbooksnetwork.substack.com/ Follow us on Instagram and Bluesky to learn about more our latest interviews: @newbooksnetwork Support our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematicsNew Books Network Nature & Ecology Science
Episodes
  • Antonio Padilla, "Fantastic Numbers and Where to Find Them: A Cosmic Quest from Zero to Infinity" (FSG,2022)

    Antonio Padilla, "Fantastic Numbers and Where to Find Them: A Cosmic Quest from Zero to Infinity" (FSG,2022)
    Feb 15 2026
    A fun, dazzling exploration of the strange numbers that illuminate the ultimate nature of reality. For particularly brilliant theoretical physicists like James Clerk Maxwell, Paul Dirac, or Albert Einstein, the search for mathematical truths led to strange new understandings of the ultimate nature of reality. But what are these truths? What are the mysterious numbers that explain the universe?In Fantastic Numbers and Where to Find Them: A Cosmic Quest from Zero to Infinity (FSG,2022), the leading theoretical physicist and YouTube star Antonio Padilla takes us on an irreverent cosmic tour of nine of the most extraordinary numbers in physics, offering a startling picture of how the universe works. These strange numbers include Graham’s number, which is so large that if you thought about it in the wrong way, your head would collapse into a singularity; TREE(3), whose finite nature can never be definitively proved, because to do so would take so much time that the universe would experience a Poincaré Recurrence—resetting to precisely the state it currently holds, down to the arrangement of individual atoms; and 10^{-120}, measuring the desperately unlikely balance of energy needed to allow the universe to exist for more than just a moment, to extend beyond the size of a single atom—in other words, the mystery of our unexpected universe.Leading us down the rabbit hole to a deeper understanding of reality, Padilla explains how these unusual numbers are the key to understanding such mind-boggling phenomena as black holes, relativity, and the problem of the cosmological constant—that the two best and most rigorously tested ways of understanding the universe contradict one another. Fantastic Numbers and Where to Find Them is a combination of popular and cutting-edge science—and a lively, entertaining, and even funny exploration of the most fundamental truths about the universe. Learn more about your ad choices. Visit megaphone.fm/adchoices Support our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics
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    1 hr and 6 mins
  • Tom Griffiths, "The Laws of Thought: The Quest for a Mathematical Theory of the Mind" (Henry Holt and Co., 2026)

    Tom Griffiths, "The Laws of Thought: The Quest for a Mathematical Theory of the Mind" (Henry Holt and Co., 2026)
    Feb 4 2026
    The Laws of Thought: The Quest for a Mathematical Theory of the Mind (Henry Holt and Co., 2026) is an exploration of the quest to use mathematics to describe the ways we think, from its origins three hundred years ago to the ideas behind modern AI systems and the ways in which they still differ from human mindsEveryone has a basic understanding of how the physical world works. We learn about physics and chemistry in school, letting us explain the world around us in terms of concepts like force, acceleration, and gravity—the Laws of Nature. But we don’t have the same fluency with concepts needed to understand the world inside us—the Laws of Thought. While the story of how mathematics has been used to reveal the mysteries of the universe is familiar, the story of how it has been used to study the mind is not.There is no one better to tell that story than Tom Griffiths, the head of Princeton’s AI Lab and a renowned expert in the field of cognitive science. In this groundbreaking book, he explains the three major approaches to formalizing thought—rules and symbols, neural networks, and probability and statistics—introducing each idea through the stories of the people behind it. As informed conversations about thought, language, and learning become ever more pressing in the age of AI, The Laws of Thought is an essential read for anyone interested in the future of technology. Learn more about your ad choices. Visit megaphone.fm/adchoices Support our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics
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    1 hr and 9 mins
  • Giuseppe Longo and Adam Nocek, "The Organism Is a Theory: Giuseppe Longo on Biology, Mathematics, and AI" (U Minnesota Press, 2026)

    Giuseppe Longo and Adam Nocek, "The Organism Is a Theory: Giuseppe Longo on Biology, Mathematics, and AI" (U Minnesota Press, 2026)
    Jan 20 2026
    A bold reimagining of life that bridges science, philosophy, cybernetics, and the complexities of biological existence The Organism Is a Theory: Giuseppe Longo on Biology, Mathematics, and AI (Giuseppe Longo and Adam Nocek, 2026) is an intriguing synthesis of decades of interdisciplinary research by eminent mathematician and biological scientist Giuseppe Longo. A unique collaboration between Longo and philosopher of technology Adam Nocek, the volume confronts foundational issues in the history of mathematics, computer science, physics, and theoretical biology. Challenging conventional approaches that apply computational and formalist models to the biological world, Longo reveals how the limitations of these models hinder the understanding of organismic complexity, development, and evolution. Through a critique of dominant scientific paradigms, he emphasizes the need for a new biological theory that accounts for the temporal and spatial intricacies of life. Enhanced by Nocek's comprehensive introduction and a fascinating three-part interview with Longo, The Organism Is a Theory offers a bold rethinking of the biosciences, integrating the work of Alan Turing, Bernhard Riemann, Henri Poincaré, Kurt Gödel, and others into Longo's vision of critical biology. Bridging scientific and philosophical discourses, this book creatively applies insights from mathematics, physics, and computing into the study of the organism to present a new theoretical approach to understanding biological complexity that resists reductive mechanistic and informatic explanations. Retail e-book files for this title are screen-reader friendly with image accompanied by short alt text and/or extended description. Learn more about your ad choices. Visit megaphone.fm/adchoices Support our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics
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    1 hr and 14 mins
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