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New Books in Mathematics: Daily Summaries Delivered
by Marshall Poe
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/mathematics
Latest Episodes
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- 2 weeks ago1h 7m
Richard Elwes, "Huge Numbers: A Story of Counting Ambitiously, from 4 1/2 to Fish 7" (Basic Books, 2026)
What if, every time you wanted to write down 1,000,000, you had to draw a picture of a god? And what if that number were the biggest you had a symbol for? If you were doing math in ancient Egypt, those were the rules: anything bigger broke math.As mathematician Richard Elwes shows i n Huge Numbers: A Story of Counting Ambitiously, from 4 1/2 to Fish 7 (Basic Books, 2026) this is the strange story of math. Even today, writing down some numbers is beyond us: try it with all the zeroes in a googolplex, or an outrageous alien number like TREE(3). Safer not to try: even harnessing every particle in the universe, you wouldn’t come close. But this book is no mere bestiary of numerical monsters. It shows how, by hunting down and studying ever-bigger numbers, arithmetic has reshaped human thought and made our modern era of science and computation possible.Where many math books celebrate abstract algebra or ineffable infinities, Huge Numbers is both more practical and far weirder. It reveals a world where most numbers remain out of reach until we discover how to chase them down and tame them, and so remake our world again. Learn more about your ad choices. Visit megaphone.fm/adchoices Support our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics
- 2 weeks ago1h 12m
Drew M. Dalton, "The Matter of Evil: From Speculative Realism to Ethical Pessimism" (Northwestern UP, 2024)
Most of us today would assume that morality and ethics, being value propositions, are questions for inspired leaders, religious creeds, poets—in other words, for the humanities. But what if I told you that we can construct a system of ethics and morality by studying math—more specifically: the laws of thermodynamics? That’s what Professor Drew M Dalton argues in his latest book. Dalton traces a line of metaphysical inquiry from Kant through Spinoza, Nietzsche, and others up to today to show how we get from E=mc2 to a full-throated call to resist evil and alleviate suffering to our very last breath. By overturning our assumptions about the nature and value of reality, The Matter of Evil: From Speculative Realism to Ethical Pessimism (Northwestern UP, 2024) presents a provocative new model of ethical responsibility that is both logically justifiable and scientifically sound. Dalton argues for “ethical pessimism,” a position previously marginalized in the West, as a means to cultivate an account of ethical responsibility and political activism that takes seriously the unbecoming of being and the moral horror of existence. Drew M. Dalton is a professor of English at Indiana University, having received his Ph.D. in Philosophy from the University of Leuven in Belgium. His research focuses on the normative implications of different metaphysical systems and, specifically, he’s interested in how questions of right and wrong, good and evil, beauty and pleasure are framed within aesthetics, literary theory, ethics, and political philosophy. He is the author of Longing for the Other: Levinas and Metaphysical Desire (Duquesne University Press, 2009), The Ethics of Resistance: Tyranny of the Absolute (Bloomsbury, 2018), and The Matter of Evil: From Speculative Realism to Ethical Pessimism (Northwestern University Press, 2023). Learn more about your ad choices. Visit megaphone.fm/adchoices Support our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics
- 3 weeks ago32 min
Counter-Revolutionary Puzzles with Guillermo Badia
In this episode Pat speaks with Dr Guillermo Badia. Dr Guillermo Badia is a philosopher working in logic. His research interests are logic in computer science, semiring-based logics and models of computation, and modal, intuitionistic and other non-classical logics. They discuss logic, murder mysteries, and the counter revolutionary search for truth. A transcript of this episode will be available on the Concept : Art website here. Concept : Art is produced on muwinina Country, lutruwita Tasmania. Always was, always will be Aboriginal land. Learn more about your ad choices. Visit megaphone.fm/adchoices Support our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics
- May 5, 20261h 35m
Antony Valentini, "Beyond the Quantum: A Quest for the Origin and Hidden Meaning of Quantum Mechanics" (Oxford UP, 2026)
Based on decades of research, Beyond the Quantum: A Quest for the Origin and Hidden Meaning of Quantum Mechanics (Oxford UP, 2026) offers a panoramic rethink of quantum physics, with potentially revolutionary implications for cosmology, quantum gravity, and quantum technology. Properly understood, 'pilot-wave theory' provides a deeper foundation for quantum mechanics, while also going beyond it. First proposed in the 1920s by French aristocrat and physicist Louis de Broglie, and revived in the 1950s by American physicist David Bohm, the theory posits hidden particle motions we cannot currently see or control. The theory is usually regarded as merely an alternative account of the same physics we already know. In fact, pilot-wave theory implies a wealth of new and radical physics beyond the reach of quantum mechanics. Pilot-wave theory tells us that quantum physics is a special case of something broader and deeper. In more general 'nonequilibrium' conditions, Einstein's relativity and Heisenberg's uncertainty break down. Superluminal signalling becomes possible, and quantum particles can be clearly seen and controlled. This new physics could have left traces in the early universe, and it might be visible today in radiation from exploding primordial black holes. Harnessing this new physics would have transformative technological implications, in particular for communication, cryptography, and computing. Drawing intriguing parallels between the present era of quantum physics and past episodes of scientific confusion, this book tells the story of how pilot-wave theory was discovered and abandoned, revived and reconstructed, and how today it can pave the way to a new and radical physics beyond the quantum. Learn more about your ad choices. Visit megaphone.fm/adchoices Support our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics
- Apr 28, 20261h 4m
Raffaele Danna, "The Craft of Indo-Arabic Numerals: How Practical Arithmetic Shaped Commerce and Mathematics in Western Europe, 1200–1600" (Harvard UP, 2026)
In the thirteenth-century Mediterranean, commerce transformed as merchants shifted from Roman to Indo-Arabic numerals—an alternative that better facilitated complex calculations. It has long been known that this transition stemmed from Europe’s increasing exchanges with India, Persia, and the Arabic world. Yet much remains to be understood about how Indo-Arabic numerals—and the practical arithmetic they enabled—actually spread across Europe. As Dr. Raffaele Danna shows in The Craft of Indo-Arabic Numerals: How Practical Arithmetic Shaped Commerce and Mathematics in Western Europe, 1200–1600 (Harvard University Press, 2026), it was hundreds of ordinary merchants, schoolmasters, and artisans who nurtured these changes, thereby driving key advances in both commerce and mathematics. Drawing on an original catalog of more than 1,200 practical arithmetic manuals, Dr. Danna charts the incremental spread of the new figures with unprecedented precision. While Italian merchants were the early adopters, it took nearly three centuries for Indo-Arabic numerals to become established in northern Europe. As Dr. Danna shows, adoption did not follow the routes of maritime trade. Rather, Indo-Arabic numerals moved gradually across the continent through inland networks of practitioners. Everywhere they went, the ten figures enhanced commercial practices and facilitated the emergence of a coherent language of mathematical craft. The growing social circulation of this knowledge, in turn, had a lasting impact on the economic trajectory of Western Europe. By the late sixteenth century, even academics were absorbing lessons from the vernacular tradition—a development that led to the first major breakthroughs in European mathematical theory since antiquity. Combining economic history with the social history of mathematics, The Craft of Indo-Arabic Numerals illuminates the integral role of practical arithmetic in both intellectual and commercial transformations across Western Europe. This interview was conducted by Dr. Miranda Melcher whose book focuses on post-conflict military integration, understanding treaty negotiation and implementation in civil war contexts, with qualitative analysis of the Angolan and Mozambican civil wars. You can find Miranda’s interviews on New Books with Miranda Melcher, wherever you get your podcasts. Learn more about your ad choices. Visit megaphone.fm/adchoices Support our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics
- Feb 15, 20261h 6m
Antonio Padilla, "Fantastic Numbers and Where to Find Them: A Cosmic Quest from Zero to Infinity" (FSG,2022)
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
- Feb 4, 20261h 8m
Tom Griffiths, "The Laws of Thought: The Quest for a Mathematical Theory of the Mind" (Henry Holt and Co., 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
- Jan 20, 20261h 13m
Giuseppe Longo and Adam Nocek, "The Organism Is a Theory: Giuseppe Longo on Biology, Mathematics, and AI" (U Minnesota Press, 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
About New Books in Mathematics
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/mathematics
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