New Books in Mathematics

Marshall Poe
  • 4.8 (25)
  • NATURAL SCIENCES
  • UPDATED BIMONTHLY

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

  1. 1D AGO

    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

    1h 4m

  2. FEB 15

    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

    1h 6m

  3. FEB 4

    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

    1h 9m

  4. JAN 20

    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

    1h 14m

  5. 12/24/2025

    Jeremiah Joven Joaquin and James Franklin eds., "The Necessities Underlying Reality: Connecting Philosophy of Mathematics, Ethics and Probability" (Bloomsbury, 2025)

    The Necessities Underlying Reality: Connecting Philosophy of Mathematics, Ethics and Probability (Bloomsbury, 2025) is an open access book that covers four decades of work by the leading Australian philosopher, mathematician and historian of ideas, James Franklin.These interlinking essays are connected by a core theme: the necessary structures in reality that allow certain knowledge of absolute truths. Franklin's Aristotelian realist philosophy of mathematics shows how mathematical truths are directly about physical reality, and at the same time certainly and provably true. Ranging from mathematics to evidence evaluation to ethics, his philosophy of probability sees the relation of evidence to hypothesis, such as in science and law, as purely logical, hence necessary.Across ethics and the philosophy of religion, the theme of necessity is repeated: basic ethical truths (such as the worth of persons and the wrongness of murder) are shown to have the same certainty as mathematics. Focus on the history of ideas connects the philosophical work in the present with the medieval scholastic tradition, which defended similar necessities but is now neglected.Here is an up-to-date introduction to Franklin's overall perspective. Recalling Western philosophy to its roots, it reveals the way absolute necessities are discoverable across the abstract fields of mathematics, logical evidence and ethics. Learn more about your ad choices. Visit megaphone.fm/adchoices Support our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

    55 min

  6. 11/25/2025

    Andrew H. Jaffe, "The Random Universe: How Models and Probability Help Us Make Sense of the Cosmos" (Yale UP, 2025)

    An award-winning astrophysicist looks at how the understanding of uncertainty and randomness has led to breakthroughs in our knowledge of the cosmos All of us understand the world around us by constructing models, comparing them to observations, and drawing conclusions. Scientists create, test, and replace these models by applying the twinned concepts of probability and randomness. Exploring how this process has refined our knowledge of quantum mechanics and the birth of the universe, In The Random Universe: How Models and Probability Help Us Make Sense of the Cosmos (Yale UP, 2025) Andrew H. Jaffe offers a unique synthesis of the philosophy of epistemology, the mathematics of probability, and the science of cosmology. As Jaffe puts Enlightenment thinkers like David Hume in conversation with contemporary philosophers such as Karl Popper and Imre Lakatos and engages with scientists ranging from Isaac Newton and Galileo to Albert Einstein and Arthur Eddington, he uses Thomas Bayes's seminal studies of statistics and probability to make sense of conflicting currents of thought. This is a deep look into how we have learned to account for uncertainty in our search for knowledge--and a reminder that science is not about facts and data as such but about creating models that correctly account for those facts and data. Learn more about your ad choices. Visit megaphone.fm/adchoices Support our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

    1h 29m

  7. 11/21/2025

    Thomas Morel, "Underground Mathematics: Craft Culture and Knowledge Production in Early Modern Europe" (Cambridge UP, 2022)

    Thomas Morel joins Jana Byars to tell the story of subterranean geometry, a forgotten discipline that developed in the silver mines of early modern Europe, talking about his book Underground Mathematics: Craft Culture and Knowledge Production in Early Modern Europe (Cambridge UP, 2022). Mining and metallurgy were of great significance to the rulers of early modern Europe, required for the silver bullion that fuelled warfare and numerous other uses. Through seven lively case studies, he illustrates how geometry was used in metallic mines by practitioners using esoteric manuscripts. He describes how an original culture of accuracy and measurement paved the way for technical and scientific innovations, and fruitfully brought together the world of artisans, scholars and courts. Based on a variety of original manuscripts, maps and archive material, Morel recounts how knowledge was crafted and circulated among practitioners in the Holy Roman Empire and beyond. Specific chapters deal with the material culture of surveying, map-making, expertise and the political uses of quantification. By carefully reconstructing the religious, economic and cultural context of mining cities, Underground Mathematics contextualizes the rise of numbered information, practical mathematics and quantification in the early modern period. Learn more about your ad choices. Visit megaphone.fm/adchoices Support our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

    46 min

  8. 11/09/2025

    Al Posamentier, "Math Makers: The Lives and Works of 50 Famous Mathematicians" (Prometheus, 2020)

    Today I talked to Alfred S. Posamentier, a co-author (with Christian Spreitzer) of Math Makers: The Lives and Works of 50 Famous Mathematicians (Prometheus, 2020). This charming book is more than just mathematics, because mathematicians are not just makers of mathematics. They are human beings whose life stories are often not just entertaining, but are sometimes interwoven with important historical events. Of course you get the math in this book –but I would have read this book just for the fascinating anecdotes. Just for openers, how many other disciplines have people who made remarkable contributions but were arrested for revolutionary activities in their teens, and then killed in a duel at age 21? This is the story of Evariste Galois, just one of the 50 fascinating lives you'll read about in this book. Learn more about your ad choices. Visit megaphone.fm/adchoices Support our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

    57 min
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Ratings & Reviews

4.8
out of 5
25 Ratings

About

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

Information

  • Creator
    Marshall Poe
  • Years Active
    2013 - 2026
  • Episodes
    170
  • Rating
    Clean
  • Copyright
    © New Books Network
  • Show Website
    New Books in Mathematics

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