New Books in Mathematics

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 in 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.
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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).
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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.
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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.
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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.
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