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 sto...

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 li...

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...

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. F...

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 arithmeti...

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...

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 phys...

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 Long...

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 absolut...

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 t...

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 b...

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 historica...

Calculus Reordered: A History of the Big Ideas (Princeton UP, 2019) takes readers on a remarkable journey through hundreds of years to tell the story of how calculus evolved into the subject we know today. David Bressoud explains why calculus is credited to seventeenth-century figures Isaac Newton and Gottfried Leibniz, and how its current structure is based on developments that arose in the ninet...

Popular music history collides with data analytics, charts, and numbers in this insightful and surprising look at the greatest hits and musicians, fads, forgotten artists, and much more. Data analyst and musician Chris Dalla Riva reframes everything you thought you knew about music. Did you know that hit songs in the late 1950s were regularly about gruesome death? That a US vice president wrote a...

Statistics are everywhere: in news reports, at the doctor's office, and in every sort of forecast, from the stock market to the weather. Blogger, teacher, and computer scientist Allen B. Downey knows well that people have an innate ability both to understand statistics and to be fooled by them. As he makes clear in this accessible introduction to statistical thinking, the stakes are big. Simple mi...

Can networks unlock secrets of AI or make sense of a social media mess? A behind-the-scenes look at how networks reveal reality. According to mathematician Anthony Bonato, the hidden world of networks permeates our lives in astounding ways. From Bitcoin transactions to neural connections, Dots and Lines: Hidden Networks in Social Media, AI, and Nature (Johns Hopkins UP, 2025) explains how networks...

A revelatory exploration of how a “theory of everything” depends upon our understanding of the human mind. The whole goal of physics is to explain what we observe. For centuries, physicists believed that observations yielded faithful representations of what is out there. But when they began to study the subatomic realm, they found that observation often interferes with what is being observed—that...

Everything we do today is recorded as data that’s sold to the highest bidder. Plugging our personal data into impersonal algorithms has made government agencies more efficient and tech companies more profitable. But all this comes at a price. It’s easy to feel like an insignificant number in a world of number crunchers who care more about their bottom line than your humanity. It’s time to flip the...

Machine learning systems are making life-altering decisions for us: approving mortgage loans, determining whether a tumor is cancerous, or deciding if someone gets bail. They now influence developments and discoveries in chemistry, biology, and physics—the study of genomes, extrasolar planets, even the intricacies of quantum systems. And all this before large language models such as ChatGPT came o...

A celebration of the seemingly simple idea that allowed us to imagine the world in new dimensions--sparking both controversy and discovery. The stars of this book, vectors and tensors, are unlikely celebrities. If you ever took a physics course, the word "vector" might remind you of the mathematics needed to determine forces on an amusement park ride, a turbine, or a projectile. You might also rem...

Most of us know something about the grand theories of physics that transformed our views of the universe at the start of the twentieth century: quantum mechanics and general relativity. But we are much less familiar with the brilliant theories that make up the backbone of the digital revolution. In Beautiful Math: The Surprisingly Simple Ideas behind the Digital Revolution in How We Live, Work, a...

Back in 2021, John and Elizabeth sat down with Brandeis string theorist Albion Lawrence to discuss cooperation versus solitary study across disciplines. They sink their teeth into the question, “Why do scientists seem to do collaboration and teamwork better than other kinds of scholars and academics?” The conversation ranges from the merits of collective biography to the influence of place and geo...

Models of the Mind: How Physics, Engineering and Mathematics Have Shaped Our Understanding of the Brain (Bloomsbury, 2021) provides a multifaceted and approachable introduction to theoretical neuroscience. It discusses some major topics of the field, including both the milestones from their history and the currently open questions. It's accessible for a general audience, not expecting any previous...

What are numbers, and where do they come from? Based on her groundbreaking study of material devices used for counting in the Ancient Near East, Karenleigh Overmann proposes a novel answer to these timeless questions. Tune in as we talk with Karenleigh Overmann about her book, The Material Origin of Numbers: Insights from the Archaeology of the Ancient Near East (Gorgias Press, 2024). Karenleigh O...

Data has become a defining issue of current times. Our everyday lives are shaped by the data that is produced about us (and by us) through digital technologies. In Critical Data Literacies: Rethinking Data and Everyday Life (MIT Press, 2023), Luci Pangrazio and Neil Selwyn introduce readers to the central concepts, ideas, and arguments required to make sense of life in the data age. Bringing toget...