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

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 minds
Everyone 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

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

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

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

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

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

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 nineteenth century. Bressoud argues that a pedagogy informed by the historical development of calculus represents a sounder way for students to learn this fascinating area of mathematics.

Delving into calculus’s birth in the Hellenistic Eastern Mediterranean—particularly in Syracuse, Sicily and Alexandria, Egypt—as well as India and the Islamic Middle East, Bressoud considers how calculus developed in response to essential questions emerging from engineering and astronomy. He looks at how Newton and Leibniz built their work on a flurry of activity that occurred throughout Europe, and how Italian philosophers such as Galileo Galilei played a particularly important role. In describing calculus’s evolution, Bressoud reveals problems with the standard ordering of its curriculum: limits, differentiation, integration, and series. He contends that the historical order—integration as accumulation, then differentiation as ratios of change, series as sequences of partial sums, and finally limits as they arise from the algebra of inequalities—makes more sense in the classroom environment.

Exploring the motivations behind calculus’s discovery, Calculus Reordered highlights how this essential tool of mathematics came to be.

David M. Bressoud is DeWitt Wallace Professor of Mathematics at Macalester College and Director of the Conference Board of the Mathematical Sciences. His many books include Second Year Calculus and A Radical Approach to Lebesgue’s Theory of Integration. He lives in St. Paul, Minnesota.

Mark Molloy is the reviews editor at MAKE: A Literary Magazine.

Learn more about your ad choices. Visit megaphone.fm/adchoices

Support our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

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 number one hit? That while TikTok has spawned countless hits, it's made artists more anonymous than ever before? That pop songs have shaped race relations in the United States? That the key change died around 2003? And that's just the beginning.

Coupling hard data with engaging anecdotes, Uncharted Territory: What Numbers Tell Us about the Biggest Hit Songs and Ourselves (Bloomsbury, 2025) is both a takedown and celebration of popular music and provides new ways to think about your favorite songs, genres, and artists from the last 6 decades using unexpected statistics and playful visualizations. This entertaining history is filled with the most popular musicians of all time from The Beatles and The Bee Gees to Michael Jackson, Mariah Carey, and beyond. Whether you danced the twist or the dougie at your senior prom, you're sure to never listen to music again in the same way.

Chris Dalla Riva lives at the intersection of music and data. Playing in bands and recording music since his teenage years, Dalla Riva is currently a Senior Product Manager at Audiomack where he focuses on data analytics and personalization.

Gregory McNiff is a Managing Director in the New York office of the Blueshirt Group, an IR firm focused on technology. Greg holds an MBA from the University of Chicago Booth School of Business, an M. Litt. in Shakespeare Studies from the University of St. Andrews and a B.A. in Classical Languages from Columbia University.

Learn more about your ad choices. Visit megaphone.fm/adchoices

Support our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

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 misunderstandings have led to incorrect medical prognoses, underestimated the likelihood of large earthquakes, hindered social justice efforts, and resulted in dubious policy decisions. There are right and wrong ways to look at numbers, and Downey will help you see which are which.

Probably Overthinking It: How to Use Data to Answer Questions, Avoid Statistical Traps, and Make Better Decisions (University of Chicago Press, 2023) uses real data to delve into real examples with real consequences, drawing on cases from health campaigns, political movements, chess rankings, and more. He lays out common pitfalls--like the base rate fallacy, length-biased sampling, and Simpson's paradox--and shines a light on what we learn when we interpret data correctly, and what goes wrong when we don't. Using data visualizations instead of equations, he builds understanding from the basics to help you recognize errors, whether in your own thinking or in media reports. Even if you have never studied statistics--or if you have and forgot everything you learned--this book will offer new insight into the methods and measurements that help us understand the world.

Allen B. Downey is a curriculum designer at the online learning company Brilliant and professor emeritus of computer science at Olin College.

Gregory McNiff is a Managing Director in the New York office of the Blueshirt Group, an IR firm focused on technology. Greg holds an MBA from the University of Chicago Booth School of Business, an M. Litt. in Shakespeare Studies from the University of St. Andrews and a B.A. in Classical Languages from Columbia University.

Learn more about your ad choices. Visit megaphone.fm/adchoices

Support our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics