Explorez tous les épisodes du podcast New Books in Mathematics

In my conversation with Professor Pablo F. Gómez about his new book, Bloody Numbers: The Early Atlantic Slave Trade and the Invention of Modern Corporeality, published by the University of Chicago Press in 2026.

Our conversation explored the unsettling relationship between slavery, the body, measurement, and knowledge. What does it mean to measure a human body within a system that has already reduced that person to a commodity? And what happens when numbers that appear neutral become entangled with violence, commerce and exploitation?

What stayed with me is the book’s invitation to think differently about numbers. Behind measurements of height, weight, health, disease and mortality were human beings whose lives could not be contained by the data recorded about them.

These questions are not only historical. We live in an increasingly quantified world, where bodies, health, productivity and risk are constantly measured and transformed into data.

So perhaps one question we should keep asking is: Who is doing the counting, why are they counting, and what happens to the people being counted?

I invite you to listen to our conversation and reflect with us on the histories behind the numbers we encounter today.

Amisah Bakuri (PhD) is an Assistant Professor in the Faculty of Social Sciences and Humanities at Vrije Universiteit Amsterdam. Her work explores the intersections of religion, sexuality, gender, and migration, especially within African diasporic communities in the Netherlands. 

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

Since the advent of computers, society has fantasized about conversing with machines. In Divination Engines: Natural Language Processing, Artificial Intelligence, and the Making of Algorithmic Culture (University of Chicago Press, 2026), Dr. Xiaochang Li shows readers how that dream both fueled the demand for data and set the stage for today’s generative AI. 

With original research and clear explanations, Dr. Li elucidates the origins of what’s known as natural language processing (NLP) and the heated twentieth-century debates between computer scientists, linguists, and communication engineers that shaped today’s technology. Starting with early devices that recorded, analyzed, and attempted to interpret human speech, she demonstrates how computer speech recognition, particularly efforts led by Bell Labs and IBM, advanced technology by deemphasizing linguistic meaning in favor of statistical prediction. In other words, researchers gradually abandoned systems that sought to understand human language, opting instead for work-arounds that simply predicted patterns in speech and text data. That solution became incredibly and surprisingly adaptable. As Dr. Li reveals, transforming linguistic questions into engineering ones ushered in the routine operation of search engines, spam filters, and the varied content sorting and recommendation mechanisms that regulate the access, circulation, and legitimacy of information across every platform. But this has all come at the cost of forever requiring copious and ever-growing amounts of new data.

At its core, Divination Engines illuminates how the artifacts of human communication—speech, text, and images—have become both the fodder for and products of computers. This connection between communication and computation, Li shows, has given rise to data-driven analytics, machine learning, and today’s algorithmic culture.

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. 

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

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.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

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).

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

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.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

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.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

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.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

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.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

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.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

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.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

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.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

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.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

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.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

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.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

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.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

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.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

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.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

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 shape everything from political landscapes to climate patterns and how deceptively simple dots and lines can unveil the wonders of technology, society, and even nature.

From a fresh and startling look at the true impact of clever keywords in politicians' social media posts to a fun breakdown of survival strategies in reality TV shows, Bonato shows us how network theory operates everywhere. Each chapter focuses on a unique aspect of networks to reveal how they provide a captivating lens for bringing diverse phenomena into clearer focus.

The book offers an accessible snapshot of networks for anyone curious about what makes the modern world tick. Bonato's insights will give readers a deeper appreciation and understanding of networks and their relevance to our everyday lives.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

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 the act of seeing changes what we see. The same is true of cosmology: our view of the universe is inevitably distorted by observation bias. And so whether they’re studying subatomic particles or galaxies, physicists must first explain consciousness—and for that they must turn to neuroscientists and philosophers of mind.
Neuroscientists have painstakingly built up an understanding of the structure of the brain. Could this help physicists understand the levels of self-organization they observe in other systems? These same physicists, meanwhile, are trying to explain how particles organize themselves into the objects around us. Could their discoveries help explain how neurons produce our conscious experience?
Exploring these questions and more in Putting Ourselves Back in the Equation: Why Physicists Are Studying Human Consciousness and AI to Unravel the Mysteries of the Universe (Picador, 2024), George Musser tackles the extraordinary interconnections between quantum mechanics, cosmology, human consciousness, and artificial intelligence. Combining vivid descriptive writing with portraits of scientists working on the cutting edge, Putting Ourselves Back in the Equation shows how theories of everything depend on theories of mind—and how they might be one and the same.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

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 equation, turning math into an empowering tool for the rest of us.

In Robin Hood Math: Take Control of the Algorithms That Run Your Life (Penguin, 2025), award-winning mathematician Noah Giansiracusa explains how the tech giants and financial institutions use formulas to get ahead—and how anyone can use these same formulas in their everyday life. You’ll learn how to handle risk rationally, make better investments, take control of your social media, and reclaim agency over the decisions you make each day.

In a society that all too often takes from the poor and gives to the rich, math can be a vital democratizing force. Robin Hood Math helps you to think for yourself, act in your own best interests, and thrive.

Noah Giansiracusa is an Associate Professor of Mathematics at Bentley University, Visiting Scholar at Harvard University, and the author of How Algorithms Create and Prevent Fake News. His writing has appeared in Scientific American, TIME, WIRED, Slate, and the Washington Post, among others, and he has been featured as a guest on CNN, BBC Radio 4, and Newsmax. Giansiracusa lives in Acton, Massachusetts, with his wife, two kids, two dogs, and 12 chickens.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

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 on the scene.
We are living through a revolution in machine learning-powered AI that shows no signs of slowing down. This technology is based on relatively simple mathematical ideas, some of which go back centuries, including linear algebra and calculus, the stuff of seventeenth- and eighteenth-century mathematics. It took the birth and advancement of computer science and the kindling of 1990s computer chips designed for video games to ignite the explosion of AI that we see today. In this enlightening book, Anil Ananthaswamy explains the fundamental math behind machine learning, while suggesting intriguing links between artificial and natural intelligence. Might the same math underpin them both?
As Ananthaswamy resonantly concludes, to make safe and effective use of artificial intelligence, we need to understand its profound capabilities and limitations, the clues to which lie in the math that makes machine learning possible.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

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 remember that a vector is a quantity that has magnitude and (this is the key) direction. In fact, vectors are examples of tensors, which can represent even more data. It sounds simple enough--and yet, as award-winning science writer Robyn Arianrhod shows in this riveting story, the idea of a single symbol expressing more than one thing at once was millennia in the making. And without that idea, we wouldn't have such a deep understanding of our world.

Vector and tensor calculus offers an elegant language for expressing the way things behave in space and time, and Arianrhod shows how this enabled physicists and mathematicians to think in a brand-new way. These include James Clerk Maxwell when he ushered in the wireless electromagnetic age; Einstein when he predicted the curving of space-time and the existence of gravitational waves; Paul Dirac, when he created quantum field theory; and Emmy Noether, when she connected mathematical symmetry and the conservation of energy. For it turned out that it's not just physical quantities and dimensions that vectors and tensors can represent, but other dimensions and other kinds of information, too. This is why physicists and mathematicians can speak of four-dimensional space-time and other higher-dimensional "spaces," and why you're likely relying on vectors or tensors whenever you use digital applications such as search engines, GPS, or your mobile phone.

In exploring the evolution of vectors and tensors--and introducing the fascinating people who gave them to us--Arianrhod takes readers on an extraordinary, five-thousand-year journey through the human imagination. She shows the genius required to reimagine the world--and how a clever mathematical construct can dramatically change discovery's direction.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

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, and Communicate (MIT Press, 2024) Chris Bernhardt explores the mathematics at the very heart of the information age. He asks questions such as: What is information? What advantages does digital information have over analog? How do we convert analog signals into digital ones? What is an algorithm? What is a universal computer? And how can a machine learn?
The four major themes of Beautiful Math are information, communication, computation, and learning. Bernhardt typically starts with a simple mathematical model of an important concept, then reveals a deep underlying structure connecting concepts from what, at first, appear to be unrelated areas. His goal is to present the concepts using the least amount of mathematics, but nothing is oversimplified. Along the way, Bernhardt also discusses alphabets, the telegraph, and the analog revolution; information theory; redundancy and compression; errors and noise; encryption; how analog information is converted into digital information; algorithms; and, finally, neural networks. Historical anecdotes are included to give a sense of the technology at that time, its impact, and the problems that needed to be solved.

Taking its readers by the hand, regardless of their math background, Beautiful Math is a fascinating journey through the mathematical ideas that undergird our everyday digital interactions.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

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 geographic location in scientific collaboration to mountaineering traditions in the sciences. As a Recallable Book, Elizabeth champions The People of Puerto Rico, an experiment in ethnography of a nation (in this case under colonial rule) from 1956, including a chapter by Robert Manners, founding chair of the Brandeis Department of Anthropology. Albion sings the praises of a collective biography of the Art Ensemble of Chicago, A Message to Our Folks. But John stays true to his Victorianist roots by praising the contrasting images of the withered humanist Casaubon and the dashing young scientist Lydgate in George Eliot’s own take on collective biography, Middlemarch.

Discussed in this episode:

• Richard Rhodes Making of the Atomic Bomb
• Ann Finkbeiner, The Jasons: The Secret History of Science’s Postwar Elite
• James Gleick, The Information
• Jon Gertner, The Idea Factory: Bell Labs and the Great Age of American Innovation
• Black Hole photographs win giant prize
• Adam Jaffe, “Geographic Localization of Knowledge Spillovers as Evidenced by Patent Citations“
• Jamie Cohen-Cole, The Open Mind
• Julian Steward et al., The People of Puerto Rico
• Paul Steinbeck, Message to Our Folks
• Jenny Uglow, Lunar Men
• George Eliot, Middlemarch

Listen to and Read the episode here.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

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 knowledge of neuroscience or maths. At the same time, neuroscientists have described it as impressive. According to Gaute Einevoll, professor of brain physics, "this is a book that belongs on the bookshelf of any computational neuroscientist and lots of other people".

In our conversation, we covered some of the overarching themes of the book. The constant push and pull between mathematics and biology: mathematical models simplifying complex phenomena and biology pointing out the importance of a specific detail. What efficiency means for a biological system, like the brain. Whether and how much we can assume that an evolved system is efficient.

Dr. Grace Lindsay also talked about how science communication has helped her explore and discuss topics not directly related to her research. She started blogging and podcasting during her PhD, which has led to further writing opportunities, including this popular science book.

Similar to Models of the Mind, the Lindsay Lab is multidisciplinary: It uses artificial neural networks for psychology, neuroscience, and climate change. In the interview, Dr. Grace Lindsay talked about her decision about the lab's profile She explains the overlap in technologies used for studying visual systems and satellite images. We also hear about examples of how scientists in various fields have taken on research topics related to climate change.

Links: 

• Dr. Grace Lindsay's homepage
• Lindsay Lab
• Dr. Grace Lindsay's blog post about Models of the Mind

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

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 Overmann earned a doctorate in archaeology from the University of Oxford, and is research fellow at the University of Bergen, Norway.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

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 together cutting-edge thinking and discussion from across education, sociology, psychology, and media and communication studies, Critical Data Literacies develops a powerful argument for collectively rethinking the role that data plays in our everyday lives and re-establishing agency, free will, and the democratic public sphere.

In the episode, Luci Pangazio discusses how the tradition of critical literacies can offer a powerful foundation to address the big concerns of the data age, such as issues of data justice and privacy, algorithmic bias, dataveillance, and disinformation. We challenge the idea that datafication is an inevitable and inescapable condition.

This interview was conducted by Shreya Urvashi, a doctoral researcher of sociology and education based in Toronto, Canada.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

Across the humanities and social sciences, scholars increasingly use quantitative methods to study textual data. Considered together, this research represents an extraordinary event in the long history of textuality. More or less all at once, the corpus has emerged as a major genre of cultural and scientific knowledge. In Literary Mathematics: Quantitative Theory for Textual Studies (Stanford UP, 2022), Michael Gavin grapples with this development, describing how quantitative methods for the study of textual data offer powerful tools for historical inquiry and sometimes unexpected perspectives on theoretical issues of concern to literary studies.

Student-friendly and accessible, the book advances this argument through case studies drawn from the Early English Books Online corpus. Gavin shows how a copublication network of printers and authors reveals an uncannily accurate picture of historical periodization; that a vector-space semantic model parses historical concepts in incredibly fine detail; and that a geospatial analysis of early modern discourse offers a surprising panoramic glimpse into the period's notion of world geography. Across these case studies, Gavin challenges readers to consider why corpus-based methods work so effectively and asks whether the successes of formal modeling ought to inspire humanists to reconsider fundamental theoretical assumptions about textuality and meaning. As Gavin reveals, by embracing the expressive power of mathematics, scholars can add new dimensions to digital humanities research and find new connections with the social sciences.

Michael Gavin is Associate Professor of English at the University of South Carolina and author of The Invention of English Criticism, 1650-1760 (2015)

Morteza Hajizadeh is a Ph.D. graduate in English from the University of Auckland in New Zealand. His research interests are Cultural Studies; Critical Theory; Environmental History; Medieval (Intellectual) History; Gothic Studies; 18th and 19th Century British Literature. YouTube channel. Twitter.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

Today I talked to Al Posamentier about his books (co-authored with Christian Speitzer) The Mathematics of Everyday Life (Prometheus Books, 2018).  We all are told – practically from the moment we enter school – that mathematics is important because it permeates practically all aspects of our lives.  But, for the most part, we don’t really notice it except for those moments, such as when we balance a checkbook, that we know we’re doing mathematics.  This book, which requires nothing more than high-school math, is a wonderful way to see that mathematics really is all around us, in our home, in our workplace, in the entertainments we enjoy, and in the world we live in.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

Our universe might appear chaotic, but deep down it's simply a myriad of rules working independently to create patterns of action, force, and consequence. In Ten Patterns That Explain the Universe (MIT Press, 2021), Brian Clegg explores the phenomena that make up the very fabric of our world by examining ten essential sequenced systems. From diagrams that show the deep relationships between space and time to the quantum behaviors that rule the way that matter and light interact, Clegg shows how these patterns provide a unique view of the physical world and its fundamental workings.

Guiding readers on a tour of our world and the universe beyond, Clegg describes the cosmic microwave background, sometimes called the "echo of the big bang," and how it offers clues to the universe's beginnings; the diagrams that illustrate Einstein's revelation of the intertwined nature of space and time; the particle trail patterns revealed by the Large Hadron Collider and other accelerators; and the simple-looking patterns that predict quantum behavior (and decorated Richard Feynman's van). Clegg explains how the periodic table reflects the underlying pattern of the configuration of atoms, discusses the power of the number line, demonstrates the explanatory uses of tree diagrams, and more.

Galina Limorenko is a doctoral candidate in Neuroscience with a focus on biochemistry and molecular biology of neurodegenerative diseases at EPFL in Switzerland. To discuss and propose the book for an interview you can reach her at galina.limorenko@epfl.ch.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

There is no shortage of books on the growing impact of data collection and analysis on our societies, our cultures, and our everyday lives. David Hand's new book Dark Data: Why What You Don't Know Matters (Princeton University Press, 2020) is unique in this genre for its focus on those data that aren't collected or don't get analyzed. More than an introduction to missingness and how to account for it, this book proposes that the whole of data analysis can benefit from a "dark data" perspective—that is, careful consideration of not only what is seen but what is unseen. David assembles wide-ranging examples, from the histories of science and finance to his own research and consultancy, to show how this perspective can shed new light on concepts as classical as random sampling and survey design and as cutting-edge as machine learning and the measurement of honesty. I expect the book to inspire the same enjoyment and reflection in general readers as it is sure to in statisticians and other data analysts.

Suggested companion work: Caroline Criado Perez, Invisible Women: Data Bias in a World Designed for Men.

Cory Brunson (he/him) is a Research Assistant Professor at the Laboratory for Systems Medicine at the University of Florida.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

A probing examination of the dynamic history of predictive methods and values in science and engineering that helps us better understand today's cultures of prediction.

The ability to make reliable predictions based on robust and replicable methods is a defining feature of the scientific endeavor, allowing engineers to determine whether a building will stand up or where a cannonball will strike. Cultures of Prediction: How Engineering and Science Evolve with Mathematical Tools (MIT Press, 2024), which bridges history and philosophy, uncovers the dynamic history of prediction in science and engineering over four centuries. Ann Johnson and Johannes Lenhard identify four different cultures, or modes, of prediction in the history of science and engineering: rational, empirical, iterative-numerical, and exploratory-iterative. They show how all four develop together and interact with one another while emphasizing that mathematization is not a single unitary process but one that has taken many forms.

The story is not one of the triumph of abstract mathematics or technology but of how different modes of prediction, complementary concepts of mathematization, and technology coevolved, building what the authors call “cultures of prediction.” The first part of the book examines prediction from early modernity up to the computer age. The second part probes computer-related cultures of prediction, which focus on making things and testing their performance, often in computer simulations. This new orientation challenges basic tenets of the philosophy of science, in which scientific theories and models are predominantly seen as explanatory rather than predictive. It also influences the types of research projects that scientists and engineers undertake, as well as which ones receive support from funding agencies.

Nikki Stevens, PhD is a critical technology researcher and software engineer. Find more of their work here.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

How does a delivery driver distribute hundreds of packages in a single working day? Why does remote Alaska have such a large airport? Where should we look for elusive serial killers? The answers lie in the crucial connection between maps and maths.

In Mapmatics: How We Navigate the World Through Numbers (Pan Macmillan, 2024), Dr Paulina Rowinska embarks on a fascinating journey to discover the mathematical foundations of cartography and cartographical influences on mathematics.

From a sixteenth-century map that remains an indispensable navigation tool despite emphasising the North–South divide to public transport maps that both guide and mislead passengers, she reveals how maps and maths shape not only our sense of space and time but also our worldview.

Through entertaining stories, surprising real-world examples and a cast of unforgettable characters, Mapmatics helps us to appreciate the mathematical methods and ideas behind maps. And, by illuminating how our world works, leaves us better equipped to understand and look after it.

This interview was conducted by Dr. Miranda Melcher whose new 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.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

David S. Richeson's book Tales of Impossibility: The 2000-Year Quest to Solve the Mathematical Problems of Antiquity (Princeton University Press, 2019) is the fascinating story of the 2000 year quest to solve four of the most perplexing problems of antiquity: squaring the circle, duplicating the cube, trisecting the angle, and constructing regular polygons. The eventual conclusion was that all four of these problems could not be solved under the conditions laid out millennia ago. But it's also an engaging tale of some of the greatest mathematicians, and some not-so-well known ones, who met the challenge and moved mathematics forward in ways that the Greek geometers could never have envisioned. Even if you never read a single proof through to its conclusion, you'll enjoy the many entertaining side trips into a geometry far beyond what you learned in high school.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

Graduate students in many programs besides mathematics will need to be familiar with the methods and results of a variety of mathematical topics. Just as importantly, these students will need to develop a level of mathematical maturity—how to think in broad strokes about the subject, how to study it, and even how to communicate their work. The gap between undergraduate training and graduate requirements can also give rise to misconceptions about how mathematics is done and what needs drive cutting-edge research.

Thomas A. Garrity's book All the Math You Missed (But Need to Know for Graduate School), now in its second edition (Cambridge UP, 2021), is a wide bridge across this gap—i do believe the material will bring any rising graduate student to readiness in the subject, whatever their needs. But it provides much more: Readers gain an intuition about the results and how they cohere that may be years coming through coursework alone; and an exposure to the culture of the mathematics community through historical vignettes, folklore, and prevailing beliefs (e.g. on the Riemann Hypothesis and whether P = NP). For such a broad introduction, the book is also surprisingly self-contained, and the chapters chart a uniformly continuous path through its topics.

In our interview, Dr. Garrity recounted the origins of the book, described his outlook on undergraduate and graduate mathematics, and elaborated on the style(s) he adopted across its topics. We also got into the choices of content and depth he made and what role both editions have played over 23 years. The discussion resonated with several of my own experiences, and in any event i plan to keep my copy of the book handy for any (undergraduate or graduate) students i teach or mentor in future.

Suggested companion works:

• Saunders MacLane, Mathematics Form and Function

• Timothy Gowers, June Barrow-Green, and Imre Leader (ed.), The Princeton Companion to Mathematics

Thomas A. Garrity is the Webster Atwell Class of 1921 Professor of Mathematics at Williams College, Massachusetts, where he was the director of the Williams College Project for Effective Teaching for many years. Among his awards are Rice University's Nicolas Salgo Outstanding Teaching award and the Haimo award of the MAA. His other books include Algebraic Geometry: A Problem Solving Approach (2013, co-authored) and Electricity and Magnetism for Mathematicians (2015).

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

The stereotype of the solitary mathematician is widespread, but practicing users and producers of mathematics know well that our work depends heavily on our historical and contemporary fellow travelers. Yet we may not appreciate how our work also extends beyond us into our physical and societal environments.

Kevin Lambert takes what might be a first crack at this perspective in his book Symbols and Things: Material Mathematics in the Eighteenth and Nineteenth Centuries (University of Pittsburgh Press, 2021). An historian of science, Dr. Lambert has shifted in his view of mathematics as a language of science to one as a material practice. Expanding on ideas from historians, archeologists, philosophers, and other scholars of human activity, and through several interweaving vignettes of mathematical work during a technologically dynamic period in British history, he argues that mathematical practice, communication, and even thought occur to a large degree outside the bodies of the persons performing them.

In this interview, we explore Kevin's journal to and through this book project. We discuss how such ideas as Andy Clark's extended mind informed his approach, and we review several of the lively stories—the co-creation of the long-distance mathematical community with the research journal, Peacock's museological argument for the adoption of symbolic algebra, and the foundational entanglement of electromagnetism, quaternions, and the philosophy of space, among others—he drew out of historical and archival sources. (Here i cannot resist mentioning Tait's collection of his intensive correspondence with Hamilton that transformed how quaternions were applied in physics and even conceptualized as mathematical objects.) We close with some thoughts on our own materially extended cognitive work and where Kevin's interests are currently driving him.

Suggested companion works:

• ChatGPT, as a cutting-edge extension of human thought

• work by Courtney Ann Roby, including the forthcoming The Mechanical Tradition of Hero of Alexandria: Strategies of Reading from Antiquity to the Early Modern Period

• Algorithmic Modernity: Mechanizing Thought and Action, 1500-2000, edited by Morgan G. Ames and Massimo Mazzotti

• work by Emily Miller Bonney, for example "A Reconsideration of Depositional Practices in Early Bronze Age Crete"

Kevin Lambert is a historian of science and mathematics in the early modern and modern periods and professor in the liberal studies department at California State University, Fullerton. His recent book Symbols and Things explores mathematics as a way of thinking outside the body and through the material environment. He also recently published a chapter in the volume Algorithmic Modernity that traces the genealogy of algorithmic practices. He is now working on the problem of writing longue durée histories of science. He is close to completing a paper called “Malthus in the Landscape” that investigates the temporalities of global histories. He is also exploring the problem of writing a global history of the early modern sciences without the prism of the so called “Scientific Revolution.” His work can be found on ResearchGate.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

What's the best way to determine what most voters want when multiple candidates are running? What's the fairest way to allocate legislative seats to different constituencies? What's the least distorted way to draw voting districts? Not the way we do things now. Democracy is mathematical to its very foundations. Yet most of the methods in use are a historical grab bag of the shortsighted, the cynical, the innumerate, and the outright discriminatory. Making Democracy Count: How Mathematics Improves Voting, Electoral Maps, and Representation (Princeton UP, 2024) sheds new light on our electoral systems, revealing how a deeper understanding of their mathematics is the key to creating civic infrastructure that works for everyone.

In this timely guide, Ismar Volic empowers us to use mathematical thinking as an objective, nonpartisan framework that rises above the noise and rancor of today's divided public square. Examining our representative democracy using powerful clarifying concepts, Volic shows why our current voting system stifles political diversity, why the size of the House of Representatives contributes to its paralysis, why gerrymandering is a sinister instrument that entrenches partisanship and disenfranchisement, why the Electoral College must be rethought, and what can work better and why. Volic also discusses the legal and constitutional practicalities involved and proposes a road map for repairing the mathematical structures that undergird representative government.

Making Democracy Count gives us the concrete knowledge and the confidence to advocate for a more just, equitable, and inclusive democracy.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

Bookshop.org is an online book retailer that donates more than 80% of its profits to independent bookstores. Launched in 2020, Bookshop.org has already raised more than $27,000,000. In this interview, Andy Hunter, founder and CEO discusses his journey to creating one of the most revolutionary new organizations in the book world. Bookshop has found a way to retain the convenience of online book shopping while also supporting independent bookstores that are the backbones of many local communities. 

Andy Hunter is CEO and Founder of Bookshop.org. He also co-created Literary Hub.

Caleb Zakarin is the Assistant Editor of the New Books Network.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

Barbara M. Sattler's book The Concept of Motion in Ancient Greek Thought: Foundations in Logic, Method, and Mathematics (Cambridge UP, 2020) examines the birth of the scientific understanding of motion. It investigates which logical tools and methodological principles had to be in place to give a consistent account of motion, and which mathematical notions were introduced to gain control over conceptual problems of motion. It shows how the idea of motion raised two fundamental problems in the 5th and 4th century BCE: bringing together being and non-being, and bringing together time and space. The first problem leads to the exclusion of motion from the realm of rational investigation in Parmenides, the second to Zeno's paradoxes of motion. Methodological and logical developments reacting to these puzzles are shown to be present implicitly in the atomists, and explicitly in Plato who also employs mathematical structures to make motion intelligible. With Aristotle we finally see the first outline of the fundamental framework with which we conceptualise motion today.

Professor Barbara Sattler is Chair in Ancient and Medieval Philosophy at the Ruhr University Bochum. The main area of her research is metaphysics and natural philosophy in the ancient Greek world.

Morteza Hajizadeh is a Ph.D. graduate in English from the University of Auckland in New Zealand. His research interests are Cultural Studies; Critical Theory; Environmental History; Medieval (Intellectual) History; Gothic Studies; 18th and 19th Century British Literature. YouTube channel.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

A defining feature of nineteenth-century Britain was its fascination with statistics. The processes that made Victorian society, including the growth of population, the development of industry and commerce, and the increasing competence of the state, generated profuse numerical data. 

Victorians and Numbers: Statistics and Society in Nineteenth Century Britain (Oxford UP, 2022) is a study of how such data influenced every aspect of Victorian culture and thought, from the methods of natural science and the struggle against disease, to the development of social administration and the arguments and conflicts between social classes. Numbers were collected in the 1830s by newly-created statistical societies in response to this 'data revolution'. They became a regular aspect of governmental procedure thereafter, and inspired new ways of interrogating both the natural and social worlds. William Farr used them to study cholera; Florence Nightingale deployed them in campaigns for sanitary improvement; Charles Babbage was inspired to design and build his famous calculating engines to process them. The mid-Victorians employed statistics consistently to make the case for liberal reform. In later decades, however, the emergence of the academic discipline of mathematical statistics - statistics as we use them today - became associated with eugenics and a contrary social philosophy. Where earlier statisticians emphasised the unity of mankind, some later practitioners, following Francis Galton, studied variation and difference within and between groups. In chapters on learned societies, government departments, international statistical collaborations, and different Victorian statisticians, Victorians and Numbers traces the impact of numbers on the era and the intriguing relationship of Victorian statistics with 'Big Data' in our own age.

Lawrence Goldman was born in London and educated at Cambridge and Yale. Following a Junior Research Fellowship at Trinity College, Cambridge, he taught British and American History for three decades in Oxford, where he was a fellow of St. Peter's College, and Editor of the Oxford Dictionary of National Biography 2004-2014. Latterly he was Director of the Institute of Historical Research, University of London. His publications include books on Victorian social science and the history of workers' education, and a biography of the historian and political thinker R. H. Tawney. He is now Emeritus Fellow of St. Peter's College, Oxford.

Morteza Hajizadeh is a Ph.D. graduate in English from the University of Auckland in New Zealand. His research interests are Cultural Studies; Critical Theory; Environmental History; Medieval (Intellectual) History; Gothic Studies; 18th and 19th Century British Literature. YouTube channel.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

One of the questions I am often asked is exactly what do mathematicians do. The short answer is that they look at different mathematical structures, try to deduce their properties, and think about how they might apply to the real world. Math Without Numbers (Dutton, 2020) does a wonderful job of explaining what mathematical structures are, and does so in a fashion that even readers who are uncomfortable with the process of doing mathematics can appreciate and enjoy. There are courses in music and art appreciation, and if there ever are courses in math appreciation, this book would certainly be at or near the top of the reading list.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

Many books explain what is known about the universe. This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own thought processes.

Yanofsky describes simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve; perfectly formed English sentences that make no sense; different levels of infinity; the bizarre world of the quantum; the relevance of relativity theory; the causes of chaos theory; math problems that cannot be solved by normal means; and statements that are true but cannot be proven. He explains the limitations of our intuitions about the world—our ideas about space, time, and motion, and the complex relationship between the knower and the known.

Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there.

Noson S. Yanofsky is Professor in the Department of Computer and Information Science at Brooklyn College and The Graduate Center of the City University of New York. He is a coauthor of Quantum Computing for Computer Scientists.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

Why are girls discouraged from doing science? Why do so many promising women leave science in early and mid-career? Why do women not prosper in the scientific workforce?

Not Just for the Boys: Why We Need More Women in Science (Oxford UP, 2023) looks back at how society has historically excluded women from the scientific sphere and discourse, what progress has been made, and how more is still needed. Athene Donald, herself a distinguished physicist, explores societal expectations during both childhood and working life using evidence of the systemic disadvantages women operate under, from the developing science of how our brains are―and more importantly aren't―gendered, to social science evidence around attitudes towards girls and women doing science.

It also discusses how science is done in practice, in order to dispel common myths: for example, the perception that science is not creative, or that it is carried out by a lone genius in an ivory tower, myths that can be very off-putting to many sections of the population. A better appreciation of the collaborative, creative, and multi-disciplinary nature of science is likely to lead to its appeal to a far wider swathe of people, especially women. This book examines the modern way of working in scientific research, and how gender bias operates in various ways within it, drawing on the voices of leading women in science describing their feelings and experiences. It argues the moral and business case for greater diversity in modern research, the better to improve science and tackle the great challenges we face today.

Athene Donald is Professor Emerita in Experimental Physics and Master of Churchill College, University of Cambridge. Other than four years postdoctoral research in the USA, she has spent her career in Cambridge, specializing in soft matter physics and physics at the interface with biology. She was the University of Cambridge's first Gender Equality Champion, and has been involved in numerous initiatives concerning women in science. She was elected Fellow of the Royal Society in 1999 and appointed DBE for services to Physics in 2010.

Morteza Hajizadeh is a Ph.D. graduate in English from the University of Auckland in New Zealand. His research interests are Cultural Studies; Critical Theory; Environmental History; Medieval (Intellectual) History; Gothic Studies; 18th and 19th Century British Literature. YouTube channel.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

The Price is Right is television's longest-running game show. Since its inception in 1956, contestants have won cars, tropical vacations, diamond jewelry, even a live horse, and the hosts' excited catchphrase "come on down!" has become part of our everyday vernacular. Part of the program's enduring appeal is the apparent ease of the game, guessing the cash value of certain prizes. But, if that's the case, then why do so many contestants come away from the show empty-handed? Solving The Price is Right (Prometheus Books, 2023) is an in-depth exploration of the underlying probability theory of the popular television program that explores how biases and behavioral pitfalls limit our ability to successfully apply logic and math both on and off the show. 

With rigorous data and analysis compiled from Seasons 47 and 48 (356 total episodes), investor and math practitioner Justin L. Bergner draws strategic and mathematical insights from all facets of the show, from Contestant's Row bidding to the Showcase Showdown, and all 77 Pricing Games, using a combination of game theory, probability theory, statistics, and pattern recognition. In each section, Bergner summarizes contestant performance, highlights the biases leading to sub-par outcomes, and shows how outcomes can be improved by executing the right strategies while avoiding cognitive biases. Throughout, Bergner applies the lessons learned to the fields of business, finance, and our real lives, shedding light on themes of reverse psychology, strategic patience, and the importance of establishing what is sufficient for success in our pursuits. The result is a truly unique and meticulously researched book that uses Solving The Price is Right as a lens to examine our own choices - and how to make better ones.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

African-Americans and women are increasingly visible in professional mathematical institutions, organizations, and literature, expanding our mental models of the mathematics community. Yet early representation also matters: We begin building these models as soon as we begin seeing and doing mathematics, and they can be slow to adapt. In her wonderful activity book Women Who Count: Honoring African American Women Mathematicians (MAA Press, 2019), Dr. Shelly Jones invites children, and their parents and educators, to immerse themselves in the lives and deeds of Black women mathematicians.

The 29 profiles trace back to "the Firsts" in their fields, such as early PhD awardee Evelyn Boyd Granville; the "Pioneers" of emerging fields and programs, including ethnomathematics co-founder Gloria Gilmer; through "Unhidden Figures" like Dorothy Johnson Vaughan of recent biopic fame; and to "Contemporary Firsts" who are living, working, and opening new doors today. Along with their mathematical contributions, Dr. Jones shares details of these mathematicians' early lives, their hobbies and interests, and how they have been shaped by and in turn shaped their communities. Each mini-biography introduces a whole person whom readers new to mathematics can relate to and be inspired by.

Each profile is accompanied by a pencil-and-paper activity that brings to life the some part of their story. Some are classics, including word searches and I-Spy, while others introduce readers to mathematical and educational concepts explored by their subjects—coloring tessellations, for example, or solving equations to decode messages. The text and activities are targeted to grades 3–8, and are ideal for elementary and middle school classrooms.

In our conversation, Dr. Jones described how she conceived the book, assembled the stories and activities, and connected with illustrator Veronica Martins. I came away with a richer perspective on the state of the field for aspiring mathematicians—in addition to a perfect gift for my second-grade nephew.

Suggested companion works:

• Mathematicians of the African Diaspora
• Mathematically Gifted and Black
• Mathematician Project
• Lathisms
• We are Indigenous Mathematicians
• Black Girl MATHgic
• Talitha Washington

Dr. Shelly M. Jones is a Professor of Mathematics Education at Central Connecticut State University. She has been an educator for 30 years and currently teaches undergraduate mathematics content and methods courses for pre-service teachers as well as graduate level mathematics content, curriculum and STEM courses for in-service teachers. Dr. Jones serves her community by working with various professional and community organizations. You can see her CCSU TEDx talk on YouTube where she talks about culturally relevant mathematics. She is also a contributing author to The Brilliance of Black Children in Mathematics: Beyond the Numbers and Toward a New Discourse and co-author of Engaging in Culturally Relevant Math Tasks: Fostering Hope.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

On this episode of the MIT Press podcast, Thomas Lin, Editor-in-Chief of Quanta Magazine, discusses the research and current climate behind the science and math in Alice and Bob Meet the Wall of Fire: The Biggest Ideas in Science from Quanta and The Prime Number Conspiracy: The Biggest Ideas in Math from Quanta. 

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

Jeffrey Carpenter and Andrea Robbett's book Game Theory and Behavior (MIT Press, 2022) is an introduction to game theory that offers not only theoretical tools but also the intuition and behavioral insights to apply these tools to real-world situations. This introductory text on game theory provides students with both the theoretical tools to analyze situations through the logic of game theory and the intuition and behavioral insights to apply these tools to real-world situations. It is unique among game theory texts in offering a clear, formal introduction to standard game theory while incorporating evidence from experimental data and introducing recent behavioral models. Students will not only learn about incentives, how to represent situations as games, and what agents “should” do in these situations, but they will also be presented with evidence that either confirms the theoretical assumptions or suggests a way in which the theory might be updated.

Jeffrey Carpenter is the James Jermain Professor of Political Economy at Middlebury College. His research interests include Experimental and Behavioral Economics with applications to Labor, Public and Development Economics. While pursuing these interests he has conducted lab and field experiments in North America, South America, Europe and Asia.

Andrea Robbett is an Associate Professor of Economics at Middlebury College. Her research uses laboratory experiments to test canonical theoretical models, new ideas, and conventional wisdom. Her work has addressed topics in public economics, labor, voting, information avoidance, financial decision-making and "attribute overload," trust and cooperation, and auctions.

Peter Lorentzen is economics professor at the University of San Francisco. He heads USF's Applied Economics Master's program, which focuses on the digital economy. His research is mainly on China's political economy.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

Seduction is not just an end result, but a process -- and in mathematics, both the end results and the process by which those end results are achieved are often charming and elegant.This helps to explain why so many people -- not just those for whom math plays a key role in their day-to-day lives -- have found mathematics so seductive. Math is unique among all subjects in that it contains end results of amazing insight and power, and lines of reasoning that are clever, charming, and elegant. James D. Stein's Seduced by Mathematics: The Enduring Fascination of Mathematics (World Scientific, 2022) is a collection of those results and lines of reasoning that make us say, 'OMG, that's just amazing, ' -- because that's what mathematics is to those who love it. In addition, some of the stories about mathematical discoveries and the people who discovered them are every bit as fascinating as the discoveries themselves.

Seduced by Mathematics contains material capable of being appreciated by students in elementary school -- as well as some material that will probably be new to even the more mathematically sophisticated. Most of the book can be easily understood by those whose only math courses are algebra and geometry, and who may have missed the magic, enchantment, and wonder that is the special province of mathematics.

James D. Stein is a professor emeritus of mathematics at Cal State Long Beach.

Caleb Zakarin is the Assistant Editor of the New Books Network (Twitter: @caleb_zakarin).

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

Innumeracy, by John Allen Paulos, was first published in 1988. In it the author brilliantly highlighted many of the sorry truths those of us who teach math and science know – not only can’t most people do algebra or geometry, they can’t estimate size, they don’t understand simple probability and statistics, and they believe in things that make no sense. In Who’s Counting? (Prometheus, 2022), Paulos investigates topics which – like Innumeracy – connect with the age in which we live.

Who's Counting? features dozens of his insightful essays-original writings on contemporary issues like the COVID-19 pandemic, online conspiracy theories, "fake news," and climate change, as well as a selection of enduring columns from his popular ABC News column of the same name. With an abiding respect for reason, a penchant for puzzles with societal implications, and a disarming sense of humor, Paulos does in this collection what he's famous for: clarifies mathematical ideas for everyone and shows how they play a role in government, media, popular culture, and life. He argues that if we can't critically interpret numbers and statistics, we lose one of our most basic and reliable guides to reality.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.

Alfred S. Posamentier's The Secret Lives of Numbers: Numerals and Their Peculiarities in Mathematics and Beyond (Prometheus Books, 2022) is the first book I’ve ever seen written by a mathematician that will absolutely, definitely, certainly appeal to people who love numbers and who don’t love mathematics. I would urge all listeners to tell everyone they know who has a fascination with numbers to listen to this podcast, especially if they don’t love mathematics because they will definitely love this book. Hopefully the love of numbers will translate into an appreciation of mathematics -- if not for them, then for their children.

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

Hosted by Simplecast, an AdsWizz company. See pcm.adswizz.com for information about our collection and use of personal data for advertising.