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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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:

Listen to and Read the episode here.

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