New Books in Mathematics

Calculus Reordered: A History of the Big Ideas (Princeton UP, 2019) takes readers on a remarkable journey through hundreds of years to tell the story of how calculus evolved into the subject we know today. David Bressoud explains why calculus is credited to seventeenth-century figures Isaac Newton and Gottfried Leibniz, and how its current structure is based on developments that arose in the nineteenth century. Bressoud argues that a pedagogy informed by the historical development of calculus represents a sounder way for students to learn this fascinating area of mathematics.Delving into calculus’s birth in the Hellenistic Eastern Mediterranean—particularly in Syracuse, Sicily and Alexandria, Egypt—as well as India and the Islamic Middle East, Bressoud considers how calculus developed in response to essential questions emerging from engineering and astronomy. He looks at how Newton and Leibniz built their work on a flurry of activity that occurred throughout Europe, and how Italian philosophers such as Galileo Galilei played a particularly important role. In describing calculus’s evolution, Bressoud reveals problems with the standard ordering of its curriculum: limits, differentiation, integration, and series. He contends that the historical order—integration as accumulation, then differentiation as ratios of change, series as sequences of partial sums, and finally limits as they arise from the algebra of inequalities—makes more sense in the classroom environment.Exploring the motivations behind calculus’s discovery, Calculus Reordered highlights how this essential tool of mathematics came to be.David M. Bressoud is DeWitt Wallace Professor of Mathematics at Macalester College and Director of the Conference Board of the Mathematical Sciences. His many books include Second Year Calculus and A Radical Approach to Lebesgue’s Theory of Integration. He lives in St. Paul, Minnesota.Mark Molloy is the reviews editor at MAKE: A Literary Magazine. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

Popular music history collides with data analytics, charts, and numbers in this insightful and surprising look at the greatest hits and musicians, fads, forgotten artists, and much more. Data analyst and musician Chris Dalla Riva reframes everything you thought you knew about music. Did you know that hit songs in the late 1950s were regularly about gruesome death? That a US vice president wrote a number one hit? That while TikTok has spawned countless hits, it's made artists more anonymous than ever before? That pop songs have shaped race relations in the United States? That the key change died around 2003? And that's just the beginning. Coupling hard data with engaging anecdotes, Uncharted Territory: What Numbers Tell Us about the Biggest Hit Songs and Ourselves (Bloomsbury, 2025) is both a takedown and celebration of popular music and provides new ways to think about your favorite songs, genres, and artists from the last 6 decades using unexpected statistics and playful visualizations. This entertaining history is filled with the most popular musicians of all time from The Beatles and The Bee Gees to Michael Jackson, Mariah Carey, and beyond. Whether you danced the twist or the dougie at your senior prom, you're sure to never listen to music again in the same way. Chris Dalla Riva lives at the intersection of music and data. Playing in bands and recording music since his teenage years, Dalla Riva is currently a Senior Product Manager at Audiomack where he focuses on data analytics and personalization. Gregory McNiff is a Managing Director in the New York office of the Blueshirt Group, an IR firm focused on technology. Greg holds an MBA from the University of Chicago Booth School of Business, an M. Litt. in Shakespeare Studies from the University of St. Andrews and a B.A. in Classical Languages from Columbia University. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

Statistics are everywhere: in news reports, at the doctor's office, and in every sort of forecast, from the stock market to the weather. Blogger, teacher, and computer scientist Allen B. Downey knows well that people have an innate ability both to understand statistics and to be fooled by them. As he makes clear in this accessible introduction to statistical thinking, the stakes are big. Simple misunderstandings have led to incorrect medical prognoses, underestimated the likelihood of large earthquakes, hindered social justice efforts, and resulted in dubious policy decisions. There are right and wrong ways to look at numbers, and Downey will help you see which are which. Probably Overthinking It: How to Use Data to Answer Questions, Avoid Statistical Traps, and Make Better Decisions (University of Chicago Press, 2023) uses real data to delve into real examples with real consequences, drawing on cases from health campaigns, political movements, chess rankings, and more. He lays out common pitfalls--like the base rate fallacy, length-biased sampling, and Simpson's paradox--and shines a light on what we learn when we interpret data correctly, and what goes wrong when we don't. Using data visualizations instead of equations, he builds understanding from the basics to help you recognize errors, whether in your own thinking or in media reports. Even if you have never studied statistics--or if you have and forgot everything you learned--this book will offer new insight into the methods and measurements that help us understand the world. Allen B. Downey is a curriculum designer at the online learning company Brilliant and professor emeritus of computer science at Olin College. Gregory McNiff is a Managing Director in the New York office of the Blueshirt Group, an IR firm focused on technology. Greg holds an MBA from the University of Chicago Booth School of Business, an M. Litt. in Shakespeare Studies from the University of St. Andrews and a B.A. in Classical Languages from Columbia University. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

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. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

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. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

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. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

Anil Ananthaswamy, an award-winning science writer and author, delves into the intricate mathematics behind modern AI. He reveals how machine learning influences critical decisions in our lives, powered by concepts as old as linear algebra. Ananthaswamy explores the journey from simple algorithms to complex neural networks, diving into Hebbian learning and the evolution of generative AI. He also ponders the connection between human cognition and AI, emphasizing the need to grasp the math that underlies these advancements for safe and effective use.

Robyn Arianrhod, a science writer and mathematician from Monash University, delves into the fascinating world of vectors and tensors in her latest book. She illuminates how these mathematical tools transformed our understanding of space and time, showcasing pivotal figures from Maxwell to Einstein. Arianrhod discusses the evolution from word-based algebra to symbolic representation, revealing the surprising historical connections that led to revolutionary ideas in physics. Her engaging narrative makes complex mathematics accessible, bridging the gap between science and storytelling.

In this engaging discussion, Chris Bernhardt, a former mathematics professor and author of 'Beautiful Math,' delves into the fundamental math behind the digital age. He simplifies concepts like information theory, explaining how digital communications thrive on principles of redundancy and compression. Bernhardt uncovers the intricacies of error correction and encryption, while also illuminating the journey from analog to digital formats. His insights into Boolean logic and machine learning invite listeners to appreciate the math that underpins modern technology.

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. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics