New Books In Mathematics

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 sha

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

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 Polit

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 sch

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 governme

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

In this episode of High Theory, Justin Joque talks with Júlia Irion Martins about Probability. This conversation is part of our High Theory in STEM series, which tackles topics in science, technology, engineering, and medicine from a highly theoretical perspective. If you want to learn more about the philosophical, technical, and economic implications of probability, check out Justin’s new book, Revolutionary Mathematics: Artificial Intelligence, Statistics, and the Logic of Capitalism (Verso, 2022). Justin Joque is a visualization librarian at the University of Michigan, Ann Arbor. Justin’s research focuses on philosophy, media, and technology and he is also the author of Deconstruction Machines: Writing in the Age of Cyberwar (University of Minnesota Press, 2018). Image: © 2022 Saronik Bosu Learn more about your ad choices. Visit megaphone.fm/adchoices Support our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

I’ve never read a book like Mathematical Tools for Real-World Applications: A Gentle Introduction for Students and Practitioners (MIT Press, 2022) – it’s a book about how engineers and scientists see math, and I found it fascinating. What intrigued me about this book was not that it just presents and solves a bunch of interesting problems, it shows how scientists and engineers differ in their approach to problem solving from mathematicians. Shame on me, but as a mathematician, I’ve always been a little uncomfortable with the way engineers and scientists use mathematics. I wish I’d seen this book when I was in college, I’d have done a lot better in my physics courses. Learn more about your ad choices. Visit megaphone.fm/adchoices Support our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

Performing Math: A History of Communication and Anxiety in the American Mathematics Classroom (Rutgers University Press, 2020) by Dr. Andrew Fiss tells the history of expectations for math communication—and the conversations about math hatred and math anxiety that occurred in response. Focusing on nineteenth-century American colleges, this book analyzes foundational tools and techniques of math communication: the textbooks that supported reading aloud, the burnings that mimicked pedagogical speech, the blackboards that accompanied oral presentations, the plays that proclaimed performers’ identities as math students, and the written tests that redefined “student performance.” Math communication and math anxiety went hand in hand as new rules for oral communication at the blackboard inspired student revolt and as frameworks for testing student performance inspired performance anxiety. With unusual primary sources from over a dozen educational archives, Performing Math argues for a new, performance-oriented hist

Freeman Dyson (1923–2020)—renowned scientist, visionary, and iconoclast—helped invent modern physics. Not bound by disciplinary divisions, he went on to explore foundational topics in mathematics, astrophysics, and the origin of life. General readers were introduced to Dyson’s roving mind and heterodox approach in his 1979 book Disturbing the Universe, a poignant autobiographical reflection on life and science.  "Well, Doc, You're In": Freeman Dyson’s Journey through the Universe (MIT Press, 2022) (the title quotes Richard Feynman’s remark to Dyson at a physics conference) offers a fresh examination of Dyson’s life and work, exploring his particular way of thinking about deep questions that range from the nature of matter to the ultimate fate of the universe. The chapters—written by leading scientists, historians, and science journalists, including some of Dyson’s colleagues—trace Dyson’s formative years, his budding interests and curiosities, and his wide-ranging work across the natural sciences, technology,

The Story of Proof: Logic and the History of Mathematics (Princeton UP, 2022) investigates the evolution of the concept of proof--one of the most significant and defining features of mathematical thought--through critical episodes in its history. From the Pythagorean theorem to modern times, and across all major mathematical disciplines, John Stillwell demonstrates that proof is a mathematically vital concept, inspiring innovation and playing a critical role in generating knowledge. Stillwell begins with Euclid and his influence on the development of geometry and its methods of proof, followed by algebra, which began as a self-contained discipline but later came to rival geometry in its mathematical impact. In particular, the infinite processes of calculus were at first viewed as "infinitesimal algebra," and calculus became an arena for algebraic, computational proofs rather than axiomatic proofs in the style of Euclid. Stillwell proceeds to the areas of number theory, non-Euclidean geometry, topology, and lo

In The New Era in American Mathematics, 1920-1950 (Princeton University Press, 2022) Karen Parshall explores the institutional, financial, social, and political forces that shaped and supported the American Mathematics community in the first half of the twentieth century. Drawing from extensive archival and primary-source research, Professor Parshall uncovers the key players in American mathematics who worked together to effect change. She highlights the educational, professional, philanthropic, and governmental entities that bolstered progress and uncovers the strategies implemented by American mathematicians in their quest for the advancement of knowledge. Through an examination of how the American Mathematical community asserted itself on the international state, The New Era in Mathematics, 1920-1950 shows the way one nation became the focal point for the field. Karen Hunger Parshall is the Commonwealth Professor of History and Mathematics at the University of Virginia. She is the author of James Joseph S

Peter Winkler has been collecting mathematical puzzles since childhood. He has had published two previous collections, and recently he compiled his largest curated collection to date. Mathematical Puzzles (A K Peters, 2021) also takes an alluring new approach to the genre: In the Roman-numbered front matter, 300+ puzzles are presented, roughly in order of increasing difficulty. Fuller discussions of the puzzles are then organized into 24 chapters according to the key insight that leads to their solutions. Each insight gets a brief mathematical treatment, and by the end of each chapter the reader is primed to appreciate an important and kindred mathematical result. In our interview, Dr. Winkler walked me through a handful of puzzles from two chapters. The first, "The Law of Small Numbers", gives a tongue-in-cheek name to the strategy of gaining insight from a smaller version of a larger problem. The puzzles lead up to a discussion of perfect matchings, whose small-number analogues reveal an elegant geometric s

In Community College Mathematics: Past, Present, and Future (CRC Press, 2022), Brian Cafarella addresses the key questions: How can we build a future model for community college gatekeeper math classes that is both successful and sustainable? Additionally, how can we learn from the past and the present to build such a model? From the 1970’s to the pandemic in the early 2020’s, the book uses interviews with 30 community college faculty members from seven community colleges to explore math curricula as well as trends, initiatives, teaching practices, and mandates that have impacted community college mathematics. Brian Cafarella is a professor in mathematics at Sinclair Community College in Dayton, Ohio. He has taught a variety of courses ranging from developmental math through pre-calculus. Brian is a past recipient of the Roeche Award for teaching excellence and a past recipient of the Ohio Magazine Award for excellence in education. Marc Goulet is Professor in mathematics and Associate Dean in the College of

Today I had the pleasure of talking to Joe Mileti, associate professor of mathematics at Grinnell College. Even if you are not "into" math, you will enjoy this conversation. We talked about how math is not what you think it is. It's not just memorizing formulas and grinding. It's about thinking and, like all thinking, it involves abstraction, logic, using analogies and metaphors, and a bunch of imagination. We also talked about how math is about talking to other mathematicians and doing a kind of "brainstorming."  Joes's new book is Modern Mathematical Logic (Cambridge UP, 2022). Marshall Poe is the founder and editor of the New Books Network. He can be reached at marshallpoe@newbooksnetwork.com. Learn more about your ad choices. Visit megaphone.fm/adchoices Support our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

In Probability and Forensic Evidence: Theory, Philosophy, and Applications (Cambridge UP, 2021), Ronald Meester and Klaas Slooten address the role of statistics and probability in the evaluation of forensic evidence, including both theoretical issues and applications in legal contexts. It discusses what evidence is and how it can be quantified, how it should be understood, and how it is applied (and, sometimes misapplied). Ronald Meester is Professor in probability theory at the Vrije Universiteit Amsterdam. He is co-author of the books Continuum Percolation (1996), A Natural Introduction to Probability Theory (2003), Random Networks for Communication (2008), and has written around 120 research papers on topics including percolation theory, ergodic theory, philosophy of science, and forensic probability. Klaas Slooten works as Statistician at the Netherlands Forensic Institute and at the Vrije Universiteit Amsterdam where he is Professor by special appointment. He as published around 30 articles on forensic p

In Formulations: Architecture, Mathematics, Culture (MIT Press, 2022), Andrew Witt examines the visual, methodological, and cultural intersections between architecture and mathematics. The linkages Witt explores involve not the mystic transcendence of numbers invoked throughout architectural history, but rather architecture’s encounters with a range of calculational systems—techniques that architects inventively retooled for design. Witt offers a catalog of mid-twentieth-century practices of mathematical drawing and calculation in design that preceded and anticipated digitization as well as an account of the formal compendia that became a cultural currency shared between modern mathematicians and modern architects. Witt presents a series of extensively illustrated “biographies of method”—episodes that chart the myriad ways in which mathematics, particularly the mathematical notion of modeling and drawing, was spliced into the creative practice of design. These include early drawing machines that mechanized cu

Formal mathematical models have provided tremendous insights into politics in recent decades. Formal Models of Domestic Politics (Cambridge UP, 2021) is the leading graduate textbook covering the crucial models that underpin current theoretical and empirical research on politics by both economists and political scientists. This textbook was recently updated to reflect the wealth of new theory-building around the functioning of authoritarian regimes, as well as to include recent developments in the theory of electoral competition, delegation, legislative bargaining, and collective action. Author Scott Gehlbach is a professor at the University of Chicago, where he is the director of their new PhD program in Political Economy. He is a widely published political economist, with influential articles published in both economics and political science journal as well as two other books. Scott also has a regional specialty in the politics of Russia, Ukraine, and other postcommunist countries. In our interview, we disc

Today I talked to Seth Stephens-Davidowitz about his new book Don't Trust Your Gut: Using Data to Get What You Really Want in LIfe (Dey Street Books, 2022) Looking for advice on how to get a date, how to have a successful marriage, or just how to have a happier life? Don’t trust your gut, don’t trust conventional wisdom, and put down that self-help book full of plausible arguments and compelling anecdotes that just happens to contradict the advice you got from the self-help book you. Instead, let Seth Stephens-Davidowitz guide you, using data! Seth Stephens-Davidowitz is a data scientist, author, keynote speaker, and recovering economist. His first book Everybody Lies, was a New York Times bestseller that showed how social scientists have used new data about our online behavior to gain new insights about who we really are and what we really think. His latest book, Don’t Trust Your Gut, is about how we can use data not just to understand other people but also how to get what we want in life, whether it’s healt

Plan S: the open access initiative that changed the face of global research.  Robert-Jan Smits and Rachael Pells's book Plan S for Shock: Science. Shock. Solution. Speed. (Ubiquity Press, 2022) tells the story of open access publishing - why it matters now, and for the future. In a world where information has never been so accessible, and answers are available at the touch of a fingertip, we are hungrier for the facts than ever before - something the Covid-19 crisis has brought to light. And yet, paywalls put in place by multi-billion dollar publishing houses are still preventing millions from accessing quality, scientific knowledge - and public trust in science is under threat. On 4 September 2018, a bold new initiative known as 'Plan S' was unveiled, kickstarting a world-wide shift in attitudes towards open access research. For the first time, funding agencies across continents joined forces to impose new rules on the publication of research, with the aim of one day making all research free and available to