New Books In Mathematics

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 thi

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

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

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 fundamen

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

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,

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

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, an

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