New Books in Mathematics

From its more mainstream, business-focused and business-friendly “Lean In” variants, to more radical, critical and intersectional understandings of feminism, the past decade has seen a flourishing of discussion from those proposing and critiquing different schools of thought for the way we think about gender in society.Dr. Eugenia Cheng’s addition to this conversation is x+y: A Mathematician's Manifesto for Rethinking Gender (Basic Books, 2020). She applies insights gained from her mathematical background to propose a new way to talk about gender and to propose an alternative: the terms “ingressive” and “congressive” behavior.In this interview, Dr. Cheng and I talk about what we gain from bringing a mathematical understanding to questions of social relations and structures. We talk about how she rethinks “gender”, and the new terms she proposes in her book. We end with a short discussion of whether these insights are applicable to conversations about other demographic and social identifiers.Dr. Eugenia Cheng is a mathematician and concert pianist. She is Scientist In Residence at the School of the Art Institute of Chicago and holds a PhD in pure mathematics from the University of Cambridge. Alongside her research in Category Theory and undergraduate teaching her aim is to rid the world of “math-phobia”. She was an early pioneer of math on YouTube and her videos have been viewed over 15 million times to date. Her other books are How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics (Basic Books: 2016), which was featured on the Late Show with Stephen Colbert, Beyond Infinity: An Expedition to the Outer Limits of Mathematics (Basic Books: 2017) which was shortlisted for the Royal Society Science Book Prize in 2017 and The Art of Logic in an Illogical World (Basic Books: 2018)You can find more reviews, excerpts, interviews, and essays at The Asian Review of Books, including its review of x+y. Follow on Facebook or on Twitter at @BookReviewsAsia.Nicholas Gordon is a reviewer for the Asian Review of Books. In his day job, he’s a researcher and writer for a think tank in economic and sustainable development. He is also a print and broadcast commentator on local and regional politics. He can be found on Twitter at @nickrigordon. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

Jason Rosenhouse's Games for Your Mind: The History and Future of Logic Puzzles (Princeton UP, 2020) is about a panoply of logic puzzles. You’ll find Mastermind and sudoku discussed early on, and then you’ll be hit with an incredible array of some of the most intriguing logic puzzles that have ever been devised. Some will be familiar to you, but some will almost certainly be brain-teasers you have never heard of. It’s absolutely amazing what a truly deep field grew from recreational pastimes – and this book is an absolute treasure trove of stuff you can’t help thinking about. If you like logic, you’re certain to be sucked in – but you’ll enjoy the ride.Logic puzzles were first introduced to the public by Lewis Carroll in the late nineteenth century and have been popular ever since. Games like Sudoku and Mastermind are fun and engrossing recreational activities, but they also share deep foundations in mathematical logic and are worthy of serious intellectual inquiry. Games for Your Mind explores the history and future of logic puzzles while enabling you to test your skill against a variety of puzzles yourself.In this informative and entertaining book, Jason Rosenhouse begins by introducing readers to logic and logic puzzles and goes on to reveal the rich history of these puzzles. He shows how Carroll's puzzles presented Aristotelian logic as a game for children, yet also informed his scholarly work on logic. He reveals how another pioneer of logic puzzles, Raymond Smullyan, drew on classic puzzles about liars and truthtellers to illustrate Kurt Gödel's theorems and illuminate profound questions in mathematical logic. Rosenhouse then presents a new vision for the future of logic puzzles based on nonclassical logic, which is used today in computer science and automated reasoning to manipulate large and sometimes contradictory sets of data.Featuring a wealth of sample puzzles ranging from simple to extremely challenging, this lively and engaging book brings together many of the most ingenious puzzles ever devised, including the Hardest Logic Puzzle Ever, metapuzzles, paradoxes, and the logic puzzles in detective stories. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

It would be simple enough to say that mathematics is being done, and that those who do it are mathematicians. Yet, the history and culture of the mathematical community immediately complicate these statements. In her book A New Year's Present from a Mathematician (CRC Press, 2020), Snezana Lawrence guides a tour of European mathematical history that broadens conventional ideas of who mathematicians are and what we do. Framed as journey across the desert out from Alexandria, the book recounts a vignette from European mathematical history anchored to each month of the year, as drops of creativity and wisdom to sustain the trek.It is not unusual for books on the history of mathematics to tell very human stories about their often famous subjects. What is remarkable about Lawrence's collection is the breadth of these stories: Her subjects were idealists, pragmatists, mystics, skeptics, radicals, ascetics, and collectives. (Contrast, for example, the self-aware spite of Isaac Newton with the defiant good humor of Jean-Baptiste d'Alembert.) They contributed a mix each of original study, stewardship, and education. (Witness the precocious and persistent advocacy of Maria Agnesi and the devoted reciprocity of Johannes Kepler.) And they may or may not have been considered in their time, or even considered themselves, mathematicians.This book also showcases the diversity of mechanisms through which mathematics is transmitted and expanded. The projects undertaken by Lawrence's subjects are inspired by surviving ancient texts, popular treatments, and personal correspondence, and they yielded instructional texts, organizational schema, reference works, and popular fiction still in circulation today. The book drove home for me that the history of mathematics is ultimately a history of dialogue, and one that any person has the potential to contribute to—and thereby to be a mathematician.Suggested companion work: "Interstellar" (dir. Christopher Nolan)Snezana Lawrence is a mathematical historian, with a particular interest in the links between mathematics, architecture, and the belief systems related to mathematics. Her work on the creativity, identity, and engagement in the learning of mathematics has taken her to be involved in national and international initiatives to promote the use of the history of mathematics in mathematics education. She maintains the website Maths Is Good For You! and tweets @snezanalawrence. Cory Brunson is a Research Assistant Professor at the Laboratory for Systems Medicine at the University of Florida. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

Math has a complicated relationship with the counterintuitive: Rigorous logic, calculation, and simulation can both help us wrap our minds around phenomena that defy our intuition, and thrust upon us whole new worlds of counterintuitive results. In his new book, Jim Stein introduces readers to several unexpected and sometimes astonishing examples, while demanding a minimal mathematical background.The Fate of Schrodinger's Cat: Using Math and Computers to Explore the Counterintuitive (World Scientific, 2020) takes the reader along a journey in three segments. The first, through only by-hand calculations, builds up to a variation on Schrödinger's notorious thought experiment in which an observer can use an unrelated random process to predict the outcome of a 50/50 trial more than half the time. The kernel of this setup is Blackwell's Bet, a simple yet extraordinary illustration of what Stein calls "probabilistic entanglement".The second section uses computer simulation to get a handle on several paradoxical episodes in the world of sports: For my favorite example, how is it that an NFL season can at the same moment be exceptional both for the number of unbeaten teams and for the number of underperforming ones? Section III brings both computational approaches together to investigate perhaps the most argued-over quantitative question since Monty Hall: Is there a "hot hand"?What makes this book of popular mathematics exceptional is its openness: Stein's explorations can be followed with only very basic (or, ahem, BASIC) knowledge of arithmetic, probability, algebra, and programming. Moreover, they can be furthered: Readers are more often left not with final answers but with many ways to continue on their own.James D. Stein completed a BA in mathematics at Yale in 1962 and a PhD in mathematics at the University of California at Berkeley in 1967. He taught mathematics for 7 years at the University of California Los Angeles and for 35 years at California State University, Long Beach. His research has focused on Banach spaces and fixed-point theory, and he has written 10 mathematics and science books for the general public. He currently teaches one course per semester at El Camino Community College and is interested in probability theory and its applications to prediction.Cory Brunson is a Research Assistant Professor at the Laboratory for Systems Medicine at the University of Florida. His research focuses on geometric and topological approaches to the analysis of medical and healthcare data. He welcomes book suggestions, listener feedback, and transparent supply chains. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

Mathematics as a subject is distinctive in its symbolic abstraction and its potential for logical and computational rigor. But mathematicians tend to impute other qualities to our subject that set it apart, such as impartiality, universality, and elegance. Far from incidental, these ideas prime mathematicians and the public to see in mathematics the answers—for example, an impartial arbiter, or a meritocratic equalizer—to many urgent societal questions. Anna Weltman's new book, Supermath: The Power of Numbers for Good and Evil (Johns Hopkins University Press, 2020), surveys a number of ways this conception of mathematics has informed scientific undertakings and public policies, not to mention our everyday behaviors, and makes a powerful case for reevaluating its assumptions.The book's five chapters contain stories of mathematical exploits from ancient to ongoing and across the spectrum from pure to applied. Many may be familiar, for example active research and journalism into the use and misuse of predictive algorithms or G. H. Hardy's enumeration of the elements of mathematical beauty. Others, including continuing work to interpret Incan documents that survived European colonial erasure and the epidemiological insights obtained from massively multiplayer online gaming, will be new even to many mathematical readers. What they share is the essential but often ignored interplay between theory and culture that makes mathematics a thoroughly human activity. Weltman's book can be read as a call for scholars, educators, and communicators of mathematics to grapple with the power our training and credentialing in mathematics grants us, and to understand that its most basic promise of solving problems is not automatic but one that we must realize.Anna Weltman is a math teacher and writer who earned her PhD in mathematics education from the University of California at Berkeley. She is also the author of This Is Not a Math Book and This Is Not Another Math Book.Cory Brunson (he/him) is a Research Assistant Professor at the Laboratory for Systems Medicine at the University of Florida. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

Alfred S. Posamentier's The Joy of Geometry (Prometheus, 2020) is a book for someone who has taken geometry but wants to go further. This book, as one might expect, is heavy on diagrams and it is sometimes hard to discuss some of the ideas without reference to a diagram. Also, to be fair, this is not a book intended to be read casually. To fully appreciate this book, it is necessary to sit down, preferably in a comfortable chair with a beverage of one’s choosing, and prepare to give the diagrams a close look. The effort will be well rewarded. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

Doing mathematics can be stimulating, deep, and sometimes fantastic. It can also be frustrating, impenetrable, and at times dispiriting. In her new collection of essays, writer and mathematician Susan D'Agostino shows how math itself can be a useful guide through these experiences. How to Free Your Inner Mathematician: Notes on Mathematics and Life (Oxford University Press) draws upon the theorems, applications, and history of mathematics to inspire lessons and advice for us along our mathematical (and other) pursuits.While the math, some familiar and some less so, has clear scientific significance, the lessons help us also appreciate its humanistic value. Delightful illustrations and an (honestly) enjoyable exercise accompany each essay, and readers can jump around the text however they please.This book will appeal to aspiring mathematicians at any career stage, but its most important audience may be the latent mathematicians who have been discouraged from the discipline but are open to a fresh invitation.Susan D'Agostino is a mathematician and writer whose essays have been published in Quanta Magazine, Scientific American, Financial Times, Nature, Undark, Times Higher Education, Chronicle of Higher Education, Math Horizons, Mathematics Teacher, and others.Cory Brunson (he/him) is a Research Assistant Professor at the Laboratory for Systems Medicine at the University of Florida. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

The book being discussed is Mathematics Entertainment for the Millions (World Scientific Publishing Co.), by Alfred Posamentier. In reading this book, it occurred to me that it might equally well have been entitled Millions of Mathematical Entertainments.There may not be millions of entertainments, but there’s an incredible amount – most of it easily accessible to a middle-school or high-school student, and that’s exactly the audience that we want to show how enticing mathematics can be.  Anyone who loves mathematics will find a number of old favorites in this book, but almost certainly there’s a lot of cool stuff you’ve never seen before.  I’ve been looking at math for more than seven decades, and there’s a lot of cool stuff I’d never seen.Alfred S Posamentier is currently Distinguished Lecturer at New York City College of Technology of the City University of New York. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/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

There are very few math books that merit the adjective ‘charming’ but Mage Merlin's Unsolved Mathematical Mysteries (MIT Press, 2020) is one of them. Satyan Devadoss and Matt Harvey have chosen a truly unique, creative and charming way to acquaint readers with some of the unsolved problems of mathematics. Some are classic, such as the Goldbach Conjecture, some are fairly well known, such as the Collatz Conjecture. Others are less well known but no less fascinating – and all are intriguing and both enjoyable and tantalizing to contemplate. The authors have woven the problems into a coherent story, and I think you’ll enjoy hearing – and reading – both the story and the associated problems. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics