New Books in Mathematics New Books Network

 Natural Sciences
Interviews with Mathematicians about their New Books
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Jonas Peters and Nicolai Meinshausen, "The Raven's Hat: Fallen Pictures, Rising Sequences, and Other Mathematical Games" (MIT Press, 2021)
Games have been of interest to mathematicians almost since mathematics became a subject. In fact, entire branches of mathematics have arisen simply to analyze certain games. The Raven's Hat: Fallen Pictures, Rising Sequences, and Other Mathematical Games (MIT Press, 2021) does something very different, and something that I think listeners will find intriguing – it uses games in order to explain mathematical concepts.
The Raven's Hat presents a series of engaging games that seem unsolvablebut can be solved when they are translated into mathematical terms. How can players find their ID cards when the cards are distributed randomly among twenty boxes? By applying the theory of permutations. How can a player guess the color of her own hat when she can only see other players' hats? Hamming codes, which are used in communication technologies. Like magic, mathematics solves the apparently unsolvable. The games allow readers, including university students or anyone with high schoollevel math, to experience the joy of mathematical discovery.
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Eugenia Cheng, "x + y: A Mathematician's Manifesto for Rethinking Gender" (Basic Book, 2020)
From its more mainstream, businessfocused and businessfriendly “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 “mathphobia”. 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.
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Milo Beckman, "Math Without Numbers" (Dutton, 2020)
One of the questions I am often asked is exactly what do mathematicians do. The short answer is that they look at different mathematical structures, try to deduce their properties, and think about how they might apply to the real world. Math Without Numbers (Dutton, 2020) does a wonderful job of explaining what mathematical structures are, and does so in a fashion that even readers who are uncomfortable with the process of doing mathematics can appreciate and enjoy. There are courses in music and art appreciation, and if there ever are courses in math appreciation, this book would certainly be at or near the top of the reading list.
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J. Rosenhouse, "Games for Your Mind: The History and Future of Logic Puzzles" (Princeton UP, 2020)
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 brainteasers 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.
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Snezana Lawrence, "A New Year's Present from a Mathematician" (CRC Press, 2019)
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 selfaware spite of Isaac Newton with the defiant good humor of JeanBaptiste 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.
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James D. Stein, "The Fate of Schrodinger's Cat: Using Math and Computers to Explore the Counterintuitive" (World Scientific, 2020)
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 byhand 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 arguedover 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 fixedpoint 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.
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