New Books in Mathematics New Books Network

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Interviews with Mathematicians about their New Books

Anna Weltman, "Supermath: The Power of Numbers for Good and Evil" (Johns Hopkins UP, 2020)
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.
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Alfred S. Posamentier, "The Joy of Geometry" (Prometheus, 2020)
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.
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Susan D'Agostino, "How to Free Your Inner Mathematician: Notes on Mathematics and Life" (Oxford UP, 2020)
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.
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Alfred Posamentier, "Mathematics Entertainment for the Millions" (World Scientific Publishing, 2020)
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 middleschool or highschool 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.
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David J. Hand, "Dark Data: Why What You Don't Know Matters" (Princeton UP, 2020)
There is no shortage of books on the growing impact of data collection and analysis on our societies, our cultures, and our everyday lives. David Hand's new book Dark Data: Why What You Don't Know Matters (Princeton University Press, 2020) is unique in this genre for its focus on those data that aren't collected or don't get analyzed. More than an introduction to missingness and how to account for it, this book proposes that the whole of data analysis can benefit from a "dark data" perspective—that is, careful consideration of not only what is seen but what is unseen. David assembles wideranging examples, from the histories of science and finance to his own research and consultancy, to show how this perspective can shed new light on concepts as classical as random sampling and survey design and as cuttingedge as machine learning and the measurement of honesty. I expect the book to inspire the same enjoyment and reflection in general readers as it is sure to in statisticians and other data analysts.
Suggested companion work: Caroline Criado Perez, Invisible Women: Data Bias in a World Designed for Men.
Cory Brunson (he/him) is a Research Assistant Professor at the Laboratory for Systems Medicine at the University of Florida.
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David Bressoud, "Calculus Reordered: A History of the Big Ideas" (Princeton UP, 2019)
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 seventeenthcentury 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.
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