New Books In Mathematics

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Synopsis

Interviews with Mathematicians about their New Books

Episodes

  • Ellen Peters, "Innumeracy in the Wild: Misunderstanding and Misusing Numbers" (Oxford UP, 2020)

    31/05/2021 Duration: 01h08min

    To many mathematicians and math enthusiasts, the word "innumeracy" brings to mind popular writing like that of John Allen Paulos. But inequities in our quantitative reasoning skills have received considerable interest and attention from researchers lately, including in psychology, development, education, and public health. Innumeracy in the Wild: Misunderstanding and Misusing Numbers (Oxford University Press, 2020) is a unified treatment of these broad-ranging studies, from the ways more and less numerate people differ in our perceptions of risk and our number-based decisions to the roots of our numeric faculties and how we can make the best of them. Dr. Ellen Peters has made significant contributions to the subject and brings her expertise and an exceptional clarity to its presentation. Precious little of the research surveyed in her book could fit into this interview! We discussed the three components of numeric ability—objective numeracy, subjective numeracy, and the innate number sense—and how they vary w

  • Dave Auckly, et al., "Inspiring Mathematics: Lessons from the Navajo Nation Math Circles" (AMS, 2019)

    27/04/2021 Duration: 01h13min

    Math circles defy simple narratives. The model was introduced a century ago, and is taking off in the present day thanks in part to its congruence with cutting-edge research in mathematics education. It is a modern approach to teaching—or facilitation—that resonates and finds mutual reinforcement with traditional practices and cultural preservation efforts. A wide range of math circle resources have become available for interested instructors, including the MSRI Math Circles Library, now in its 14th year of publication by the AMS. I was excited to talk with three editors and contributors to a recent volume in the series, Inspiring Mathematics: Lessons from the Navajo Nation Math Circles (American Mathematical, 2019). Drs. Dave Auckly, Amanda Serenevy, and Henry Fowler have been instrumental to the Navajo Nation Math Circles Project, along with co-editors Tatiana Shubin and Bob Klein and a broader contact and support network. Their book showcases scripts developed and facilitated in Navajo Nation, including an

  • Jonas Peters and Nicolai Meinshausen, "The Raven's Hat: Fallen Pictures, Rising Sequences, and Other Mathematical Games" (MIT Press, 2021)

    02/04/2021 Duration: 57min

    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 unsolvable--but 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 school-level math, to experience the joy

  • Eugenia Cheng, "x + y: A Mathematician's Manifesto for Rethinking Gender" (Basic Book, 2020)

    01/04/2021 Duration: 42min

    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 Che

  • Milo Beckman, "Math Without Numbers" (Dutton, 2020)

    22/02/2021 Duration: 55min

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

  • J. Rosenhouse, "Games for Your Mind: The History and Future of Logic Puzzles" (Princeton UP, 2020)

    25/01/2021 Duration: 56min

    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 a

  • Snezana Lawrence, "A New Year's Present from a Mathematician" (CRC Press, 2019)

    08/01/2021 Duration: 55min

    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

  • James D. Stein, "The Fate of Schrodinger's Cat: Using Math and Computers to Explore the Counterintuitive" (World Scientific, 2020)

    07/12/2020 Duration: 01h15min

    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 e

  • Anna Weltman, "Supermath: The Power of Numbers for Good and Evil" (Johns Hopkins UP, 2020)

    01/12/2020 Duration: 01h47min

    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

  • Alfred S. Posamentier, "The Joy of Geometry" (Prometheus, 2020)

    11/11/2020 Duration: 57min

    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/adchoices

  • Susan D'Agostino, "How to Free Your Inner Mathematician: Notes on Mathematics and Life" (Oxford UP, 2020)

    29/09/2020 Duration: 01h04min

    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.

  • Alfred Posamentier, "Mathematics Entertainment for the Millions" (World Scientific Publishing, 2020)

    09/09/2020 Duration: 57min

    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/adchoices

  • David J. Hand, "Dark Data: Why What You Don't Know Matters" (Princeton UP, 2020)

    04/09/2020 Duration: 01h17min

    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 wide-ranging 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 cutting-edge 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. Suggeste

  • David Bressoud, "Calculus Reordered: A History of the Big Ideas" (Princeton UP, 2019)

    24/08/2020 Duration: 01h27min

    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 Galil

  • Satyan Devadoss, "Mage Merlin's Unsolved Mathematical Mysteries" (MIT Press, 2020)

    13/08/2020 Duration: 57min

    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/adchoices

  • Cailin O’Connor, "Games in the Philosophy of Biology" (Cambridge UP, 2020)

    10/07/2020 Duration: 01h06min

    The branch of mathematics called game theory – the Prisoners Dilemma is a particularly well-known example of a game – is used by philosophers, social scientists, and others to explore many types of social relations between humans and between nonhuman creatures. In Games in the Philosophy of Biology (Cambridge University Press, 2020), Cailin O’Connor introduces the basics of game theory and its particular branch, evolutionary game theory, and discusses how game theoretic models have helped explain the genesis of the meanings of linguistic and nonlinguistic signals, altruistic behavior, the spread of misinformation, and the origins of fair and unfair distributions of benefits in society. O’Connor, who is associate professor of logic and philosophy of science at the University of California–Irvine, also considers some of the drawbacks of game theoretic models. Her short introduction makes a major area of social scientific investigation accessible to readers without mathematical background.   Learn more about you

  • B. Fong and D. I. Spivak, "An Invitation to Applied Category Theory: Seven Sketches in Compositionality" (Cambridge UP, 2019)

    08/07/2020 Duration: 02h01min

    Category theory is well-known for abstraction—concepts and tools from diverse fields being recognized as specific cases of more foundational structures—though the field has always been driven and shaped by the needs of applications. Moreover, category theory is rarely introduced even to undergraduate math majors, despite its unifying role in theory and its flexibility in application. Postdoctoral Associate Brendan Fong and Research Scientist David I. Spivak, both at MIT, have written a marvelous and timely new textbook that, as its title suggests, invites readers of all backgrounds to explore what it means to take a compositional approach and how it might serve their needs. An Invitation to Applied Category Theory: Seven Sketches in Compositionality (Cambridge University Press, 2019) has few mathematical prerequisites and is designed in part as a gateway to a wide range of more specialized fields. It also centers its treatment on applications, motivating several key developments in terms of real-world use cas

  • Ben Cohen, "The Hot Hand: The Mystery and Science of Streaks" (Custom House, 2020)

    25/06/2020 Duration: 43min

    For decades, statisticians, social scientists, psychologists, and economists (among them Nobel Prize winners) have spent massive amounts of precious time thinking about whether streaks actually exist. After all, a substantial number of decisions that we make in our everyday lives are quietly rooted in this one question: If something happened before, will it happen again? Is there such a thing as being in the zone? Can someone have a “hot hand”? Or is it simply a case of seeing patterns in randomness? Or, if streaks are possible, where can they be found? In The Hot Hand: The Mystery and Science of Streaks (Custom House, 2020), Wall Street Journal reporter Ben Cohen offers an unfailingly entertaining and provocative investigation into these questions. He begins with how a $35,000 fine and a wild night in New York revived a debate about the existence of streaks that was several generations in the making. We learn how the ability to recognize and then bet against streaks turned a business school dropout named Dav

  • Brian Greene, "Until the End of Time: Mind, Matter, and Our Search for Meaning in an Evolving Universe" (Random House, 2020)

    02/06/2020 Duration: 02h37s

    Brian Greene is a Professor of Mathematics and Physics at Columbia University in the City of New York, where he is the Director of the Institute for Strings, Cosmology, and Astroparticle Physics, and co-founder and chair of the World Science Festival. He is well known for his TV mini-series about string theory and the nature of reality, including the Elegant Universe, which tied in with his best-selling 2000 book of the same name. In this episode, we talk about his latest popular book Until the End of Time: Mind, Matter, and Our Search for Meaning in an Evolving Universe (Random House, 2020) Until the End of Time gives the reader a theory of everything, both in the sense of a “state of the academic union”, covering cosmology and evolution, consciousness and computation, and art and religion, and in the sense of showing us a way to apprehend the often existentially challenging subject matter. Greene uses evocative autobiographical vignettes in the book to personalize his famously lucid and accessible explanati

  • sarah-marie belcastro, "Discrete Mathematics with Ducks" (CRC Press, 2018)

    29/05/2020 Duration: 32min

    Introductory courses in discrete mathematics cover a variety of distinctive but interconnected topics, from the underpinnings of logic and set theory through overviews of combinatorics and graph theory, which lend themselves to equally diverse presentation styles. In Discrete Mathematics with Ducks (Second Edition; CRC Press, 2018), dr. sarah-marie belcastro has reimagined both course and text. The book is written in an accessible and lighthearted style yet covers the full breadth of conventional topics and several more besides: Early chapters include much valuable advice on how to read, do, and write mathematics—essential points of reference for the mathematically inexperienced or disinclined. Meanwhile, the book includes an introductory chapter on algorithms and several bonus chapters, for example on number theory and on complexity, which instructors and interested students can subset as they please. Each chapter is arranged to support a week of gentle prep reading and discovery-based classroom activity. Th

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