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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

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/adchoices

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

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.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. Learn more about your ad choices. Visit megaphone.fm/adchoices

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/adchoices

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

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 David Booth into a billionaire, and how the subconscious nature of streak-related bias can make the difference between life and death for asylum seekers. We see how previously unrecognized streaks hidden amidst archival data helped solve one of the most haunting mysteries of the twentieth century, the disappearance of Raoul Wallenberg.Cohen also exposes how streak-related incentives can be manipulated, from the five-syllable word that helped break arcade profit records to an arc of black paint that allowed Stephen Curry to transform from future junior high coach into the greatest three-point shooter in NBA history.Crucially, Cohen also explores why false recognition of nonexistent streaks can have cataclysmic results, particularly if you are a sugar beet farmer or the sort of gambler who likes to switch to black on the ninth spin of the roulette wheel.Paul Knepper was born and raised in New York and currently resides in Austin. He used to cover basketball for Bleacher Report and his first book titled Knicks of the Nineties: Ewing, Oakley, Starks and the Brawlers Who Almost Won It All is due out this year. You can reach Paul at paulknepper@gmail.com and follow him on Twitter @paulieknep. Learn more about your ad choices. Visit megaphone.fm/adchoices

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 explanations, and we discuss these episodes further in the interview. Greene also reiterates his arguments for embedding a form of spiritual reverie within the multiple naturalistic descriptions of reality that different areas of human knowledge have so far produced.John Weston is a University Teacher of English in the Language Centre at Aalto University, Finland. His research focuses on academic communication. He can be reached at john.weston@aalto.fi and @johnwphd. Learn more about your ad choices. Visit megaphone.fm/adchoices

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. This makes the book a solid resource for active learning in the mathematics curriculum as well as for independent and group study.Suggested companion work: Daniel Pinkwater, Ducks!Cory Brunson (he/him) is a Postdoctoral Fellow at the Center for Quantitative Medicine at UConn Health. Learn more about your ad choices. Visit megaphone.fm/adchoices

Slavery and the University: Histories and Legacies (University of Georgia Press, 2019), edited by Leslie M. Harris, James T. Campbell, and Alfred L. Brophy, is the first edited collection of scholarly essays devoted solely to the histories and legacies of this subject on North American campuses and in their Atlantic contexts. Gathering together contributions from scholars, activists, and administrators, the volume combines two broad bodies of work: (1) historically based interdisciplinary research on the presence of slavery at higher education institutions in terms of the development of proslavery and antislavery thought and the use of slave labor; and (2) analysis on the ways in which the legacies of slavery in institutions of higher education continued in the post–Civil War era to the present day.The collection features broadly themed essays on issues of religion, economy, and the regional slave trade of the Caribbean. It also includes case studies of slavery’s influence on specific institutions, such as Princeton University, Harvard University, Oberlin College, Emory University, and the University of Alabama. Though the roots of Slavery and the University stem from a 2011 conference at Emory University, the collection extends outward to incorporate recent findings. As such, it offers a roadmap to one of the most exciting developments in the field of U.S. slavery studies and to ways of thinking about racial diversity in the history and current practices of higher education.Today I spoke with Leslie Harris about the book. Dr. Harris is a professor of history at Northwestern University. She is the coeditor, with Ira Berlin, of Slavery in New York and the coeditor, with Daina Ramey Berry, of Slavery and Freedom in Savannah (Georgia).Adam McNeil is a History PhD student at Rutgers University-New Brunswick. Learn more about your ad choices. Visit megaphone.fm/adchoices

Alex Berke's Beautiful Symmetry (MIT Press, 2020) is both a fascinating book and a concept -- it's like no other book I’ve ever read. It's a coloring book about math, inviting us to engage with mathematical concepts visually through coloring challenges and visual puzzles. We can explore symmetry and the beauty of mathematics playfully, coloring through ideas usually reserved for advanced courses. The book is for children and adults, for math nerds and math avoiders, for educators, students, and coloring enthusiasts.Through illustration, language that is visual, and words that are jargon-free, the book introduces group theory as the mathematical foundation for discussions of symmetry, covering symmetry groups that include the cyclic groups, frieze groups, and wallpaper groups. The illustrations are drawn by algorithms, following the symmetry rules for each given group. The coloring challenges can be completed and fully realized only on the page; solutions are provided. Online, in a complementary digital edition, the illustrations come to life with animated interactions that show the symmetries that generated them.Traditional math curricula focus on arithmetic and the manipulation of numbers, and may make some learners feel that math is not for them. By offering a more visual and tactile approach, this book shows how math can be for everyone. Combining the playful and the pedagogical, Beautiful Symmetry offers both relaxing entertainment for recreational colorers and a resource for math-curious readers, students, and educators. Learn more about your ad choices. Visit megaphone.fm/adchoices

Hot Molecules, Cold Electrons: From the Mathematics of Heat to the Development of the Trans-Atlantic Telegraph Cable (Princeton University Press, 2020), by Paul Nahin, is a book that is meant for someone who is comfortable with calculus, but for those readers who are, it is a treat. It is a thorough study of the history and mathematics of the heat equation, which is not only important as an analysis of heat, its analysis marked the beginning of Fourier series. It came as a surprise to me that the heat equation was also instrumental in analyzing the problem of laying the transatlantic cable that was one of the great engineering feats of the nineteenth century. Although it isn’t necessary to work through the math to appreciate this book, I think that students studying this material would not only find Paul’s treatments easy to follow, but would benefit greatly by learning something of the history that surrounds the development of the analysis and applications of the heat equation. Learn more about your ad choices. Visit megaphone.fm/adchoices

Paradox is a sophisticated kind of magic trick. A magician's purpose is to create the appearance of impossibility, to pull a rabbit from an empty hat. Yet paradox doesn't require tangibles, like rabbits or hats. Paradox works in the abstract, with words and concepts and symbols, to create the illusion of contradiction. There are no contradictions in reality, but there can appear to be. In Sleight of Mind: 75 Ingenious Paradoxes in Mathematics, Physics, and Philosophy (MIT Press, 2020), Matt Cook and a few collaborators dive deeply into more than 75 paradoxes in mathematics, physics, philosophy, and the social sciences. As each paradox is discussed and resolved, Cook helps readers discover the meaning of knowledge and the proper formation of concepts―and how reason can dispel the illusion of contradiction.The journey begins with “a most ingenious paradox” from Gilbert and Sullivan's Pirates of Penzance. Readers will then travel from Ancient Greece to cutting-edge laboratories, encounter infinity and its different sizes, and discover mathematical impossibilities inherent in elections. They will tackle conundrums in probability, induction, geometry, and game theory; perform “supertasks”; build apparent perpetual motion machines; meet twins living in different millennia; explore the strange quantum world―and much more. Learn more about your ad choices. Visit megaphone.fm/adchoices

Today I talked to Alfred S. Posamentier, a co-author (with Christian Spreitzer) of Math Makers: The Lives and Works of 50 Famous Mathematicians (Prometheus, 2020). This charming book is more than just mathematics, because mathematicians are not just makers of mathematics. They are human beings whose life stories are often not just entertaining, but are sometimes interwoven with important historical events. Of course you get the math in this book –but I would have read this book just for the fascinating anecdotes. Just for openers, how many other disciplines have people who made remarkable contributions but were arrested for revolutionary activities in their teens, and then killed in a duel at age 21? This is the story of Evariste Galois, just one of the 50 fascinating lives you'll read about in this book. Learn more about your ad choices. Visit megaphone.fm/adchoices

From an undergraduate perspective, coming from the rigid proofs and concrete constructions of middle- or high-school courses, the broad discipline of geometry can be at once intimately familiar and menacingly exotic. For most of its history, and perhaps for many of the same reasons, geometers struggled to come to terms with the unsolved problems, unstated assumptions, and untapped generalizability contained in the "bible of mathematics", Euclid's Elements.In their recent text, Geometry: The Line and the Circle (MAA Press, 2018), Maureen T. Carroll and Elyn Rykken have produced a unified survey of Euclidean and many significant non-Euclidean geometries, one that draws from the patterns of historical development to immerse students into progressively new territory. Their book is organized around the Elements but soon (and often) detours into spherical, finite, and other geometries that bring the limitations of the classic text—and the contributions of subsequent geometers—to the fore. Throughout, they examine the shifting roles and behaviors of two fundamental geometric concepts, the line and the circle—a narrative hook that might deserve more play in mathematics texts! In addition to their historical vignettes, Carroll and Rykken include rich selections of exercises and incorporate a variety of tactile and online tools, and their treatment is held together in an accessible and absorbing writing style. The book is tailored to an upper-level undergraduate course but could also support a history of mathematics or introduction to proofs course.Suggested companion works:Edwin A. Abbott, Flatland: A Romance of Many Dimensions (+ sequels & film adaptations)Norton Juster, The Dot and the Line (+ film adaptation)Cory Brunson (he/him) is a Postdoctoral Fellow at the Center for Quantitative Medicine at UConn Health. Learn more about your ad choices. Visit megaphone.fm/adchoices

How does the world of book reviews work? In Inside the Critics’ Circle: Book Reviewing in Uncertain Times (Princeton University Press, 2020), Phillipa Chong, assistant professor in sociology at McMaster University, provides a unique sociological analysis of how critics confront the different types of uncertainty associated with their practice. The book explores how reviewers get matched to books, the ethics and etiquette of negative reviews and ‘punching up’, along with professional identities and the future of criticism. The book is packed with interview material, coupled with accessible and easy to follow theoretical interventions, creating a text that will be of interest to social sciences, humanities, and general readers alike. Learn more about your ad choices. Visit megaphone.fm/adchoices

If you’re a grad student facing the ugly reality of finding a tenure-track job, you could easily be forgiven for thinking about a career change. However, if you’ve spent the last several years working on a PhD, or if you’re a faculty member whose career has basically consisted of higher ed, switching isn’t so easy. PhD holders are mostly trained to work as professors, and making easy connections to other careers is no mean feat. Because the people you know were generally trained to do the same sorts of things, an easy source of advice might not be there for you.Thankfully, for anybody who wishes there was a guidebook that would just break all of this down, that book has now been written. Going Alt-Ac: A Guide to Alternative Academic Careers (Stylus Publishing, 2020) by Kathryn E. Linder, Kevin Kelly, and Thomas J. Tobin offers practical advice and step-by-step instructions on how to decide if you want to leave behind academia and how to start searching for a new career. If a lot of career advice is too vague or too ambiguous, this book corrects that by outlining not just how to figure out what you might want to do, but critically, how you might go about accomplishing that.Zeb Larson is a recent graduate of The Ohio State University with a PhD in History. His research deals with the anti-apartheid movement in the United States. To suggest a recent title or to contact him, please send an e-mail to zeb.larson@gmail.com. Learn more about your ad choices. Visit megaphone.fm/adchoices

The so-called Sabermetrics revolution in baseball that began in the 1970s, popularized by the book—and later Hollywood film—Moneyball, was supposed to represent a triumph of observation over intuition. Cash-strapped clubs need not compete for hyped-up prospects when undervalued players provide better price per run scored. Q.E.D., right?In Scouting and Scoring: How We Know What We Know About Baseball (Princeton University Press, 2019), historian of science Christopher J. Phillips rejects his titular dualism. He shows us that baseball can be, in the words of seminal anthropologist and noted Tampa Bay Rays fan* Claude Lévi-Strauss, “good to think with.” Both traditional amateur scouts and statistically-savvy scorers rely on metrics and bureaucracy to make their judgments count, as it were. Some like to say that baseball is quantitative at its core, but by tracing the co-evolution of the sport’s competing data sciences—with episodes that bear witness to the development of the modern press and digital computers—Phillips crafts a compelling narrative sure to delight baseball fans and historians of the human sciences alike.*kiddingMikey McGovern is a PhD candidate in Princeton University’s Program in the History of Science. He is writing a dissertation on how people used discrimination statistics to argue about rights in 1970s America, and what this means for histories of bureaucracy, quantification, law, politics, and race. Learn more about your ad choices. Visit megaphone.fm/adchoices

The book we are discussing is by Brian Clegg, a well-known author of books on math and science -- but this is not exactly a book on math or science, although these subjects play a significant role. His latest book is Conundrum: Crack the Ultimate Cipher Challenge (Icon Books, 2019), which should delight and intrigue not only those who love math and science, but those who love solving puzzles. This book is a literary escape room, with a series of puzzles to be solved, all of which contribute to a final puzzle that concludes the book. And like the clues one finds in an escape room, Brian mercifully offers hints for the puzzles. Learn more about your ad choices. Visit megaphone.fm/adchoices

Today's guest is distinguished researcher and statistician, Sir David Spiegelhalter. A fellow of the Royal Society, he is currently Chair of the Winton Centre for Risk and Evidence Communication at the University of Cambridge. He has dedicated his career, in his words to, “improving the way that quantitative evidence is used in society.” This includes (of particular interest to us) biostatistics and medical research.David is an ISI highly cited researcher who has also focused much of his time and energy to public education through numerous media appearances, documentaries such as his recent BBC series geared towards children, and books such as the one we are discussing today.That book, The Art of Statistics: How to Learn from Data, was published in the UK by Penguin in March, 2019 and recently released here in the US by Basic Books in September 2019.Colin Miller and Dr. Keith Mankin host the popular medical podcast, PeerSpectrum. Colin works in the medical device space and Keith is a retired pediatric orthopedic surgeon. Learn more about your ad choices. Visit megaphone.fm/adchoices