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 v...
Jan 08, 2021•56 min•Ep. 58
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 Scie...
Dec 07, 2020•1 hr 16 min•Ep. 57
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 Po...
Dec 01, 2020•1 hr 47 min•Ep. 65
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...
Nov 11, 2020•57 min•Ep. 55
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 mathematic...
Sep 29, 2020•1 hr 5 min•Ep. 54
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...
Sep 09, 2020•58 min•Ep. 53
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 re...
Aug 24, 2020•1 hr 27 min•Ep. 77
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 bo...
Aug 13, 2020•58 min•Ep. 51
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 explai...
Jul 10, 2020•1 hr 7 min•Ep. 223
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 marvelou...
Jul 08, 2020•2 hr 1 min•Ep. 50
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 random...
Jun 25, 2020•43 min•Ep. 164
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...
Jun 02, 2020•2 hr 1 min•Ep. 20
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 conventiona...
May 29, 2020•33 min•Ep. 49
Slavery and the University: Histories and Legacies (University of Georgia Press, 2019), edited by Leslie M. Harris , J ames 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 re...
Apr 28, 2020•1 hr•Ep. 193
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...
Apr 22, 2020•54 min•Ep. 48
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 t...
Apr 03, 2020•52 min•Ep. 47
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...
Mar 30, 2020•54 min•Ep. 46
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 Li...
Feb 26, 2020•50 min•Ep. 44
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...
Feb 25, 2020•42 min•Ep. 154
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 s...
Jan 30, 2020•40 min•Ep. 103
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 tit...
Jan 29, 2020•43 min•Ep. 245
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 ...
Jan 28, 2020•54 min•Ep. 43
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 ...
Dec 13, 2019•1 hr 3 min
From the pyramids of Giza, to quasicrystals, to the proportions of the human face, the golden ratio has an infinite capacity to generate shapes with exquisite properties. This book invites you to take a new look at this timeless topic, with a compilation of research and information worthy of a text book, accompanied by over 200 beautiful color illustrations that transform this into the ultimate coffee table book. In The Golden Ratio: The Divine Beauty of Mathematics (Race Point Press, 2018), Gar...
Nov 22, 2019•41 min•Ep. 31
Today I talked to Julian Havil about his latest book Curves for the Mathematically Curious: An Anthology of the Unpredictable, Historical, Beautiful, and Romantic (Princeton University Press, 2019). You don’t have to be mathematically curious to appreciate Julian’s talent for weaving mathematics and history together – but mathematical curiosity and a year or two of calculus will greatly add to your enjoyment of it. This is not your father’s – or grandfather’s – standard collection of conic secti...
Nov 15, 2019•1 hr•Ep. 41
Throughout the Age of Exploration, European maritime communities bent on colonial and commercial expansion embraced the complex mechanics of celestial navigation. They developed schools, textbooks, and instruments to teach the new mathematical techniques to sailors. As these experts debated the value of theory and practice, memory and mathematics, they created hybrid models that would have a lasting impact on applied science. In Sailing School: Navigating Science and Skill, 1550-1800 (Johns Hopk...
Nov 14, 2019•57 min•Ep. 240
As you may know, university presses publish a lot of good books. In fact, they publish thousands of them every year. They are different from most trade books in that most of them are what you might called "fundamental research." Their authors--dedicated researchers one and all--provide the scholarly stuff upon which many non-fiction trade books are based. So when you are reading, say, a popular history, you are often reading UP books at one remove. Of course, some UP books are also bestsellers, ...
Nov 03, 2019•38 min•Ep. 45
The things that make people academics -- as deep fascination with some arcane subject, often bordering on obsession, and a comfort with the solitude that developing expertise requires -- do not necessarily make us good teachers. Jessamyn Neuhaus ’s Geeky Pedagogy: A Guide for Intellectuals, Introverts, and Nerds Who Want to Be Effective Teachers (West Virginia University Press, 2019) helps us to identify and embrace that geekiness in us and then offers practical, step-by-step guidelines for how ...
Oct 24, 2019•33 min•Ep. 81
The institutional history of mathematics in the United States comprises several entangled traditions—military, civil, academic, industrial—each of which merits its own treatment. David Lindsay Roberts , adjunct professor of mathematics at Prince George's Community College, takes a very different approach. His unique book, Republic of Numbers: Unexpected Stories of Mathematical Americans through History (Johns Hopkins University Press, 2019), anchors 20 biographical chapters to a decadal series o...
Oct 17, 2019•1 hr 14 min•Ep. 38
Our guest today is Al Posamentier , the lead author of Tools to Help Your Children Learn Math (WSPC, 2019). Helping your children with math is one of the most important things a parent can do to further their children’s educational progress, and Al has teamed with other math educators, psychologists, and counselors to write a book which many will find extremely helpful in what is often a difficult and frustrating job. Learn more about your ad choices. Visit megaphone.fm/adchoices Support our sho...
Sep 16, 2019•58 min•Ep. 38
