New Books In Mathematics

Today I’m talking with Lynn Gamwell about Mathematics and Art: A Cultural History (Princeton University Press, 2015). This book is a breathtaking combination of scholarship and beauty, tracing the interplay of mathematics and art throughout mankind’s history, East and West. Gamwell is a lecturer in the history of mathematics and science at the School of Visual Arts in New York, and thus she is uniquely positioned to write a book that brings together the two disparate cultures described by C.P. Snow in his 1959 essay. Snow would have appreciated how the author communicates the depth, passion, and beauty that characterize each culture, while describing how each inspires the other. The in-depth discussion is brought to life by 440 stunning artworks and 102 crystal-clear math diagrams. This is a big, beautifully produced book that you will want to place on your coffee table.Learn more about your ad choices. Visit megaphone.fm/adchoices

Brian Clegg, who is arguably the most prolific science writer since Isaac Asimov, and almost certainly the most prolific British one, has written a delightfully tantalizing book entitled How Many Moons Does the Earth Have? The Ultimate Science Quiz Book (Icon Books, 2015). It’s a delectable collection of science quiz questions – and although it includes classics such as “Why Is the Sky Blue?”, many will seriously challenge even the most knowledgeable. You may finish the quiz a lot more humble about your scientific knowledge (as did your humbled correspondent), but that is more than compensated by how much you’ll learn about some of the more intriguing and sometimes lesser-known aspects of science — and how much you’ll enjoy it. And isn’t that why you want to read about science in the first place?Learn more about your ad choices. Visit megaphone.fm/adchoices

Who made life risky? In his dynamic new book, How Our Days Became Numbered: Risk and the Rise of the Statistical Individual (University of Chicago Press, 2015), historian Dan Bouk argues that starting in the late nineteenth century, the life-insurance industry embedded risk-making within American society and American psyches. Bouk is assistant professor of history at Colgate University, and his new book shows how insurers categorized individuals and grouped social classes in ways that assigned monetary value to race, class, lifestyles, and bodies. With lively prose, Bouk gives historical context and character to the rise of the “statistical individual” from the Guided Age to the New Deal. Bouk’s primary argument is that risks did not always already exist, nor was risk invented by the medical establishment. Instead, the threat (and reality) of economic crisis helped insurers to create risk as a commodity, and eventually to control the lives it measured. As Bouk phrases it in the interview, &#

John Allen Paulos, who has accomplished the unheard-of double of writing best-sellers about mathematics and inserting a word (‘innumeracy’) into the language, has attempted another ambitious feat – bringing mathematics to bear on one of the few subjects it has yet to examine: biography and autobiography. A Numerate Life (Prometheus Books, 2015) is simultaneously a charming memoir and a highly entertaining venture into mathematics, literature, and philosophy. This is one of those rare books that, when you have finished a section, you are torn between going on to the next section and re-reading the last section to make sure that you got everything out of it. The subtitle of the book is “A Mathematician Explores the Vagaries of Life, His Own and Probably Yours”. You’ll be a little skeptical about that subtitle before you read the book, but when you finish it, you’ll realize the subtitle nails it — he’s talking, not just about himself, but about you. fascinati

Today we’ll be talking about The Magic of Math (Basic Books, 2015)by Arthur Benjamin. This is a book that has the gee-whiz feeling you got when you first encountered George Gamow’s classic One, Two, Three … Infinity, but brought up to date and with much more in the way of solid mathematics that students can actually use. What makes this book especially appealing is that Benjamin emphasizes the magic that can be found in the mathematics that students study as they proceed through elementary and secondary schools. Students study arithmetic, algebra, geometry, and trigonometry, but too often the way these courses are taught resembles hospital food – nourishing but tasteless. Every teacher should have a copy of The Magic of Math to help combat the blandness and boredom that students too often experience in the classroom.Learn more about your ad choices. Visit megaphone.fm/adchoices

Almost 400 years ago, Galileo wrote that the book of nature is written in the language of mathematics. Today, mathematics is integral to physics and chemistry, and is becoming so in biology, economics, and other sciences, although amid great controversy. The messy reality of biological creatures and their social relations cannot be captured in mathematical models or computer simulations, it is argued. But what is the relation between mathematics and physical reality? Do highly abstract mathematical formalisms and computer simulations yield empirical knowledge? If so, when, and how? In Reconstructing Reality: Models, Mathematics and Simulations (Oxford University Press, 2015), Margaret Morrison, Professor of philosophy at the University of Toronto, considers the epistemological status of the results of modeling and simulation as compared, and typically contrasted with, the results of experiment. She argues that no sharp distinction between simulating the world and measuring the world can be drawn in modern sci

Christopher J. Phillips‘ new book is a political history of the “New Math,” a collection of curriculum reform projects in the 1950s & 1960s that were partially sponsored by the NSF and involved hundreds of mathematicians, teachers, professors, administrators, parents, and students. The New Math: A Political History (University of Chicago Press, 2015) explores the formation of an idea of the “American subject” in an environment where math was considered to be a component of intelligent citizenship. As classrooms became sites shaped by Cold War politics, efforts to reform mathematics curricula were bound up in ideas of subjectivity and discipline. Phillips pays special attention to the work of the School Mathematics Study Group (SMSG) in this context, looking closely at the textbooks that the SMSG produced for children studying at a range of levels. Importantly, The New Math explores not just the production of these textbooks but also what happened when they were actually broug

The book discussed in this interview is Zombies and Calculus (Princeton University Press, 2014) by Colin Adams.   This is a truly unique book; a novel written in the first-person by the survivor of a zombie apocalypse who has managed to make it that far thanks to his knowledge of calculus.  The author starts his narrative by warning the reader that the book is not for the squeamish, but you shouldn’t be deterred by that, as I found the zombies to be more comical than horrific.  The book is especially worthwhile for the way it introduces some of the really intriguing applications of calculus that are not typically found in the standard three-semester calculus sequence, and the author has done a good job of making those applications relevant to his tale.  In an era when education competes with entertainment for attention – and generally fights a losing battle – books such as Zombies and Calculus are to be applauded.  They may prevent some of those taking math courses from becoming classroom zo

The book discussed in this interview is How Not To Be Wrong: The Power of Mathematical Thinking (Penguin Press, 2014), by Jordan Ellenberg.  This is one of those rare books that belong on the reading list of every educated person, especially those who love mathematics, but more importantly, those who hate it.  Ellenberg succeeds in explaining the value of mathematical reasoning without ever needing to go into technical detail, which makes the book ideal for those who want to learn why mathematics is so important.  What makes the book doubly delightful is Ellenberg’s writing style; he intersperses the math with amusing anecdotes, dispensed with a sense of humor rarely found in books such as this.  The book is chock-full of OMG moments; the introductory anecdote about Abraham Wald and the missing bullet holes absolutely whets the appetite for more and Ellenberg never fails to deliver.Learn more about your ad choices. Visit megaphone.fm/adchoices

[Re-published with permission from Inspired by Math] Sue VanHattum is a math professor, blogger, mother, author/editor, and fundraiser. She’s a real powerhouse of motivation for making math fun and accessible to more of our young folks. Sue has teamed up with a number of writers to compile a book, Playing With Math, which she is producing in partnership withMaria Droujkova in a community sponsored publication model. Sue and I shared a delightful chat about what math is, what the book is about, and how we can all get more inspired to engage in math with our kids. And, Sue sprinkles the conversation with some interesting open-ended math problems. Think part coffee table conversation part math circle.Learn more about your ad choices. Visit megaphone.fm/adchoices

[Re-published with permission from Inspired by Math] The MAA (Mathematical Association of America) sent me a review copy of their new book Learning Modern Algebra: From Early Attempts to Prove Fermat’s Last Theorem. I don’t typically review textbooks but the title and then the contents of the book convinced me that I needed to interview the authors. Joe Rotman wasn’t available but I was able to chat with the other co-author, Al Cuoco. I was really struck with Al’s passion about teaching the teachers as well as the students. Al shared some great insights about the ingredients that I think should go into every math textbook to help teachers and students to develop the right habits of mind to succeed. Here are some of the questions we discussed. 1. What is your background and your experience teaching high school math to students and to teachers? 2. I attended the Ross program and you have a key role in a program that has its roots in the Ross program. Tell me about this program and your i

[Re-posted with permission from Sol Lederman’s Wild About Math] I love novel ways of looking at arithmetic. I’m fascinated with how computers compute in binary, with tricks for simplifying calculations and with how Vedic mathematicians handle difficult arithmetic efficiently. So, when Princeton University Press sent me a review copy of their new book Count Like an Egyptian: A Hands-on Introduction to Ancient Mathematics (Princeton University Press, 2014), I immediately fell in love with it. I was delighted to learn even more techniques and the ideas behind them to deepen my appreciation of the beauty of what most consider to be mundane arithmetic. Count Like an Egyptian is a delightful book, full of color illustrations, fun stories, lots of hands-on exercises, and an appreciation for the power of simple but deep ideas. David Reimer was a pleasure to interview. He is a brilliant mathematician who hasn’t lost sight of the power and beauty of mathematics. He taught me and modeled that, despite

A conceptual space sounds like a rather nebulous thing, and basing a semantics on conceptual spaces sounds similarly nebulous. In The Geometry of Meaning: Semantics Based on Conceptual Spaces (MIT Press, 2014), Peter Gardenfors demonstrates that this need not be the case. Indeed, his research is directed towards establishing a formal, mathematically-grounded account of semantics, an account which – as expounded here – is nevertheless accessible. In this interview we discuss the essence of this proposal, focusing in particular on its implications for linguistic analysis, but also touching upon its relation to cognitive science and other related fields. The proposal makes testable predictions about the organization of individual linguistic systems, as well as their acquisition (and potentially their evolution over time). Notably, the “single domain constraint” posits that individual lexical items refer to convex regions of single domains. We discuss the significance of this idea as a bri

The book discussed in this interview is Everyday Calculus: Discovering the Hidden Math All around Us (Princeton University Press, 2014) by Oscar E. Fernandez, who teaches mathematics – and calculus in particular – at Wellesley College.  While it can be read by someone who wants to obtain a sense of what calculus is and how it’s used, it is even more enjoyable and enlightening if the reader has taken the first semester of a calculus course.  The author takes the reader through a day in the author’s life, during which things one typically encounters – stock price quotations, cooling cups of coffee, getting good seats at a movie – afford an opportunity to investigate how calculus explains these everyday occurrences.  Fernandez also introduces some instances where calculus has totally unexpected applications to our lives – why our GPS system relies upon Einstein’s Theory of Relativity, and why we obtain electricity via alternating current rather than direct current.

When we’re faced with a choice between Door #1, Door #2, and Door #3, how do we infer correctly that there’s an equal chance of the prize being behind any of the doors? How is it that we are generally correct to choose the shorter of two checkout lines in the supermarket when we’re in a hurry? In his new book, Tychomancy: Inferring Probability from Causal Structure (Harvard University Press, 2013), Michael Strevens – professor of philosophy at New York University, argues that we are all equipped with a reliable, probable innate, and not fully conscious skill at probabilistic reasoning—a “physical intuition” that enables us to infer physical probabilities from perceived symmetries. This skill is found in six-month-old infants watching as red and white balls are removed in different proportions from an urn. But it also underlies important advances in the sciences, such as James Clerk Maxwell’s reasoning when he hit upon the correct distribution of velocities of a

[Re-posted with permission from Wild About Math] My favorite kind of math challenges are those that children can understand and professional mathematicians can’t solve easily (or at all.) Math Bytes: Google Bombs, Chocolate-Covered Pi, and Other Cool Bits in Computing (Princeton University Press, 2014) is a brand new book from Princeton University Press that has a great collection of fun problems that kids (middle school and above) and their parents can work on together. Author Tim Chartier does a fantastic job of weaving some wonderful stories into his sharing of a number of challenges that are either original or new spins on old problems. And, many (all?) of the puzzles in the book are classroom tested. Tim is a mathematician and a professional mime. He’s got a neat relationship with the Mathematical Association of America, and with the Museum of Mathematics in New York City. He’s got a DVD course coming out, and a second book. Tim is quite the math celebrity and a really great guy. I thin

[Re-posted with permission from Wild About Math] I’ve admitted before that Physics and I have never gotten along. But, science fiction is something I enjoy. So, when Princeton University Press sent me a copy of Physics Professor Chuck Adler‘s new book Wizards, Aliens, and Starships: Physics and Math in Fantasy and Science Fiction (Princeton University Press, 2014), I was intrigued enough that I wanted to interview the author. This interview rambled, but in a good way. Chuck is a great guest, he’s passionate about physics and math as well as fantasy and science fiction. We flowed through a number of subjects and had a grand time.Learn more about your ad choices. Visit megaphone.fm/adchoices

Beautiful Geometry (Princeton UP, 2014), by the mathematician prof. Eli Maor and the noted artist Eugen Jost.  It’s a fascinating collaboration which helps to bridge the gap deplored by C. P. Snow in his classic The Two Cultures.  If you’re a lover of geometry, you’ll find some of your favorites depicted here – as well as a number of theorems that will undoubtedly be new to many readers (including the interviewer).  Each result is accompanied by an original work of art by Eugen Jost.  It’s fascinating not only to read about some of the more piquant results in a field (geometry) that is more than 2,500 years old, but just as delightful to see how these results inspire the creativity of an artist.  If you come for the geometry, you’ll certainly stay for the artwork – and if your interest is in art, you’ll be intrigued by how a presumably dry subject such as geometrical theorems can give birth to works of exquisite beauty.Learn more about your ad choices. Visit meg

The book discussed in this interview is Love and Math: The Heart of Hidden Reality Basic Books, 2013) by Edward Frenkel of the University of California at Berkeley.It’s a toss-up which is more interesting – the description of Frenkel’s life or his description of his interest in – and love for – mathematics and physics. Before he was twenty years old, Frenkel had written a paper that a visiting Swedish physicist thought so intriguing that he smuggled it out of Russia.That paper started Frenkel on a career which resulted in his collaborating with some of the world’s foremost mathematicians and physicists – and to his writing Love and Math. It’s a fascinating read.Learn more about your ad choices. Visit megaphone.fm/adchoices

[Re-posted with permission from Wild About Math] I had the pleasure of interviewing mathematician and mathematical card magic innovator Colm Mulcahy. Dr. Mulcahy just published a book, Mathematical Card Magic: Fifty-Two New Effects (A K Peters, 2013) We spent a delightful hour discussing his book, his love of math and magic, and the inspiration behind writing the book. Plus, Dr. Mulcahy shares a few challenges listeners might enjoy chewing on, sprinkled throughout the interview. And, we discuss Martin Gardner, who Colm Mulcahy knew for the last decade of his life and met with several times. You may also enjoy Shecky’s text interview with Colm Mulcahy at Math Tango.  Learn more about your ad choices. Visit megaphone.fm/adchoices