New Books in Mathematics

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 ne...

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 ente...

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 mag...

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 arg...

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 “Ameri...

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 should...

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 needin...

[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...

[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 ch...

[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...

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...

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 tak...

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)...

[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...

[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 wa...

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 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 Sw...

[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 f...

The book discussed in this interview is Dice World: Science and Life in a Random Universe (Icon Books, 2013), by Brian Clegg, an acclaimed British writer of books on science for the general public. Brian has a knack for taking concepts that seem abstruse and explaining them in ways that those who lack a technical background can readily understand. This talent is on display inDice World, where he t...

Today I talked to Leonard Wapner about his new book Unexpected Expectations: The Curiosities of a Mathematical Crystal Ball (A.K. Peters, 2012).  Prof. Wapner’s previous book, The Pea and the Sun, was an in-depth investigation of the Banach-Tarski Theorem, one of the most counterintuitive results in mathematics.  Expectation is an extension of the idea of average value, and is a basic tool of prob...

Today we’ll be discussing Lance Fortnow‘s bookThe Golden Ticket:P, NP, and the Search for the Impossible (Princeton University Press, 2013).The book focuses on the challenges associated with solving problems requiring significant computation, such as “What is the largest group of Facebook users, all of whom know each other?”If it is shown that all computational problems can be solved relatively ea...

You may well have seen “Numb3rs,” a TV show in which mathematicians help solve crimes. It’s fiction. But, as Leila Schneps and Coralie Colmez show in their eye-opening new book Math on Trial: How Numbers Get Used and Abused in the Court Room (Basic Books, 2013) math does play a role in criminal prosecution. Alas, it’s often bad math and, as such, often leads to bad outcomes: people get off who sho...

Challenging conventional modes of understanding China and the circulation of knowledge within the history of science, Catherine Jami‘s new book looks closely at the imperial science of the reign of the Kangxi Emperor (r. 1662-1722). It focuses on the history of mathematics in this context, but situates the story of mathematics and Kangxi within a larger framework that extends from the late Ming th...

Roger Hart‘s The Chinese Roots of Linear Algebra (Johns Hopkins University Press, 2011) is the first book-length study of linear algebra in imperial China, and is based on an astounding combination of erudition and expertise in both Chinese history and the practice and history of linear algebra. Alternating among an interdisciplinary array of materials and ideas that range from the Nine Chapters o...