Matthew L. Jones’s wonderful new book traces a history of failed efforts to make calculating machines, from Blaise Pascal’s work in the 1640s through the efforts of Charles Babbage in the nineteenth century, incorporating an account of both the work and relationships of scholars and artisans, and their reflections on the nature of invention. Innovative in its approach and its form, Reckoning with Matter: Calculating Machines, Innovation, and Thinking about Thinking from Pascal to Babbage (Univer...
Jan 23, 2017•1 hr 5 min
Brian Clegg’s Are Numbers Real? The Uncanny Relationship of Mathematics and the Physical World (St. Martin’s Press, 2016) is a compact, very readable, and highly entertaining history of the development and use of mathematics to answer the important practical questions involved in advancing civilization. The question “Are Numbers Real?” is a terrific way to attack the problem so compellingly stated by the physicist Eugene Wigner what accounts for the unreasonable effectiveness of mathematics in d...
Jan 04, 2017•53 min
The book discussed here is Ian Stewart’s Calculating the Cosmos: How Mathematics Unveils the Universe (Basic Books, 2016). If you would like to read a book that in my opinion represents the nicest job of presenting astronomy and cosmology in one volume since Isaac Asimov wrote The Universe half a century ago, this is absolutely the one to get. In addition, for those of us who are lovers of math, this book does a far better job than Asimov of presenting the close relationship between mathematics,...
Dec 29, 2016•56 min
From the title, you might guess that Alfred Posamentier and Stephen Krulik’s Effective Techniques to Motivate Mathematics Instruction (Routledge, 2016) is aimed at mathematics teachers which it is. However, the techniques and strategies discussed in the book can be effectively employed by a much larger group of people, and one who hasconsiderably more influence with students. Those people are parents, who play as large or larger a role in their children’s education than do teachers. Learn more a...
Oct 01, 2016•55 min
Alfred S. Posamentier and Robert Geretschlager, The Circle: A Mathematical Exploration Beyond the Line (Prometheus Books, 2016) goes considerably beyond what its modest title would suggest. The circle has played a pivotal role–that’s “role” with an ‘e,’ but its ability to “roll” with an ‘l’–has helped produce our industrial civilization. Moreover, the circle appears in our art, our literature, and our culture as well. This delightful book will not only reacquaint readers with the pleasures of th...
Sep 11, 2016•56 min
Jennifer Beineke and Jason Rosenhouse‘s new book The Mathematics of Various Entertaining Subjects: Research in Recreational Math (Princeton University Press, 2015) covers a multitude of topics and is in many ways as entertaining as the various subjects it describes. Even though the book can be skimmed simply to expose one to various aspects of recreational mathematics, I think it’s fair to say that some mathematical background is needed to fully appreciate it. But even if you’re only willing to ...
May 23, 2016•55 min
Adam Kucharski, who won the 2012 Wellcome Trust Science Writing Prize, has delivered another winner in an area rife with both winners and losers. The Perfect Bet: How Science and Math Are Taking the Luck Out of Gambling (Basic Books, 2016) is a brilliant, fascinating, and sometimes slightly terrifying look at how math and science are not just conquering gambling, the algorithms that math has devised and the computerized means of implementing them are paradoxically simultaneously removing risk an...
Mar 31, 2016•53 min
Romance. Crime. Mathematics. These things do not go together. Or do they? James D. Stein thinks they do, and he admirably shows us how in his wonderful collection of stories L.A. Math: Romance, Crime, and Mathematics in the City of Angels (Princeton University Press, 2016). Jim’s a mathematician, but don’t let that put you off: he’s the author of several popular books and an excellent writer at that. In this interview we talk about writing “clean”, math-phobia, and what everyone should really kn...
Feb 24, 2016•1 hr
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. S...
Jan 05, 2016•59 min
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 ab...
Dec 07, 2015•54 min
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 m...
Nov 23, 2015•44 min
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,...
Nov 12, 2015•54 min
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 s...
Sep 30, 2015•56 min
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 mathemati...
Jul 15, 2015•1 hr 9 min
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 citizenshi...
Mar 26, 2015•1 hr 8 min
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 especiall...
Oct 15, 2014•53 min
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 ...
Jul 08, 2014•55 min
[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, a...
Jun 26, 2014•1 hr 3 min
[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 teac...
Jun 20, 2014•1 hr 15 min
[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 wa...
Jun 09, 2014•1 hr 18 min
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 p...
Jun 09, 2014•45 min
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...
Apr 17, 2014•54 min
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...
Apr 15, 2014•1 hr 1 min
[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...
Apr 08, 2014•1 hr 13 min
[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’...
Feb 14, 2014•2 hr 36 min
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 fascinati...
Feb 11, 2014•52 min
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...
Nov 08, 2013•57 min
[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 ...
Sep 26, 2013•1 hr 16 min
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 takes the reader on an intriguing trip through the world of probability and statistics, and shows how...
Jun 04, 2013•53 min
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 probability theory that underlies both the gaming and insurance industries. Unexpected Expectations is a f...
May 06, 2013•57 min
