New Books in Mathematics

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 His...

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...

From 1667 to 1676, a pivotal controversy played out among several mathematical luminaries of the time, partly in the proceedings of the Royal Society but partly in private correspondence. The controversy concerned whether an infamous problem of Ancient Greek geometry, the quadrature of the central conic sections (better known as squaring the circle), could be solved using the classical tools of st...

Today I talked with Chris Bernhardt about his book Quantum Computing for Everyone (MIT Press, 2019). This is a book that involves a lot of mathematics, but most of it is accessible to anyone who survived high school algebra.  Even a math-phobic can read the book, skip the math, and then more than hold his or her own in any but the highest-level discussion of quantum computing.  For those of us who...

In the information age, knowledge is power. Hence, facilitating the access to knowledge to wider publics empowers citizens and makes societies more democratic. How can publishers and authors contribute to this process? This podcast addresses this issue. We interview Professor Austin Choi-Fitzpatrick, whose book, The Good Drone: How Social Movements Democratize Surveillance (forthcoming with MIT Pr...

Our guest today is Kartik Hosanagar, the author of A Human’s Guide to Machine Intelligence: How Algorithms Are Shaping Our Lives and How We Can Stay in Control(Viking, 2019). This is one of those rare books that I think everyone can read and I think everyone should read. In fact, knowledge of algorithms can in some sense be considered to be the literacy of the 21st century, and the author has writ...

Andrew C. A. Elliott‘s Is That a Big Number? (Oxford University Press, 2018) is a book that those of us who feast on numbers will absolutely adore, but will also tease the palates of those for whom numbers have previously been somewhat distasteful.  This book helps us not only to realize the relative magnitudes of many of the numbers which surround us, but also helps us understand precisely how an...

Most of us have heard of the math-music connection, but Eli Maor’s Music by the Numbers: From Pythagoras to Schoenberg (Princeton University Press, 2018) is THE book that explains what that connection is, and how both math and music connect to both physics and biology.  There are wonderful anecdotes detailing the lives and creations of many of the great musicians, mathematicians, scientists, and p...

Today I talked to Vicky Neale about her new book Closing the Gap: The Quest to Understand Prime Numbers (Oxford University Press, 2017). The book details one of the most exciting developments to happen in the last few years in mathematics, a new approach to the Twin Primes Conjecture. The story involves mathematicians from five different centuries and probably every continent except Antarctica. Vi...

The book discussed here is the The Joy of Mathematics (Prometheus Books, 2017), whose lead author, Alfred Posamentier, is our guest today. The subtitle Marvels, Novelties, and Neglected Gems That Are Rarely Taught in Math Classdescribes the book nicely. Much of the book can be read by someone with only a couple of years of high school math, and the book does a terrific job of showing the reader wh...

Big Data: How the Information Revolution Is Transforming Our Lives (Icon Books, 2017), by Brian Clegg, is a relatively short book about a subject that has emerged only recently, but is rapidly becoming a significant force in the evolution of society. Most of us have heard the term “big data,” but many of us erroneously assume that its just a lot of little data. It’s considerably more than that, an...

Brian Clegg is one of England’s most prolific and popular writers on science. His latest work, The Reality Frame: Relativity and Our Place in the Universe (Icon Books, 2017), covers Einstein’s Theories of Relativity and a whole lot more. Simply as an exposition of Einstein’s theories, the book is excellent its beautifully organized and delivered, with Clegg’s usual clarity and insight. But what ma...

The book discussed here is entitled The Calculus of Happiness: How a Mathematical Approach to Life Adds Up to Health, Wealth, and Love (Princeton University Press, 2017) by Oscar Fernandez. If the thought of calculus makes you nervous, don’t worry, you won’t need calculus to enjoy and appreciate this book. Its actually an intriguing way to introduce some of the precalculus topics that will later b...

For many cognitive scientists, psychologists, and philosophers of mind, the best current theory of cognition holds that thinking is in some sense computation “in some sense,” because that core idea can and has been elaborated in a number of different ways that are or at least seem to be incompatible in at least some respects. In Unifying the Mind: Cognitive Representations as Graphical Models (MIT...

If ever there were a course that needs a book like Raffi Grinberg’s The Real Analysis Lifesaver: All the Tools You Need to Understand Proofs (Princeton University Press, 20170, analysis is unquestionably it, and I only wish that Raffi had gotten into the wayback machine and delivered me a copy when I was taking this course more than half a century ago. I got a C+, and almost certainly would have d...

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...

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...

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, t...

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 pare...

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...

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 tha...

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 devis...

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 th...

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 uni...

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?”, man...