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 straightedge and compass. While its impossibility would not be rigorously proven for two more centurie...
Aug 28, 2019•1 hr 1 min•Ep. 37
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 love math, the underlying math is elegantly simple and beautifully presented – and the same can be sa...
May 02, 2019•56 min•Ep. 36
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 Press ) is undergoing a Massive Online Peer-Review (MOPR) process, where everyone can make comments o...
Mar 19, 2019•32 min•Ep. 15
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 written a book which can greatly held advance this type of literacy. If you want to become 21st-centur...
Mar 12, 2019•56 min•Ep. 35
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 and why our understanding of the universe often comes down to the numbers which describe it. It’s just...
Nov 09, 2018•53 min
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 philosophers who have contributed to creating music and our understanding of it. If you love music – a...
Jul 18, 2018•56 min
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. Vicky does a great job of telling not only what the problem is and how work on it has proceeded, but a...
Dec 12, 2017•55 min
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 why those of us who love math do so. We like arithmetic, algebra, geometry, infinity, and the count...
Oct 16, 2017•57 min
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, and Big Data, which is an easy and fun read, serves as a terrific introduction to a topic which has a...
Sep 19, 2017•55 min
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 makes the book transcend the usual work on this subject is that Clegg looks at relativity as a concept...
Jun 29, 2017•52 min
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 be needed in a calculus class, through the examination of some of the basic mathematical ideas that ...
Jun 11, 2017•54 min
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 Press, 2014), David Danks proposes a version of this basic theory that links the mind closely with ...
May 15, 2017•1 hr 9 min
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 done a lot better if I’d had this book, and so will present and future students who struggle with thi...
Feb 15, 2017•54 min
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 t...
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 a...
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 a...
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 ...
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 citiz...
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 especial...
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
