Mathematics: Rhyme and Reason

Mathematics: Rhyme and Reason is like a good thriller novel — you can’t put it down. I read this relatively short book (177 pages, including appendices) in one sitting. Currie’s book is part of the Mathematical Circles Library series, which is published “in the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life (among) young people, their parents and teachers, and the mathematics profession.” Based on a sample of one I would say Currie’s book should go a long way towards accomplishing this goal.

The book is partly a biography of a truly fascinating man and partly a tour of what Currie thinks are some of math’s greatest treasures — he chose very well indeed. Currie grew up in Pittsburgh’s Little Italy and first developed an interest in mathematics when he attended a lecture at what was then Carnegie Institute of Technology (now Carnegie Mellon University). He ended up at Yale due to a fascinating sequence of events which I will leave for you to discover as you read the book.

This immensely interesting (and slightly quirky) book consists of the author’s take on a set of increasingly difficult ideas from all branches of mathematics along with wonderful anecdotes of various mathematicians Currie has met through the years. Spoiler alert — Currie is by far the most interesting of the many interesting people he introduces to us. Nonetheless, many of math’s most interesting folk crossed paths with the author, including Abraham Robinson (the inventor of non-standard analysis), who taught him set theory, and the eccentric genius Paul Erdős. Read the book to discover why Curie thinks those who hosted Erdős in their homes should post a sign outside proclaiming that Paul Erdős Never Slept Here. Here’s a hint as to why in the form of a poem:

It is six in the morning
The house is asleep
Nice music is playing
I prove and conjecture.

Paul Erdős for Vera Sos

I really enjoyed the chapters on primes, the Fibonacci Sequence, Gandhi’s formula for the next prime, and the Euler Line. That being said my favorite was titled Which is Bigger (\(a^b\) versus \(b^a\)), which I plan on using as an example of max/min problems in my next Calculus class. In Chapter 5: Some Things Add Up. Some Don’t we meet the author’s daughter at age 9 or 10. Currie reports asking her what the series \[\frac12+\frac14+\frac18+\dots\] might add up to. A few days later he asks her if she had thought much about it. In response she offers her opinion that it probably adds up to one and provides and nice argument in support of her claim!

In a chapter entitled simply Dissertation the author describes his Ph.D. work at the University of Pittsburgh, which he began after 6 years away from formal mathematics: three as an economic analyst for Gulf Oil and three more in Dusseldorf teaching mathematics. His thesis constructs what he calls a unique-point topological space \(S\) in which for each point \(p\) and each non-negative real number \(r\) there is a unique point in \(S\) that is \(r\) units from \(p\). Currie doesn’t offer as much detail as I would have liked, but informs us that the space consists of a metric on the irrational numbers.

I’m going to stop here so as to leave the fun of reading this little gem to you. Buy this book. Give a copy to any high school or early college students you hope to recruit to mathematics. If you ever get a chance to meet Currie or hear him speak — go!

Buy Now

Richard Wilders is Professor of Mathematics and Marie and Benice Gantzert Professor of the Liberal Arts and Sciences and North Central College in Naperville. While he did not have the pleasure of taking a course from Abraham Robinson he did attend a lecture on non-standard analysis he gave at The Ohio State University. To the horror of the graduate students in attendance, a large contingent of the analysis faculty at Ohio State stood up and walked out in the middle of Robinson’s lecture!