## Review: The Mystery of the Prime Numbers

Matthew Watkins contacted me out of the blue a while ago, offering me a review copy of his new book, "The Mystery of the Prime Numbers." Not really having a sense of what the book was about but knowing that I like mysteries and prime numbers I happily accepted. When the book arrived I opened it to a few random pages to get a feel for the material. I was immediately hooked. Bear with me while I tell a bit of a story and then I'll get back to what hooked me.

When I was in high school I attended the summer Ross program at the Ohio State University. Professor Arnold Ross taught us number theory. The course was hard, really hard. The problem sets were brutal. But, there was something exhilarating about the program. Part of the thrill was Professor Ross' way of conveying difficult concepts. An equal part of the thrill was the subject itself. Number theory is the kind of subject that lends itself to very rich exploration. It was thrilling that, as a high school student, without a background in advanced mathematics, I could dive into such a rich subject matter that so many consider to be out of reach. I vividly remember Professor Ross telling us to "think deeply of simple things." The message stuck. Much of what we consider to be "advanced" mathematics -- calculus, number theory, and other branches -- are accessible to us if we think deeply of simple things.

Back to Matthew's book. It's about prime numbers. The concepts are simple. There are no equations to scare readers off. There are fun illustrations, by Matt Tweed. The concepts are deep. Matthew dives into the Prime Number Theorem, harmonic decomposition, spiral waves, and much more. The book reads like a fairy tale - a journey for children of all ages into the depths of truly simple mathematics. The book, in my judgment, lives up to its promise of being accessible. It is very entertaining yet remarkably rigorous. It renews my pleasure of finding joy in deep and simple things.

With Matthews's permission I am reproducing the introductory email he sent me.

You may be interested in having a look at (and hopefully blogging about) my new book "The Mystery of the Prime Numbers."

This is volume 1 of a trilogy, with volumes 2 and 3 to follow in 2011–2. This project has grown out of the "Number Theory and Physics Web-Archive" which I created in 2000 and have since curated (current URL here).

Although the highly visual presentation of the book is somewhat unusual, the mathematical content is entirely rigorous. It's aimed at the widest possible audience, so I've been forced to develop explanatory tools that don't involve anything resembling a variable or an equation.

You may recall that there was a sudden proliferation of books about prime numbers a few years ago (du Sautoy's, Sabbagh's, Derbyshire's and a lesser known one by D. Rockmore). These were all ultimately concerned with the Riemann Hypothesis (the Clay Foundation's $1,000,000 prize offer having generated some public interest at that time) and attempted to present compelling historical narratives. This book has a significantly different emphasis: it's concerned solely with *what is known* rather than *how we came to know it* (which has been adequately explored elsewhere). The Riemann Hypothesis will not appear until Volume 2. Volume 1 ends having demonstrated to the reader, in wholly visual terms, how the system of positive integers can be (in a sense) decomposed into a sequence of waves, as discovered by Riemann in the 1850s. It has always struck me as odd that this truly remarkable fact is not generally taught as part of undergraduate mathematics curricula, and many (quite possibly a great majority of) professional mathematicians outside number theory seem unaware, or only vaguely aware, of it. But I believe that I've succeeded in explaining it in a way that anyone with a basic level of intelligence and focus can understand.

Robert Fuller (former Columbia University physicist, author of the seminal text book "Mathematics for Classical and Quantum Physics") has described it as a "pedagogical tour de force" (and "clearer than du Sautoy"). Brian Josephson (Cambridge Nobel physics laureate) has responded to the book with similar enthusiasm, both scientists having expressed an eagerness to read the next two volumes.

If you could provide me with a postal address, I'll happily send you a review copy.

Thanks!

Matthew Watkins

The Mystery of the Prime Numbers is self-published. You can order it from Matthew's web-site for $27.41USD (price for US citizens varies based on the relatonship between British pounds and US dollars.)

I'm absolutely thrilled to see a book that doesn't dumb down serious Math but simplifies it and communicates it so clearly. I remember having loved Math so much in junior high school and in high school where so much of what I did was to dive into interesting explorations. Then, when I got to college, Math became so dry and lifeless. I can only imagine what college Math would have been like with this book as a text. I sincerely believe that "The Mystery" is a real paradigm changer and I sincerely hope that other brilliant minds will write picture books that invite readers to think deeply of simple things.

"Shecky R"September 24th, 2010 - 12:50

Thanks for this encouraging review… I’d heard of this book awhile back, but received the impression it was somewhat of a picture book for youngsters, and didn’t pursue it further. Sounds like while the approach is very accessible, the material covered is actually quite interesting and ‘rigorous’ so maybe I may need to take another look… as if I don’t have enough books on my shelf about prime nos. already! 8-(

Ihor CharischakSeptember 24th, 2010 - 15:43

I just checked out the book on his website and ordered it. Thanks for the review.

SolSeptember 24th, 2010 - 15:47

Ihor – You won’t be disappointed. It truly is an amazing book. I don’t get so exuberant in most of my reviews.

Ihor CharischakOctober 5th, 2010 - 13:41

I just got it in the mail. I’ve read the first few pages and I’m hooked. I’ve had a incurable desire to really understand the Riemann hypothesis and it sounds like he is going in that direction in this trilogy.

Jeffrey VentrellaJanuary 7th, 2011 - 07:11

I will have to get this book. The illustrations look nice. Thanks!

Also, a quick plug for my book, which is also heavily illustrated:

“Divisor Drips and Square Root Waves”:

http://www.divisorplot.com/

http://www.lulu.com/product/paperback/divisor-drips-and-square-root-waves/12991531

Ihor CharischakJanuary 10th, 2011 - 16:57

I just downloaded a copy of your book, Jeffrey. I look forward to reading it!