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Tuesday, September 25, 2012

Joy To The World (of Math)

"…there's a profound but little-recognized hunger for math among the general public. Despite everything we hear about math phobia, many people want to understand the subject a little better. And once they do they find it addictive.
"The Joy of X is an introduction to math's most compelling and far-reaching ideas….

"Math swaggers with an intimidating air of certainty. Like a Mafia capo, it comes across as decisive, unyielding, and strong. It'll make you an argument you can't refuse.
"But in private, math is occasionally insecure. It has doubts. It questions itself and isn't always sure it's right."

-- from the Preface and next-to-last chapter of "The Joy of X" by Steven Strogatz

A review of Steven Strogatz's latest gift to math lovers:

Why even bother writing a review of Steven Strogatz's new book, "The Joy of X"?-- what a waste of my writing time… You already know you want it without any prodding from me, right! ;-)

Still, coming on the heels of Paul Lockhart's "Measurement" (which I also recommended here a short while back) I think it worth contrasting Strogatz's offering from the latter. They are very different books (though Strogatz, like Lockhart, is enthralled with math, and wishing to pass along some of that delight), so this is not meant as a direct comparison, except that both are directed at a mass audience.

In reviewing Lockhart's volume I mentioned being annoyed with all the books (UNlike Lockhart's) that come out pretending to be for lay folks, but really requiring some clear math aptitude to get through them (Lockhart is refreshingly upfront in telling readers ahead of time that his material will at times be difficult).

Well, Steven Strogatz (a Cornell University math professor) has, as one familiar with his writing might expect, truly written a math book for lay people. The book is a compendium of the popular 15-part series he did for the NY Times back in 2010, plus new essays (so if you read that series you know what type of writing to expect here, AND Strogatz is currently running a new set of essays in the Times as well).

The six parts of the book, in order, are labeled: Numbers, Relationships, Shapes, Change, Data, Frontiers (each part containing 5-6 short essays). I very much like the layout of the book going from more basic/elementary topics to more complex ones. The book starts off with Sesame Street (on arithmetic) and ends at Hilbert's Hotel… gotta love that! ;-) Strogatz says the chapters stand on their own as independent pieces that can be "snacked on" in any order, which is true, but I still recommend reading from beginning to end, and experiencing the natural progression of ideas/complexity as the best way to take in the volume.

The usual sorts of topics that appear in popular math books are all here… infinity, group theory, complex numbers, functions, differential equations, e, Mobius strips, statistics, and on and on. If you have an extensive math library, there won't be much new here that isn't covered, and likely more fully, by other volumes on your shelf. So why buy yet another math book?… because Steven's treatment of each topic is THAT enjoyable!

When I mini-reviewed Clifford Pickover's "The Math Book," my biggest complaint was that he introduced the reader to topics just enough to pique their interest and then dropped the ball by not giving them more. What Strogatz does so well, so expertly, is give you an introduction, a main body or discussion, and a tidy little wrap-up on each topic, all in a handful of pages (Pickover restricted himself to a single page per topic).
The range of topics is great (30 chapters); the writing is succinct and descriptive... erudite, without being over people's heads. As in the Goldilocks story, Strogatz serves up math, not too hot, not too cold, but j-j-j-just right!!

My favorite chapters (and believe me, it's hard to choose) are these:

Chapter 8: 'Finding Your Roots' on imaginary numbers
Chapter 9: 'My Tub Runneth Over' on word problems
Chapter 10: 'Working Your Quads' on the quadratic equation
Chapter 12: 'Square Dancing' on proofs
Chapter 17: 'Change You Can Believe In' on derivatives
Chapter 22: 'The New Normal' on the Bell Curve
Chapter 24: 'Untangling the Web' on the algorithms behind Web searching
Chapter 25: 'The Loneliest Numbers' on prime numbers
Chapter 27: 'Twist and Shout' on the Mobius strip
Chapter 29: 'Analyze This! on series

(…ohh, did I mention, it's really, really hard to choose favorites)
And, by the way, don't skip over the 40 pages of "Notes" at the end of the book, which are a cornucopia of links to other worthwhile reads (including a LOT of interesting internet pages that could keep you busy for a long time).

I highly recommend both the new Paul Lockhart and Strogatz volumes, and find it a joy to behold so many wonderful mass appeal mathematics books being put out these days. Having said that, I'd caution that Lockhart's book is especially for teachers, students, and math fans already enamored of the subject, whereas I believe Strogatz's offering really can appeal in a rare way to a wider swath of avid and normally-non-mathy readers out there.

So, if you're not a math buff, but secretly always wanted to be, you can do no better than start with this volume. If you are already an established math buff I don't promise you'll learn a lot new from Strogatz, but you'll be highly entertained along the way, and likely see some things you already knew from fresh or different angles.
Thanks for the book Steven… and, the joy is all OURS!

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