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The Princeton Companion to Mathematics

October 24, 2008 Leave a comment

I received my copy of the new book The Princeton Companion to Mathematics a few days ago and I’ve been wanting to say something about it ever since, but I’ve been waiting until I’ve had a chance to read more of its 1014 two-columned pages. However, I won’t be making any additional progress on the book in the next few days, since I’m leaving early tomorrow morning for New York and I don’t plan to carry it on the plane with me, so I’ll make some preliminary comments now.

First, the book is beautiful. Despite its weight, it’s a joy to hold and to look at. And no matter where you open it, there’s something fascinating to read. The Table of Contents gives a good idea of the book’s layout and underlying conception. Part II, The Origins of Modern Mathematics, and Part VIII, Final Perspectives, are excellent starting points. I have not yet spent much time in Part VII, The Influence of Mathematics, but I’m eager to jump in. Part VI, Mathematicians, contains 96 short biographies of mathematicians, arranged chronologically by birth. The few I’ve read were superb, even given the severe space constraints. The first and last mathematicians treated are Pythagoras (born ca. 569 B.C.E.), about whose life nothing is known, and Bourbaki (1935), who didn’t even have a life. Two of the ninety-six are women: Sonya Kovalevskaya (1850) and Emmy Noether (1882).

So far, what I’ve enjoyed most are the Final Perspectives, especially the last section, Advice to a Young Mathematician (provided by Atiyah, Bollobas, Connes, McDuff, and Sarnak), and Michael Harris’s essay “‘Why Mathematics?’ You Might Ask.” I need to re-read Harris’s article. It’s filled with ideas, and very provocative. (Michael and I were colleagues decades ago, first in a summer undergraduate research program at Rutgers in 1972, between our junior and senior years, and then again for three years at Brandeis.)

Timothy Gowers is to be congratulated for his accomplishment as editor of the book. Order the book now.* And while you wait for your copy to arrive, have a look at his blog.

*Well, if you’re a mathematician, order the book now. If you’re not, be sure to borrow it from a mathematician or from the library.

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Categories: Books, Math