The Princeton Companion to Mathematics

by Timothy Gowers (Editor), June Barrow-Green (Editor) Imre Leader (Editor)

book data

3 ratings, 4.67 average rating, 6 reviews (more data...)

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5		66%
4		33%
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published

October 5th 2007 by Princeton University Press

binding

Hardcover, 1008 pages

url

http://press.princeton.edu/titles/8350.h...

isbn

0691118809 (isbn13: 9780691118802)

description

This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it pre...more

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05/10/09

Javier rated it:

bookshelves: currently-reading

I should say something about this one: Mathematics is a strange subject, it complex, rich, broad and diverse. This book, however, manages to offer a general account of what doing math in the 21st century feels like. In that sense it is a big success.

The book is not for everybody but it has things for everybody. Some of the introductions to concepts and problems are definitely thought to appeal the general public with only some basic knowledge of calculus and highschool algebra. Some ...more

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06/04/08

Nick marked it as to-read

bookshelves: to-read

Amazon 2008-10-24. It finally got published (on my 28th birthday, none the less!), after a long year of eager waiting! Ooooooooh, I'm excited! I forget where I first heard about this, but here's a recent review from Not Even Wrong:

I just recently got my hands on a copy of the new Princeton Companion to Mathematics, and I fear that this is likely to seriously impact my ability to get things done for a while, as I devote too much time to happily reading many of its more than 1000 pages...more Amazon 2008-10-24. It finally got published (on my 28th birthday, none the less!), after a long year of eager waiting! Ooooooooh, I'm excited! I forget where I first heard about this, but here's a recent review from Not Even Wrong:

I just recently got my hands on a copy of the new Princeton Companion to Mathematics, and I fear that this is likely to seriously impact my ability to get things done for a while, as I devote too much time to happily reading many of its more than 1000 pages.

The book is an amazing document (and physically, a beautiful, if weighty object), unlike anything else I know of. Its coverage of mathematics and mathematical culture is very wide and sometimes deep, but it makes no attempt to be comprehensive. Thus, the accurate title “Companion to” rather than “Encyclopedia of”. The most remarkable aspect of the book is the extremely high quality of the contributions from a large number of different authors. It includes many wonderful long expository articles, mostly at a level that a good undergraduate math student could hope to appreciate, with much of the book accessible to an even wider audience. The articles are often written by some of the best researchers and expositors around. For example, one can find Barry Mazur writing on Algebraic Numbers, Janos Kollar on Algebraic Geometry, Cliff Taubes on Differential Topology, Ingrid Daubechies on Wavelets, Persi Diaconis on Mathematical Statistics, and many, many others of similar quality. The table of contents is available here.

The book also includes extensive articles on historical topics in mathematics and short biographies of a large number of mathematicians, as well as coverage of applications and a section largely devoted to describing the art of problem-solving and how mathematics really gets created. This section includes a beautiful set of five essays called “Advice to a Young Mathematician”, which give five different equally fascinating perspectives from some of the best in the subject about how they achieved what they did, as well as what they have learned from years of helping students become researchers. The authors of these pieces are Michael Atiyah, Bela Bollobas, Alain Connes, Dusa McDuff, and Peter Sarnak. Luckily for all young (and old) mathematicians, this chapter is freely available here.

The person most responsible for this is clearly the editor (and author of some of the pieces), Fields Medalist Timothy Gowers, who had help from many others, including fellow Fields Medalist Terry Tao. Gowers has a weblog, and he has written about the book in these entries (and there’s a podcast interviewing him on the book web-site at PUP). Terry Tao has a posting about the book here.

If you’re looking for a gift for someone with a serious interest in mathematics, no matter what their background, you won’t do any better than this.(less)

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06/16/09

Linda rated it:

This is a thorough and outstanding reference to the more complex ideas in mathematics. It also has a lengthy section on biographies of noteworthy mathematicians and the history of mathematics. Other sections include concepts, branches of mathematics, theorems and problems, influences,, and perspectives. Not one for the bookbag though, at 1034 pages. I do refer to it often, however!

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03/04/09

fbuser611578 added it

Read in March, 2009

incomprehensible

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11/14/08

Dimitrios Diamantaras marked it as to-read

bookshelves: to-read

The editor is Timothy Gowers, not Imre Leader, who is listed as the second of two associate editors, the first of whom is June Barrow-Green. A recent purchase from Amazon, this is a beautiful book, to be read in bits here and there and savored for the exquisite beauty of the mathematics it surveys. I am one of those people who seek out mathematical texts to read for pleasure.

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12/25/08

Sonny marked it as to-read

bookshelves: to-check, to-read

http://news.ycombinator.com/item?id=4068...
http://scottaaronson.com/blog/?p=384

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