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The Princeton Companion to Mathematics http://www.amazon.com/Princeton-Companion-Mathematics-Timothy-Gowers/dp/0691118809 http://www.amazon.com/Princeton-Compa

by Maro 16y ago

The Princeton Companion to Mathematics http://www.amazon.com/Princeton-Companion-Mathematics-Timothy-Gowers/dp/0691118809 http://www.amazon.com/Princeton-Companion-Mathematics-Timoth...

acangiano 16y ago
Yes, it's #26 on the list.
- tygorius 16y ago
  This highlights one of the weaknesses of the list -- the apparent lack of an editor. Whereas shou4577's comments explains the book's strengths and target audience, the original submission's description was so concise as to be near useless ("Coherent overview of all of pure mathematics.") This isn't intended as a slam of the original suggester, but to point out that the blog listing is only a starting point and in some regards less useful than the topic book lists some Amazon reviewers compile.
shou4577 16y ago
I own this book, and I use it occasionally, but it really requires the right audience. Firstly, it has several parts. Some of these are historical, philosophical, or otherwise interesting to a general audience, but some of them are technical (I would put most of pages 157-729, nearly 60% of the book, in this category). For people that are interested in mathematics, but do not have a fairly extensive background (I would estimate 2-3 courses beyond the calculus series), these technical sections are probably not very useful (and certainly not entertaining). For people (like me), who are still pursuing an education in mathematics, I would say this book is indispensable. It gives a great overview of individual branches of mathematics, including fairly rigorous explanations of important results and conjectures. The exposition portions of the book are good, but don't warrant the high price of the book on their own. Overall, though, it is a tremendous reference. Edit: I forgot to mention that the folks who write the articles are all outstanding mathematicians - many of them Fields medalists or other award winners. That makes for some very good reading.
- omaranto 16y ago
  I agree with everything you said and would only add that if you have studied lots (for example, are a graduate student in mathematics), then it will probably be frustratingly shallow on anything you know reasonably well (or not mention it at all, if it's specialized), but it is still an amazing resource to get started in fields of math that are not your own.

by Maro 16y ago

The Princeton Companion to Mathematics http://www.amazon.com/Princeton-Companion-Mathematics-Timothy-Gowers/dp/0691118809 http://www.amazon.com/Princeton-Companion-Mathematics-Timoth...

acangiano 16y ago

Yes, it's #26 on the list.

tygorius 16y ago
This highlights one of the weaknesses of the list -- the apparent lack of an editor. Whereas shou4577's comments explains the book's strengths and target audience, the original submission's description was so concise as to be near useless ("Coherent overview of all of pure mathematics.") This isn't intended as a slam of the original suggester, but to point out that the blog listing is only a starting point and in some regards less useful than the topic book lists some Amazon reviewers compile.

shou4577 16y ago

I own this book, and I use it occasionally, but it really requires the right audience. Firstly, it has several parts. Some of these are historical, philosophical, or otherwise interesting to a general audience, but some of them are technical (I would put most of pages 157-729, nearly 60% of the book, in this category). For people that are interested in mathematics, but do not have a fairly extensive background (I would estimate 2-3 courses beyond the calculus series), these technical sections are probably not very useful (and certainly not entertaining). For people (like me), who are still pursuing an education in mathematics, I would say this book is indispensable. It gives a great overview of individual branches of mathematics, including fairly rigorous explanations of important results and conjectures. The exposition portions of the book are good, but don't warrant the high price of the book on their own. Overall, though, it is a tremendous reference. Edit: I forgot to mention that the folks who write the articles are all outstanding mathematicians - many of them Fields medalists or other award winners. That makes for some very good reading.

omaranto 16y ago
I agree with everything you said and would only add that if you have studied lots (for example, are a graduate student in mathematics), then it will probably be frustratingly shallow on anything you know reasonably well (or not mention it at all, if it's specialized), but it is still an amazing resource to get started in fields of math that are not your own.