The Princeton Companion to Mathematics
by Timothy Gowers · first published 2008
75% recommend25% neutral
Why HN recommends it
Readable survey of modern mathematics with chapters by leading mathematicians and a helpful introduction for orientation. Suits curious non-mathematicians and self-learners wanting breadth and a feel for the field.
Summarised by Claude from recommending comments
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 presents nearly two hundred entries, written especially for this book by some of the world's leading mathematicians, that introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and concepts; examine core ideas in major areas of mathematics; describe the achievements of scores of famous mathematicians; explore the impact of mathematics on other disciplines such as biology, finance, and
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Another great book, starting with the basics and then exploring a wide range of mathematical subjects, is The Princeton Companion to Mathematics: http://press.princeton.edu/titles/8350.html It's fun to just flip it open and start reading.
on “Great books about mathematics” ↗The Princeton Companion to Mathematics.
on “Ask HN: good math books” ↗In terms of depth and breadth, the Princeton companions get close to Feynman.[1][2] A more formal approach appears in handbooks.[3][4] [1] Gowers et al., The Princeton Companion to Mathematics. https://press.princeton.edu/books/hardcover/9780691118802/th... [2] Higham and Dennis, The Princeton Companion to Applied Mathematics. https://press.princeton.edu/books/hardcover/9780691150390/th...…
on “Ask HN: Are there books for mathematics like Feynman's lectures on physics?” ↗I've also found these to be helpful: The Language and Grammar of Mathematics, from The Princeton Companion to Mathematics, by James Gowers: http://press.princeton.edu/chapters/gowers/gowers_I_2.pdf Reading Mathematics, by John Hamal Hubbard: http://www.math.cornell.edu/~hubbard/readingmath.pdf
on “The Mathematics Autodidact’s Aid (2005) [pdf]” ↗…teach yourself. Watch lectures on the web. Pepper your fellow HN readers with questions about Haskell or Lisp macros or whatever. Buy a subscription to Nature. Or work your own way through Knuth or the Princeton Companion to Mathematics or The Molecular Biology of the Cell. [1] If you've got a good job and friends and romance and an open-source project, try to consider the possibility that you might be happy and successful. --- [1]…
on “Ask HN: Staying Sharp” ↗This is a good book, although I agree with others that truly learning from it would be difficult. If you like this, another book you might really enjoy is the Princeton Companion to Mathematics.
on “A Software Engineer’s Adventures in Learning Mathematics” ↗I have a hard copy of the Princeton Companion to Mathematics and find it incredibly useful -- highly recommended. http://www.amazon.com/Princeton-Companion-Mathematics-Timoth...
on “A Mathematical Atlas” ↗Nice! This book is modeled after the The Princeton Companion to Mathematics [1] which is simply awesome in every sense of the word, and extremely recommended for any person who is interested in mathematics. I'm very glad to see more books being modeled after it, and I hope this…
on “The Princeton Companion to Applied Mathematics” ↗Looks really interesting, I'm going to try to read it, and thanks for your suggestion of the MacLane book. Another really excellent resource along those lines is the Princeton Companion to Mathematics, in particular the introductory essay by Tim Gowers (who is also the editor of the book). By along those lines, I mean pointing to advanced mathematics, from the point of view of someone who is kind of…
on “A View of Mathematics (2005) [pdf]” ↗this is his article in the princeton companion to mathematics https://www.amazon.com/Princeton-Companion-Mathematics-Timot... a great (even if expensive) math book
on “Differential Forms and Integration (2008) [pdf]” ↗Assuming you are asking in general and not specifically Bourbaki authored; * Mathematics: Its Content, Methods and Meaning by Aleksandrov, Kolmogorov, Lavrentev * The Princeton Companion to Mathematics by Timothy Gowers et al. * The Princeton Companion to Applied Mathematics by Higham et al.
on “The Secret Math Society Known as Nicolas Bourbaki” ↗…Encyclopedia of Philosophy: Encyclopedia by professional philosophers, covers many mathematics topics. Dense but certainly in-depth. https://plato.stanford.edu/ ... And a few that you have to pay for: * The Princeton Companion to Mathematics, edited by Timothy Gowers: You probably already know about this one. It's an amazing opus that covers pure mathematics. * Mathematics: Its Content, Methods and Meaning by Aleksandrov, et al: Encyclopedia,…
on “Snapshots of modern mathematics from Oberwolfach” ↗If you're really interested in learning a lot about mathematics, I would definitely recomment the Princeton Companion to Mathematics (see below for URL). It came out very recently, and while i'm only about 100 pages in (of well over 1000), it's down to earth writing and low prerequisites are very appealing to me. http://www.amazon.com/gp/product/0691118809?ie=UTF8&tag=...…
on “I suck at math, please divulge resources” ↗Book recommendation: Princeton Companion to Mathematics It's a good way to skim a lot of different mathematical topics for further exploration. http://www.amazon.com/Princeton-Companion-Mathematics-Timoth...
on “Ask HN: Independent Math Study” ↗The Princeton Companion to Mathematics (http://www.amazon.com/Princeton-Companion-Mathematics-Timoth...)
on “Ask HN: Graduation Present for Aspiring Math Major?” ↗