The Princeton Companion to Mathematics (Hardcover)

The Princeton Companion to Mathematics makes a heroic attempt to keep [abstract concepts] to a minimum . . . and conveys the breadth, depth and diversity of mathematics. It is impressive and well written and it's good value for [the] money.
(Ian Stewart The Times )

This is a panoramic view of modern mathematics. It is tough going in some places, but much of it is surprisingly accessible. A must for budding number-crunchers.
(The Economist )

Although the editors' original goal of text that could be understood by anyone with a good background in high school mathematics provided short-lived, this wide-ranging account should reward undergraduate and graduate students and anyone curious about math as well as help research mathematicians understand the work of their colleagues in other specialties. The editors note some advantages a carefully organized printed reference may enjoy over a collection of Web pages, and this impressive volume supports their claim.
(Science )

Accessible, technically precise and thorough account of all math's major aspects. Students of math will find this book a helpful reference for understanding their classes; students of everything else will find helpful guides to understanding how math describes it all.
(Tom Siegfried Science News )

Once in a while a book comes along that should be on every mathematician's bookshelf. This is such a book. Described as a 'companion', this 1000-page tome is an authoritative and informative reference work that is also highly pleasurable to dip into. Much of it can be read with benefit by undergraduate mathematicians, while there is a great deal to engage professional mathematicians of all persuasions.
(Robin Wilson London Mathematical Society )

This volume is an enormous, far-reaching effort to survey the current landscape of (pure) mathematics. Chief editor Gowers and associate editors Barrow-Green and Leader have enlisted scores of leading mathematicians worldwide to produce a gorgeous volume of longer essays and short, specific articles that convey some of the dense fabric of ideas and techniques of modern mathematics. . . . This volume should be on the shelf of every university and public library, and of every mathematician--professional and amateur alike.
(S.J. Colley Choice )

Overall [The Princeton Companion to Mathematics] is an enormous achievement for which the authors deserve to be thanked. It contains a wealth of material, much of a kind one would not find elsewhere, and can be enjoyed by readers with man different backgrounds.
(Simon Donaldson Notices of the American Mathematical Society )

This is an enormously ambitious book, full of beautiful things; I would wish to keep it on my bedside table, but that could only be possible relays, since of course it is far too large. . . . To sum up, [The Princeton Companion to Mathematics] is really excellent. I know of no book that will give a young student a better idea of what mathematics is about. I am certain that this is the only single book that is likely to tell me what my colleagues are doing.
(Bryan Birch Notices of the American Mathematical Society )

The book is so rich and yet it is well done. A rare achievement indeed!
(Gil Kalai Notices of the American Mathematical Society )

My advice to you, reader is to buy the book, open it to a random page, read, enjoy, and be enlightened.
(Richard Kenyon Notices of the American Mathematical Society )

Massive . . . endlessly fascinating.
(Gregory McNamee The Bloomsbury Review )

The book I'm talking about is The Princeton Companion to Mathematics. If you are in an absolute rush, the short version of my post today is, buy this book. You don't have to click on the link with my referral if you don't want to, seriously just pick up a copy of this book, I can guarantee you that it will be love at first sight. . . . The Princeton Companion to Mathematics is not only a beautiful book from an aesthetic standpoint, with its heavy, high quality pages and sturdy binding, but above all it's a monumental piece of work. I have never seen a book like this before. . . . [T]he bible of mathematics. . . . I believe this is the kind of book that will still be in use a hundred years from now.
(Antonio Cangiano Math-Blog.com )

The Princeton Companion to Mathematics is a friendly, informative reference book that attempts to explain what mathematics is about and what mathematicians do. Over 200 entries by a panel of experts span such topics as: the origins of modern mathematics; mathematical concepts; branches of mathematics; mathematicians that contributed to the present state of the discipline; theorems and problems; the influences of mathematics and some perspectives. Its presentations are selective, satisfying, and complete within themselves but not overbearingly comprehensive. Any reader from a curious high school student to an experienced mathematician seeking information on a particular mathematical subject outside his or her field will find this book useful. The writing is clear and the examples and illustrations beneficial.
(Frank Swetz Convergence )

This has been a long time coming, but the wait was worth it! After many years of slogging through textbooks that presented too many proofs and demonstrations that were left to the student or lacking numerous intermediate steps, after encountering numerous 'introductions' that were obtuse and highly theoretical and after digesting far too many explanations with maximal equations and minimal verbiage, we arrive at the happy medium. This book is a companion in every sense of the word and a very friendly one at that. . . . For a comprehensive overview of many areas of mathematics in a readable format, there has never been anything quite like this. I would urge a trip to the local library to have a look.
(John A. Wass Scientific Computing )

Edited by Gowers, a recipient of the Fields Medal, this volume contains almost 200 entries, commissioned especially for this book from the world's leading mathematicians. It introduces basic mathematical tools and vocabulary, traces the development of modern mathematics, defines essential terms and concepts, and puts them in context. . . . Packed with information presented in an accessible style, this is an indispensable resource for undergraduate and graduate students in mathematics as well as for researchers and scholars seeking to understand areas outside their specialties.
(Library Journal )

I'm completely charmed. This is one of those books that makes you wish you had a desert island to be marooned on.
(Brian Hayes bit-player.org )

This is a wonderful book. The content is overwhelming. Every practicing mathematician, everyone who uses mathematics, and everyone who is interested in mathematics must have a copy of their own.
(Simon A. Levin, Princeton University )