Product 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 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 music--and much, much more.

Unparalleled in its depth of coverage, The Princeton Companion to Mathematics surveys the most active and exciting branches of pure mathematics, providing the context and broad perspective that are vital at a time of increasing specialization in the field. Packed with information and 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.

• Features nearly 200 entries, organized thematically and written by an international team of distinguished contributors
• Presents major ideas and branches of pure mathematics in a clear, accessible style
• Defines and explains important mathematical concepts, methods, theorems, and open problems
• Introduces the language of mathematics and the goals of mathematical research
• Covers number theory, algebra, analysis, geometry, logic, probability, and more
• Traces the history and development of modern mathematics
• Profiles more than ninety-five mathematicians who influenced those working today
• Explores the influence of mathematics on other disciplines
• Includes bibliographies, cross-references, and a comprehensive index

Contributors incude:

Graham Allan, Noga Alon, George Andrews, Tom Archibald, Sir Michael Atiyah, David Aubin, Joan Bagaria, Keith Ball, June Barrow-Green, Alan Beardon, David D. Ben-Zvi, Vitaly Bergelson, Nicholas Bingham, Béla Bollobás, Henk Bos, Bodil Branner, Martin R. Bridson, John P. Burgess, Kevin Buzzard, Peter J. Cameron, Jean-Luc Chabert, Eugenia Cheng, Clifford C. Cocks, Alain Connes, Leo Corry, Wolfgang Coy, Tony Crilly, Serafina Cuomo, Mihalis Dafermos, Partha Dasgupta, Ingrid Daubechies, Joseph W. Dauben, John W. Dawson Jr., Francois de Gandt, Persi Diaconis, Jordan S. Ellenberg, Lawrence C. Evans, Florence Fasanelli, Anita Burdman Feferman, Solomon Feferman, Charles Fefferman, Della Fenster, José Ferreirós, David Fisher, Terry Gannon, A. Gardiner, Charles C. Gillispie, Oded Goldreich, Catherine Goldstein, Fernando Q. Gouvêa, Timothy Gowers, Andrew Granville, Ivor Grattan-Guinness, Jeremy Gray, Ben Green, Ian Grojnowski, Niccolò Guicciardini, Michael Harris, Ulf Hashagen, Nigel Higson, Andrew Hodges, F. E. A. Johnson, Mark Joshi, Kiran S. Kedlaya, Frank Kelly, Sergiu Klainerman, Jon Kleinberg, Israel Kleiner, Jacek Klinowski, Eberhard Knobloch, János Kollár, T. W. Körner, Michael Krivelevich, Peter D. Lax, Imre Leader, Jean-François Le Gall, W. B. R. Lickorish, Martin W. Liebeck, Jesper Lützen, Des MacHale, Alan L. Mackay, Shahn Majid, Lech Maligranda, David Marker, Jean Mawhin, Barry Mazur, Dusa McDuff, Colin McLarty, Bojan Mohar, Peter M. Neumann, Catherine Nolan, James Norris, Brian Osserman, Richard S. Palais, Marco Panza, Karen Hunger Parshall, Gabriel P. Paternain, Jeanne Peiffer, Carl Pomerance, Helmut Pulte, Bruce Reed, Michael C. Reed, Adrian Rice, Eleanor Robson, Igor Rodnianski, John Roe, Mark Ronan, Edward Sandifer, Tilman Sauer, Norbert Schappacher, Andrzej Schinzel, Erhard Scholz, Reinhard Siegmund-Schultze, Gordon Slade, David J. Spiegelhalter, Jacqueline Stedall, Arild Stubhaug, Madhu Sudan, Terence Tao, Jamie Tappenden, C. H. Taubes, Rüdiger Thiele, Burt Totaro, Lloyd N. Trefethen, Dirk van Dalen, Richard Weber, Dominic Welsh, Avi Wigderson, Herbert Wilf, David Wilkins, B. Yandell, Eric Zaslow, Doron Zeilberger

Product Details

• Amazon Sales Rank: #14738 in Books
• Published on: 2008-10-05
• Original language: English
• Number of items: 1
• Binding: Hardcover
• 1008 pages

Review
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 )

Review
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 )

From the Inside Flap

"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

"The Princeton Companion to Mathematics fills a vital need. It is the only book of its kind."--Victor J. Katz, professor emeritus, University of the District of Columbia

"I think that this is a wonderful book, completely different from anything that has been written before about mathematics and mathematicians."--Endre Süli, University of Oxford

"The Princeton Companion to Mathematics is a much needed--and will become a much used--reference work. In fact, it will stand alone as the reference work in mathematics."--John J. Watkins, Colorado College

Customer Reviews

An unusual and outstanding guide
I received a copy of this book for my birthday this year, and was immediately drawn towards the material on algebra with which I was most familiar. The most striking thing about the book as a whole, both in the bits I know well, and the bits I don't know much about, is the way in which it combines large portions of accessible text with substantial mathematical content - it is the lack of actual serious content which frustrates me most about popular books about maths (Fermat's Last Theorem and the Riemann Hypothesis have received the popular treatment with limited content). But in this companion there are clues to enable an enthusiast to engage with the material.

It is right to say, as the introduction does, that there is material in this book which will require some knowledge beyond what you might learn at school. But do not let that put you off (it is no more daunting than the physical size of the book, which mirrors only its extensive coverage). For the genius of this companion is in the way that it engages with real mathematics and how it is actually done by real mathematicians. It is not simply a presentation of particular subject matter (as in a text book) nor is it an encyclopedia of mathematics, for it seeks to convey an understanding of the nature and importance of pure mathematics, rather than simply definitions of the component parts - and through disciplined editing and clear exposition it sets a standard which will not easily be matched.

There is a huge amount which will challenge and excite a good A-level student. My one observation is that the suggested further reading is sometimes a great deal more demanding than the component articles of the Companion (which is partly a reflection of just how good these articles are) - but more consistency, or a scheme for marking references accessible at or just beyond A-level is the only improvement I could think of.

If this book had been in my school library when I was 17 ... well every school with a 6th form should have one. And anyone with a true interest in mathematics should have it to browse (and will want to read it).

Great
This is a great book. Its entries are well written by recognisable experts and at a high enough level so that people attempting research may use them as a starting point or even as a guide to the main people in the field. It can be read by the amateur too. Other good points are: the quality and depth of coverage, the connections made between fields, and the broad perpective it provides on the subject.

A wide yet not especially detailed range of content
Apparently this should cover the whole of my undergraduate maths course. It doesn't cover everything and is not particularly specific. Probably good as a reference book but not as a study companion or something to depend on. Having said that, things that were covered were explained clearly, eg. Countability, and since it tends to cover things briefly it explains them more in 'English' than maths, which is often useful.