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The Princeton Companion to Mathematics


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    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




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    Couldn't be better2010-03-035 / 5
    Little if anything to add to what has already been said at length by other reviewers. The Princeton Companion to Mathematics is a genuine joy. Very well edited, presented, written. Accessible to a wide variety of readers (I studied a good deal of math in college, but very little in the years since). And above all, extraordinarily thorough. Along with something like the outstanding "What is Mathematics?" by Courant (et al.), almost any competent reader of any background can find something rewarding here.
    An (almost) non-human companion2010-02-105 / 5
    This is a huge collection of essays and mathematical knowledge. The book is not an encyclopedia, but rather a "companion" in the human sense of the word. It knows some of (almost) everything. Worth to mention are the essays at the end titled "Advice to a young mathematician", which really inspired me in my mathematics studies. A must-have for every student of mathematics :)
    Math wannabe2010-01-175 / 5
    At times heavy going, but mostly readable by those with minimal advanced maths, Well worth the money.
    Mathematics Companion2009-12-215 / 5
    This is the second copy of the book I purchase. The first one was for me and my son. This one is a gift for a friend of my son, a high school student, with a hope that it will remain her companion for many years. This clearly indicates how I rate the book. In my currency (rupee) the price is at the higher side. But I do not complain much. It is worth buying this magnum opus. It has wide coverage in a mostly understandable form. I really enjoy reading. I cannot compare it with Timothy Gowers earlier text, Mathematics: a short Introduction. I do not have a copy. But then I believe that they cannot be compared simply because of difference in sizes. I do not have anything similar to PMC in my collection. It is just great.
    better than I could have hoped for2009-12-125 / 5
    I first heard about this book on Gowers' blog, where he linked to a collection of sample articles (to read some of them, just google the title and explore the first few links). When I began reading the articles, I had no intention of buying the book. But from the first few articles, I was awed by the clarity of exposition, and by the frequency of deep and illuminating insights. Very soon, I ordered Princeton Companion to Mathematics (PCM) from . This book has far exceeded my expectations.

    The place where PCM really shines is mathematical exposition using non-technical language. Don't mistakenly think the minimum of equations means the book shies away from very deep math. On the contrary. I think non-technical language emphasizes the big picture and the connections between seemingly disparate areas. Just for context, I am a math professor at a research school. I got my bachelor's and master's in math, and PhD in theoretical computer science (don't worry, though; this book offers a lot for an undergrad, or even a motivated high school student). Although grad school taught me a lot, that experience was more about depth. Reading PCM has greatly increased my breadth. I can't say enough good things about this book; it's perhaps my favorite book ever written about mathematics (compare with, "Proofs from the book"; but PCM is accessible to a wider audience). I wish I could rate it 6 stars out of 5.

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