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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 B

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I bought this book because I was interested in knowing more about mathematics in general, in a broader sense, not just how to calculate a perimeter or an exponential function, but how it was first founded, who are the most influential scientists to have improved mathematics, what are the different fields and how they articulate. And, well, this book did just that and much more.
It is very well organized in order to lead you step by step from basic concepts to more complicated mathematics with a middle section that tells you everything you need to know about the people who made mathematics what it is today. In short, it is a must-have for anybody who's mathcurious : from novice to expert.
Beware though, it is not an introduction or a student module. It is not conceived to actually teach mathematics. It is a companion, a guide-through, not a textbook with keys at the end.

But on top of everything, the book is a wonder to the eye and fingers. It is marvelously edited and a piece of jewelry to stand on any bookshelf. A perfect gift for enthusiasts.
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This book is divided in parts. The first part is a brief history of mathematics, gives somei insights into why math is the way it is today. The second part gives an overview of fields of mathematics. It is of extraordinarily high quality and easy to understand, written by experts in the respective fields and cover quiet sizable breadth.
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Je l'ai offert à un mathématicien qui dès le premier parcours m'a dit que ce livre était très bien fait
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This book is huge and it only scratches the surfaces of most of its topics. There is enough material to give you a teste of the fruit though. We writing style is very readable and I definitely recommend it. Beware that you bookshelf should be large enough.
The physical book is also high quality material.
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Amazon.com: 4.7 étoiles sur 5 78 commentaires
239 internautes sur 244 ont trouvé ce commentaire utile 
5.0 étoiles sur 5 A major event in mathematical publishing 8 novembre 2008
Par Timothy Chow - Publié sur Amazon.com
Format: Relié Achat vérifié
The Princeton Companion to Mathematics is such an extraordinary book that I am still amazed that the chief editor, Timothy Gowers, managed to pull it off. The renowned mathematician Doron Zeilberger announced that if he could take only one book with him to a desert island, it would be the Princeton Companion to Mathematics.

Why such high praise? Simply put, the PCM gives a single-volume overview of all of pure mathematics, with a clarity and coherence that cannot be found anywhere else. To be sure, there do exist several good books on the history of mathematics that give a good overview of elementary mathematics and introduce the reader to some of the great mathematicians of the past. There also exist excellent "popular science" books by writers such as Martin Gardner and Ian Stewart, that explain selected topics in advanced mathematics to the lay reader in an engaging and clear manner. And there are also encyclopedias (including Wikipedia) that delineate the main branches of mathematics and give succinct definitions of all the main concepts. But only the PCM does all of these things at once, in only a thousand pages.

The PCM is all things to all people. If your mathematical background is limited, you can still learn a great deal from the more elementary sections of the book, as well as from the biographical sketches of nearly a hundred famous mathematicians of the past. At the other end of the scale, even professional mathematicians will learn something from the articles on branches of mathematics other than their own specialty. Gowers made a systematic effort to find contributors who are not only world experts in their subject, but who write extremely well. He also forced the contributors to write in as accessible and elementary a manner as possible. The result is that even highly abstruse areas of mathematics are explained here with a clarity that is difficult to find anywhere else in the mathematical literature. The PCM is thus especially valuable to mathematics majors and graduate students.

Despite the ambitious scope of the book, it retains a strong sense of unity and coherence, by consistently emphasizing the forest rather than the trees. It also gives the reader a holistic view of mathematics by devoting different sections of the book to different perspectives on the subject. For example, one section organizes mathematics by sub-discipline, while another section highlights the main results and open problems of mathematics, while yet another section picks out the most important concepts. By putting all these aspects together in one volume, the PCM gives the reader a bird's-eye view of the whole subject that is not available from Wikipedia or from a shelf full of popular books on disparate topics.

The PCM is so well-written that it can be read either cover-to-cover, or browsed at random, or consulted as a reference when needed.

One word of warning: As Gowers himself notes, the book would be more accurately titled, "The Princeton Companion to Pure Mathematics." While applications of mathematics to other fields are touched on briefly, Gowers consciously limited the book primarily to pure mathematics, in order to keep the scope of the book manageable.

Should you still have doubts about the book, you can browse parts of the book for free: Selections from the book may be found at the book's official website, and many of the contributing mathematicians have posted their own sections on their own websites (you can find these easily using Google). And for more reviews of the book, see Gowers's blog.
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5.0 étoiles sur 5 A physicist's perspective 1 février 2009
Par J. Koelman - Publié sur Amazon.com
Format: Relié Achat vérifié
Got my copy a week ago. What an exceptional book! Any of the random samples I read so far provides a informative, yet pleasant read. Gowers (Rouse Ball Professor of Mathematics in Cambridge) did a fantastic job in editing the many articles into a coherent and surprisingly accessible overview of modern mathematics. From inception to publication of this book took Gowers and his associate editors some 6 years. The amount of editorial attention given to this publication clearly shows and translated into a book that is - unlike any other math book I know of - easy to read and of high quality.

This book provides lots of material that is of interest to non-mathematicians. As is mentioned in one of the other reviews here, this heavy volume does not contain a separate chapter on mathematical physics, yet as a physicist I found lots of material directly relevant to physics. There is a very interesting chapter on the general theory of relativity, and lots of material on quantum mechanics. Also fundamental concepts highly relevant in physics such as spherical harmonics, dynamical systems, deterministic chaotic behavior, phase transitions, Lie groups, etc. are covered in inviting shorter sections. Each of the subjects is introduced in such a way that the reader first gains an intuitive understanding of the concept, that subsequently gets deepened via a more rigorous approach.

If only there was a similar 'companion' to modern physics! (The book of Oxford's Emeritus Rouse Ball professor Roger Penrose, The Road to Reality: A Complete Guide to the Laws of the Universe comes close, but falls short of being truly PCM's equivalent in physics.)

If you're interested in math, don't hesitate and buy this book. (And be quick: I bought it here at Amazon for just over US$71. In the meantime, the price has increased already by more than US$5... ;-)
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5.0 étoiles sur 5 Four Books For Any Math Article... 28 novembre 2012
Par Let's Compare Options Preptorial - Publié sur Amazon.com
Format: Relié Achat vérifié
This wonderful volume is one of four works I always keep in digital or desk drawer reach while reading/studying/ referencing any other math book or journal article, the complete list being:

-- Encyclopedia Of Mathematics (Science Encyclopedia)

-- The Princeton Companion to Mathematics

-- Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables (Dover Books on Mathematics)

-- NIST Handbook of Mathematical Functions (Being of course the 2010 update of the Abramowitz classic above).

Given these four, there is hardly a topic from among the current 495 math fields of study that isn't at least explained in enough detail to save LOTS of time on link expeditions. At minimum, these give head starts on alphabetized keywords that will quickly fill holes in any research project, class, or syllabus.
5.0 étoiles sur 5 Excellent window into many areas of math 30 novembre 2016
Par C. L. Wilson - Publié sur Amazon.com
Format: Format Kindle Achat vérifié
If you have a working math background and want to look at areas you never studied this is a great introduction. The preface says it was designed to introduce various areas of math to people with a math background in other areas. It works very well in that role. Although it displays only on my PC not on my paper-white the display is convenient and works very well. I am not a great typo hunter but have not found any.
5.0 étoiles sur 5 A Fine Companion Indeed ! 29 septembre 2016
Par RML - Publié sur Amazon.com
Format: Relié Achat vérifié
This is an outstanding depiction of the mathematical landscape compiled by a team of subject matter experts. The beautifully written articles are easy to read and yet substantive. If you spend your days wading through the silos of specified texts, fragmented course handouts and assignments and wish that someone would make your life easier by describing the broader picture, this is a truly great book to buy.
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