The Princeton companion to mathematics

What is a modular form? What is the point of symplectic geometry? This one-of-a-kind reference illuminates modern pure mathematics in all its diversity.

More than 200 articles, organized thematically and written by many of the world's leading mathematicians, explain the major ideas and branches of mathematics in a clear, accessible style.

Presenting not only definitions but also motivation and context for concepts, methods, theorems, and other topics of mathematical study, this is an indispensable resource for everyone with a serious interest in the field.

What is Mathematics? It introduces the language and grammar of mathematics, fundamental definitions, general goals of mathematical research - the subject matter of mathematics.

It explores algebra, algorithms, geometry, how analysis became rigorous numbers, the crisis in the foundations of mathematics, and the development of the idea of proof.

It defines and explains more than 75 mathematical objects, concepts, and buzzwords, from axiom of choice to zeta function.

It includes detailed coverage of algebra algebraic geometry analysis, combinatorics computation geometry logic and set theory, number theory probability.It profiles 70 mathematicians, from Apollonius to Weyl, who influenced the field.

It also discusses notable theorems and open problems, from the four-color theorem to the Reimann hypothesis.

It covers the intellectual and practical influence of mathematics on other disciplines such as analytic philosophy, art, biology, chemistry, economics, finance, and music.

Including miscellaneous advice to a young mathematician, it features a chronology of Mathematics, computer experiments in mathematics, the art of problem solving and more.Contributors are (partial list): Graham Allan, Noga Alon, George Andrews, Tom Archibald, Michael Atiyah, David Aubin, Joan Bagaria, Keith Ball, Alan Beardon, David Ben-Zvi, Vitaly Bergelson, Nick Bingham, Bela Bollabas, Henk Bos, Bodil Branner, Haim Brezis, Martin Bridson, John Burgess, Kevin Buzzard, Peter Cameron, Jean-Luc Chabert, Eugenia Cheng, Clifford Cocks, Alain Connes, Leo Corry, Wolfgang Coy, Tony Crilly, Serafina Cuomo, Mihalis Dafermos, Partha Dasgupta, Ingrid Daubechies, Joseph Dauben, John Dawson, Francois de Gandt, Persi Diaconis, Robbert Dijkgraaf, Jordan Ellenberg, Florence Fasanelli, Solomon Feferman, Anita Feferman, Charles Fefferman, Jose Ferreiros, Terry Gannon, Tony Gardiner, Charles Gillespie, Oded Goldreich, Catherine Goldstein, Francois Golse, Fernando Gouvea, Andrew Granville, Ivor Grattan-Guinness, Jeremy Gray, Ben Green, Niccolo Guicciardini, Michael Harris, Ulf Hashagen, Nigel Higson, Andrew Hodges, Kollar Janos, Frank Johnson, and Mark Joshi.Contributors are: Dominic Joyce, Jean-Pierre Kahane, Frank Kelly, Sergiu Klainerman, Jon Kleinberg, Israel Kleiner, Jacek Klinowski, Eberhard Knobloch, Joe Kohn, Tom Korner, Peter Lax, Jean-Francois Le Gall, Raymond Lickorish, Martin Liebeck, Jesper Lutzen, Des MacHale, Lech Maligranda, David Marker, Adrian Mathias, Jean Mawhin, Barry Mazur, Colin McLarty, Peter Neumann, Catherine Nolan, James Norris, Marco Panza, Karen Parshall, Jeanne Peiffer, Carl Pomerance, Helmut Pulte, Bruce Reed, Mike Reed, Adrian Rice, Jeremy Rickard, Eleanor Robson, Igor Rodnianski, John Roe, Mark Ronan, Edward Sandifer, Norbert Schappacher, Andrzej Schinzel, Erhard Scholz, Joachim Schwermer, Gordon Slade, David Spiegelhalter, Neil Strickland, Arild Stubhaug, Madhu Sudan, Terence Tao, Jamie Tappenden, Cliff Taubes, Rudiger Thiele, Nick Trefethen, Dirk van Dalen, Richard Weber, Dominic Welsh, Avi Wigderson, Herbert Wilf, David Wilkins, Ben Yandell, and Doron Zeilberger.