See our review of the second edition. The main goal of this edition is to include contributions by the Fields Medalists up to 2010 (not, therefore the latest ones). Added to the collection are lectures by John Milnor, Enrico Bombieri, Gerd Faltings, Andrei Okounkov, Terence Tao, Cédric Villani, Elon Lindenstrauss, Ngô Bâu Châu, and Stanislav Smirnov. Also added are survey lectures on the work of Michael Atiyah, Alexander Grothendieck, Stephen Smale, and Jean-Christophe Yoccoz; these are newly translated from French, but presumably were the original ICM lectures about their work.
As we noted in our previous review, not all Fields Medalists are represented. Most readers will find the survey articles on each mathematician’s work the most accessible and interesting part of the book. (The so-called “biographical notices” are typically very brief, though there are some welcome exceptions to that rule.) The “lectures” themselves can be quite technical.
Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College in Waterville, ME.