The volume contains 15 articles surveying some of the most exciting recent developments in pure mathematics, ranging from set theory (Woodin's work on the continuum hypothesis), through the geometric group theory (new results on Kazhdan's property, Gromov's work on random groups, elementary theory of free groups) and algebraic geometry (amoebas and tropical geometry, Pop's work on the birational anabelian conjecture, congruences for the number of points of algebraic varieties over finite fields) to number theory (proof of Catalan's conjecture, results on irrationality of the values (2n + 1) of the dzeta function, deterministic primality testing in polynomial time, Kato's work on the p-adic conjecture of Birch and Swinnerton-Dyer).

Reviewer:

jnek