Yuri Ivanovich Manin was born on February 16,1937, in the city of Simferopol—the capital of Crimea. His father died in the war; his mother was a specialist in literature. Manin's mathematical capabilities became apparent early in his life: when he was still a schoolboy he wrote a paper in which he slightly improved an estimate by I. M. Vinogradov on the number of integer points on a sphere. In 1953 he entered Moscow University. This was a rare period in the history of Mekh-Mat (the mechanics-mathematics faculty), which has played a role in the mathematical life of the USSR roughly equivalent to that of the Ecole Normale in France. Anosov and Golod were in the same year as Manin, and one course below him were Amol'd, Kirillov, Novikov and Tyurin. Such a blossoming of talent has not been repeated since. Manin immediately immersed himself in the atmosphere of intense creative work which is characteristic of Mekh-Mat. By his second year he was already an active participant in the seminar led by A. O. Gel'fond and I. R. Shafarevich. The goal of the seminar was to acquaint specialists in analytic number theory with the work of H. Hasse and A. Wed on the analogues of the Riemann hypotheses for algebraic varieties over a finite field. These results gave excellent estimates of trigonometric sums which were neces-
