Vladimir Voevodsky – Work and Destiny

[摘要] Vladimir started his mathematical education as ahigh school student attending the Shafarevich seminarat the Steklov Institute of the Russian Academy of Sciences in Moscow. He bypassed the “usual” mathematical Olympiad training and moved directly into research.His exceptional talent and focus were already apparentthen to all who interacted with him. As an undergraduatestudent at Moscow State University, he fully immersedhimself in the study of Grothendieck’s anabelian geometry, formulated in 1984 in Esquisse d’un programme. Hisearly work, jointly with G. Shabat, concerned Dessinsd’enfants, the study of Galois groups of curves over number fields via their representation by special graphs onRiemann surfaces. The inspiration came partially froma result of Belyi, who proved that all such curves admitspecial meromorphic functions, with only three ramification points; moreover, the existence of such functionscharacterises these curves among all complex projective curves. At that time, it seemed that this result mightopen the door to the solution of major open problemsin arithmetic geometry, such as Mordell’s conjectureand Fermat’s last theorem, as well as another importantconjecture that is still open: the Section Conjecture ofGrothendieck. Vladimir’s interest in this area showed hisdetermination, early on, to tackle the most difficult andchallenging conjectures in mathematics.