Elon Lindenstrauss was born in Israel in 1970. He has been awarded the Fields medal for his work on ergodic theory (the study of measure preserving transformations) and its applications to number theory. Using his methods he has made significant progress on the Littlewood conjecture which remains an open problem in Diophantine approximation.
Lindeanstrauss also proved the arithmetic quantum unique ergodicity conjecture of Rudnick and Sarnak which relates to modular forms. Many other unexpected applications of his work have been found in classical number theory.
Curiously Lindenstrauss turned 40 on the 1st of August. I am not sure if there have been any other Fields medalists who were over 40 on the day of the award. Presumably the official cut-off date for the 40 year age limit is earlier.