Pierre Deligne proves in 1973-74, in a paper published in Publications Mathématiques de l'IHÉS, the last and most difficult of the Weil conjectures: the analogue of the Riemann hypothesis for algebraic varieties over finite fields. The conjectures, formulated by André Weil in 1949, had driven much of the development of modern algebraic geometry for more than two decades, including Alexander Grothendieck's scheme program, whose tools Deligne uses decisively in his final proof. The result deeply unifies algebraic geometry and number theory. Deligne received the Fields Medal in 1978.