Born in Paris, he studied in Paris, Rome and Göttingen and received his doctorate in 1928. A conscientious objector and Jew, Weil fled France for Finland when World War II broke out. A famous anecdote was confirmed in his autobiography: after having been arrested under suspicion of espionage in Finland, he was saved from being shot only by the intervention of Rolf Nevanlinna.
He made substantial contributions in many areas, the most important being profound connections between algebraic geometry and number theory. Among his accomplishments were the so-called Weil conjectures (later proved by Bernard Dwork, Alexander Grothendieck and Pierre Deligne), the Riemann hypothesis for function fields, laying proper foundations for algebraic geometry, and discovery that the so-called Weil representation, previously introduced in quantum mechanics by Segal and Shale, gave a proper framework for understanding the classical theory of quadratic forms.