André Weil was born in Paris to agnostic Alsatian Jewish parents who fled the annexation of Alsace-Lorraine by the German Empire after the Franco-Prussian War in 1870–71.

Weil was arrested in Finland at the outbreak of the Winter War on suspicion of spying; however, accounts of his life having been in danger were shown to be exaggerated.

For two years, he taught undergraduate mathematics at Lehigh University, where he was unappreciated, overworked and poorly paid, although he did not have to worry about being drafted, unlike his American students.

He quit the job at Lehigh and moved to Brazil, where he taught at the Universidade de São Paulo from 1945 to 1947, working with Oscar Zariski.

[6] He then returned to the United States and taught at the University of Chicago from 1947 to 1958, before moving to the Institute for Advanced Study, where he would spend the remainder of his career.

Among his major accomplishments were the 1940s proof of the Riemann hypothesis for zeta-functions of curves over finite fields,[13] and his subsequent laying of proper foundations for algebraic geometry to support that result (from 1942 to 1946, most intensively).

The so-called Weil conjectures were hugely influential from around 1950; these statements were later proved by Bernard Dwork,[14] Alexander Grothendieck,[15][16][17] Michael Artin, and finally by Pierre Deligne, who completed the most difficult step in 1973.

[18][19][20][21][22] Weil introduced the adele ring[23] in the late 1930s, following Claude Chevalley's lead with the ideles, and gave a proof of the Riemann–Roch theorem with them (a version appeared in his Basic Number Theory in 1967).

[27] He introduced the concept of a uniform space in general topology, as a by-product of his collaboration with Nicolas Bourbaki (of which he was a Founding Father).

He also chose the symbol ∅, derived from the letter Ø in the Norwegian alphabet (which he alone among the Bourbaki group was familiar with), to represent the empty set.

[28] Weil also made a well-known contribution in Riemannian geometry in his very first paper in 1926, when he showed that the classical isoperimetric inequality holds on non-positively curved surfaces.

He discovered that the so-called Weil representation, previously introduced in quantum mechanics by Irving Segal and David Shale, gave a contemporary framework for understanding the classical theory of quadratic forms.