The general notion of cohomology, which concerns the topological properties of spaces described by algebraic equations, was itself first developed in the 1920s and 30s, and Weil recognized that it would be needed to prove his hypotheses. Grothendieck laid the foundations for finding the right cohomology, but his student Deligne found the final proof alone — and in a different way from what Grothendieck had imagined.
In 1978 Deligne’s proof won him the Fields Medal, the original ‘maths Nobel’, which can only be awarded to recipients under 40 years of age. The Abel Prize has no age limitations. Since completing the work that secured his reputation, he has applied tools such as l-adic cohomology to extend algebraic geometry and to relate it to other areas of maths.
“Even if you took away his most famous result on the Weil conjectures”, says Gowers, “you would still be left with a great mathematician.”
Deligne said he had not thought yet about how he would spend the money that came with his Abel Prize, but that he would like to find a way to make it useful for mathematics. “To some extent, I feel that this money belongs to mathematics, not to me.”