He is best known for his exceptional work in algebraic geometry
Alexander Grothendieck has had an influence on the mathematics of the second half of the 20th century well beyond the scale of his publications. Grothendieck started off as an especially prolific contributor to each of the areas to which he turned, including functional analysis, algebraic geometry, and category theory, only to move away from mathematics later in his career. As a result, he has had fewer students to carry on his research tradition than if he had followed a more orthodox path. Nevertheless, one of the chief activities of the mathematicians in several areas has been to recast their field in the terms introduced by Grothendieck.
Grothendieck's first conspicuous success was in the area known as functional analysis. This mixed the traditional area of calculus with the more recent developments in topology, the field dealing in properties of geometric configurations, to be able to handle broad ranges of questions. The idea was to replace detailed and lengthy calculations with shorter and more insightful proofs. It is not surprising that such an area attracted Grothendieck, who did not feel that his greatest strength was in long, technical arguments. His contributions came in the area of reconsidering disciplines from new perspectives.
Grothendieck's first conspicuous success was in the area known as functional analysis. This mixed the traditional area of calculus with the more recent developments in topology, the field dealing in properties of geometric configurations, to be able to handle broad ranges of questions. The idea was to replace detailed and lengthy calculations with shorter and more insightful proofs. It is not surprising that such an area attracted Grothendieck, who did not feel that his greatest strength was in long, technical arguments. His contributions came in the area of reconsidering disciplines from new perspectives.