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 early years have been difficult to reconstruct, due to his reluctance to deal in ordinary reminiscences and his distrust of biographers. The generally accepted date and place of his birth are March 28, 1928, and Berlin, but the identity of his parents is...