Born in Berlin to anarchist parents—the Ukrainian Sacha Schapiro and the German Hanka Grothendieck—he bears his mother's surname. After fleeing Nazi Germany, the family settled in France, and Alexandre acquired French nationality in 1971. In 1966, he was awarded the Fields Medal but refused to travel to the USSR to receive it, in solidarity with dissident writers. The following year, he gave his medal to the North Vietnamese government to protest against the American bombing. In 1990, he withdrew to a village in the Pyrenees, where he lived almost as a hermit for the rest of his life.
Regarded as having refounded algebraic geometry and, on that account, as one of the greatest mathematicians of the 20th century, Grothendieck also wrote the monumental Récoltes et Semailles: réflexions et témoignage sur un passé de mathématicien, which had been available online for years before being published by Gallimard in 2022.