While living in an internment camp in Vichy France, Alexander Grothendieck was tutored in mathematics by another prisoner, a girl named Maria. Maria taught Grothendieck, who was twelve, the definition of a circle: all the points that are equidistant from a given point. The definition impressed him with “its simplicity and clarity,” he wrote years later. The property of perfect rotundity had until then appeared to him to be “mysterious beyond words.”
Grothendieck became a revered mathematician. His work involved finding the right vantage point—from there, solutions to problems would follow easily. He rewrote definitions, even of things as basic as a point; his reframings uncovered connections between seemingly unrelated realms of math. He spoke of his mathematical work as the building of houses, contrasting it with that of mathematicians who make improvements on an inherited house or construct a piece of furniture. Colin McLarty, a logician and philosopher of math at Case Western Reserve, told me, “Lots of people today live in Grothendieck’s house, unaware that it’s Grothendieck’s house.” The M.I.T. mathematician Michael Artin, who worked with Grothendieck in the early sixties, laughed when I asked him about Grothendieck’s contributions. “Well, everything changed in the field,” he said. “He came, and it was like night and day. It was a revolution.”
When Grothendieck was forty-two years old, he abruptly left the field of mathematics. For a while, he still did occasional private mathematical work—“to my own surprise, and despite my long-standing conviction,” he later wrote, “that I would never publish a single new line of mathematics in my lifetime.” By the time he was sixty-three, his whereabouts were known by almost no one. Nor was it known whether he was still pursuing solutions to the problems that had obsessed him for decades. Stories circulated of a bearded man wearing a long robe, hermited away somewhere in the Pyrenees.
Grothendieck wrote that his central work had been cruelly abandoned by others—but that wasn’t entirely true. Research was still ongoing in mathematical domains termed “Grothendieck universes,” and although his work wasn’t always cited, his methods were used so often that to cite him would be like citing Leibniz or Newton every time you used calculus. In 1992, two mathematicians, Leila Schneps and Pierre Lochak, decided that they would find Grothendieck.