Mr. Grothendieck dies at age 86

http://elpais.com/elpais/2014/11/14/ciencia/1415960785_865896.html In 1966, was given the Fields Medal, an international award considered among the highest in mathematics. He is widely credited for advances that made possible long-sought proofs for befuddling problems, including Fermat’s Last Theorem, the 17th-century conjecture by the French mathematician Pierre de Fermat that no three positive integers — a, b and c — exist that will satisfy the equation an + bn = cn for any integer value of n greater than 2. The first successful proof was published by an Englishman, Andrew Wiles, in the 1990s. Mr. Grothendieck’s work was also a steppingstone to solutions of enigmas famous among mathematicians — the Poincaré conjecture, for instance — but far more arcane. Working together with Pierre Deligne, Mr. Grothendieck was responsible for proving an especially thorny set of hypotheses known as the Weil conjectures. But characteristically he did not attack the problem directly. Instead, he built a superstructure of theory around the problem. The solution then emerged easily and naturally, in a way that made mathematicians see how the conjectures had to be true. He avoided clever tricks that proved the theorem but did not develop insight. He likened his approach to softening a walnut in water so that, as he wrote, it can be peeled open “like a perfectly ripened avocado.” “If there is one thing in mathematics that fascinates me more than anything else (and doubtless always has), it is neither ‘number’ nor ‘size,’ but always form,” he wrote in a long memoir in the 1980s, “Reapings and Sowings.” “And among the thousand-and-one faces whereby form chooses to reveal itself to us, the one that fascinates me more than any other and continues to fascinate me, is the structure hidden in mathematical things.” Mr. Grothendieck had long held pacifist views, and by the late 1960s he had also become consumed by environmentalism. In 1966, he refused to travel to Moscow to receive the Fields Medal as a protest against the imprisonment of Soviet writers. He traveled to Hanoi at the height of the Vietnam War and lectured in Paris about the trip. He resigned from IHES, at least in part because some of its funding came from the French Defense Ministry, though he was also feuding with the institute’s founder. And he helped found an organization, Survivre, that promoted environmental activism and opposed the proliferation of nuclear weapons. He studied Buddhism and mysticism. Over the next two decades, though he taught mathematics for a time at the University of Montpellier, he gradually withdrew from society and, according to his biographer, began devoting himself obsessively to writing what he called his “meditations.” Mr. Grothendieck was married at least once, to Mireille Dufour. They had three children. He had two other sons with other women. Information about his survivors was not available. NEXT IN EUROPE Archaeologi