By Sophie des Beauvais
Alexander Grothendieck was a mystery—not just to the world, but to his own family. The reclusive German-born French mathematician and Fields Medal winner died quietly on November 13, at age 86, in Ariège, France.
He is most famous for his work in algebraic geometry, a field of mathematics that focuses on the relationship between equations and geometric spaces. Being a stateless person for most of his life, he was granted French citizenship in 1971. He was known to be an extremely prolific mathematician, even though most of his work was never published. Applications of his work can be found in various scientific fields, and he is also known for his radical environmental and pacifist engagement.
Grothendieck turned away from mathematics in the prime of his career and lived in seclusion for his remaining years. Despite his departure from the field, he is considered one of the greatest mathematicians of the 20th century. “He was one of the giants of mathematics, who transformed mathematics entirely with his work,” French mathematician Cedric Villani, who won the Fields Medal in 2010, told Agence France-Presse. François Hollande described him as “an out-of-the-ordinary personality in the philosophy of life.”
He was born in Berlin in 1928, the son of a Russian anarchist father, Alexander “Sacha” Shapiro, and a revolutionary journalist and mother, Johanna “Hanka” Grothendieck. His parents left him and Berlin for Paris, as the Nazis took power in Germany, and then moved to Spain to fight in the Spanish civil war alongside the Popular Front. Grothendieck eventually reunited with his parents in 1940 in southern France, but his father was soon sent to Le Vernet and Auschwitz camps, where he died in 1942.
Grothendieck went to college in Montpellier, where he studied mathematics, and then went on to begin his research in Nancy. By the late 1940s, he had entered the elite European mathematician society. However, to pursue his career, he had to find a job in teaching or research. Due to citizenship issues, he could not enter the French public service. He was stateless at the time, traveling under the Nansen passport, and since he was reluctant to participate in the military draft, he did not apply for French citizenship. He decided to move to Saõ Paulo and the United States to teach as a university professor. Two years later, after going back to France, he had the opportunity to research at the newly created Institut des Hautes Études Scientifiques (IHÉS), but he quit in 1970 when he discovered it was partially funded by the French Ministry of Defense.
He was awarded the Fields Medal in 1966, an international award considered among the highest in mathematics, and often compared to the Nobel Prize. He refused to go to Moscow to receive the prize for political reasons. Indeed, in the 1960s, he started to distance himself from the scientific community and its institutions, mainly for political and ideological reasons. Even though he never explicitly stated his reasoning, he is thought to have been frustrated by the scientific communities’ refusal to embrace his environmental concerns.
Later, in a letter he wrote to explain why he refused the Crafoord Prize, a similarly high caliber math award, he said the evolution of the scientific community was led by an “unwholesome spirit.” In 1970, he, along with two other mathematicians, founded a pacifist and environmental group called Vivre et Survivre (literally “Live and Survive”) This group was opposed to the proliferation of nuclear weapons and promoted environmental activism.
At that time, the Collège de France, a higher education and research establishment where attendance is free and open to anyone, offered him a temporary chair in mathematics, but he used it as a political tribune. Instead of teaching mathematics, he titled his class “Must we continue scientific research?” (“Faut-il continuer la recherche scientifique?”). He then taught at the University of Montpellier, from 1973 to the end of his career, and gradually withdrew from society during that time.
He retired in 1990, in a location that he kept secret, and he asked the few people he was still in contact with to destroy all of his unpublished work. He lived in a secluded, small village in the Pyrenees for the rest of his life, apart from his relatives, family, the science community, and the world.
Sophie des Beauvais is an editorial assistant at World Policy Journal.