The Hermit of the Pyrenees

In August of 1991, Alexander Grothendieck, who is thought by many to be one of the most important mathematicians of the 20^th century and whose influence is often compared to that of the likes of Albert Einstein, suddenly left his home in the south of France and headed for the Pyrenees. Since then, he has been living as a hermit high in the mountains somewhere between France and Spain, completely cut off from civilization. In the mid-nineties, a few mathematicians still managed to reach his wilderness dwelling, but for the last couple of years he has remained unseen. His mail is still piling up at the University of Montpellier, but he explicitly prohibited even the handful of his friends who, at the beginning, knew where in the mountains he lived, to bring it to him. Today, even his closest relatives are not completely certain if he is still alive.

Even before his departure into the deep wilderness, Grothendieck lived a very secluded, ascetic life in an old house with no electricity in a village near Montpellier in France. After a successful mathematical career in the fifties and sixties, when he was also one of the principal members of the infamous Bourbaki group (see article The Genius Who Wasn’t), he became increasingly interested in ecological and anti-war political movements in the seventies. He became so involved with the struggle for social justice that he traveled to Vietnam in protest, participated in numerous demonstrations and even went so far with his ideals as to refuse a national research scholarship in order to avoid tactically supporting the national politics which he strongly opposed.

To be able to at least come near understanding Grothendieck’s utter and complete devotion to first mathematics and then politics and ecology, one must look back to his childhood. His father Sasha was a convinced anarchist and had already taken part in several rebellions in the imperial Russia at the beginning of the 20^th century. In 1921, he moved from Russia to Berlin where he moved in radical circles and met Hanka who came from a wealthy bourgeois family, but associated with members of avant-garde movements. They had little Alexander on the 28^th of March 1928. At the time, the young family also supported Hanka’s daughter Maidi from her first marriage.

In 1933, when Nazis came to power, Alexander’s father Sasha fled Berlin for Paris and was soon followed by Alexander’s mother, but she did not take her son and daughter with her. She placed Alexander into foster care with a family that lived near Hamburg, and left her daughter in an institution for handicapped children, even though she was a perfectly healthy child. Alexander lived with his foster family from his fifth to his eleventh year. He rarely received letters from his mother and never even heard from his father nor from his other relatives who lived in the nearby Hamburg. Naturally, this period of separation from his parents left a deep mark on young Alexander.

In 1939, the political pressure became too great and the foster family could no longer take care of all the children. The trouble with Alexander was that he looked distinctly Jewish which could be dangerous for him as well as for the rest of the family. So they found Hanka with the help of the French consulate, sat little Alexander on a train and sent him from Hamburg to Paris. Both of his parents spent some of the years away from their son in Spain where they fought against Franco. On his return to France his father was arrested as a “dangerous foreigner” by the French authorities of the time and sent to an internment camp. He died a few years later in Auschwitz.

Hanka in Alexander spent the war in different internment camps, but as soon as the war was over Alexander enrolled at a University and started studying mathematics. He was not impressed with his teachers, so he mostly studied on his own. Before his twentieth birthday, and much like young Einstein, he independently came upon several important mathematical findings for which he did not know that they had already been published before by other mathematicians.

When he moved to Paris he started to spend time with the most prominent French mathematicians of the time and joined the Bourbaki circle of which he quickly became a driving force. He was becoming more and more famous for his highly abstract approach to solving mathematical problems. His friends later claimed that he was unable to think about concrete things, because his mind only functioned on a universal level.

After a long and productive collaboration with the Bourbaki, he left the group in protest, because most of the members refused to accept his suggestion to use the more general category theory, which he had also helped create, as the foundation for the formalization of mathematics instead of the set theory. The set theory was limited by several paradoxes and so it became too narrowly oriented to be appropriate for describing the entire diversity of modern mathematics. The mathematician Pierre Cartier, one of the more important members of the Bourbaki group summed up the essence of the problem: “The set theory is to constraining; an element can either be a member of a set or not, there is no intermediate possibility.”

The decision of the Bourbaki to refuse Grothendieck’s suggestion to move away from the set theory to the category theory was, as it soon turned out, a big mistake. It was the category theory that became a very important area in mathematics in the years to follow, and Grothendieck received many awards for his achievements, among others the Fields Medal, also known as the “Nobel Prize of Mathematics”.