In August of 1991, Alexander Grothendieck, generally regarded as one of the most important mathematicians of the 20th century and whose influence is often compared to that 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 managed to reach him at his home in the wilderness, 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. Later, even his closest relatives were not completely certain if he is still alive. (Grothendieck died on 13 November 2014, aged 86, in the hospital of Saint-Girons, Ariège.)
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 1950s and ‘60s, when he was also one of the principal members of the infamous Bourbaki group, he became increasingly interested in ecological and anti-war political movements in the 1970s. He became so involved with the struggle for social justice that he traveled to Vietnam in protest, participated in numerous demonstrations and even went took his ideals so far as to refuse a national research scholarship, in order to avoid even tacitly supporting a system of national politics he utterly opposed.
Merely to begin understanding Grothendieck’s complete devotion first to mathematics and then politics and ecology, one must look back to his childhood. His father Sasha was a convinced anarchist and participated in several rebellions in imperial Russia at the beginning of the 20th century. In 1921, he moved from Russia to Berlin where he moved in radical circles and met his future partner, Hanka, who came from a wealthy bourgeois family, but associated with members of avant-garde movements. They had little Alexander on March 28, 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 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 problem with Alexander was that he looked distinctly Jewish, an appearance with ominous implications not only for him but also the rest of the family. So his relatives 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 had 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 he enrolled at university to study mathematics. He was not impressed with his teachers, so he mostly studied on his own. Before his twentieth birthday, much like young Einstein, he independently made several important mathematical discoveries, unaware that they had already been made and published 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 replace the old set theory for formalizing mathematics with the new more general category theory which he had helped create. The set theory was constrained by a number of paradoxes and so it became too narrowly oriented to be appropriate for describing the entire diverse scope of modern mathematics. The mathematician Pierre Cartier, one of the more important members of the Bourbaki group summed up the essence of the problem: “Set theory is too restrictive: an element is either a member of a set or not, there is nothing in between.”
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. Category theory 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”.