Folha: ‘Grothendieck, the most complex of mathematicians’
Reproduced from Marcelo Viana’s column in Folha.
He was one of the greatest mathematicians of the 20th century and probably the most complex. It’s no exaggeration to say that his work refounded several areas of mathematics on a much broader basis, as well as leading the creation of the important area of algebraic geometry. Laureate in 1966 of the Fields medal, the most important prize in mathematics, four years later he left his position at the renowned Institute for Advanced Scientific Studies (IHES) in Paris, in protest at the fact that the Institute received military funding. By then, his love of mathematics was beginning to be replaced by militancy on issues of politics, ethics and religion, which would lead him to leave the scientific community.
Alexander Grothendieck was born in Germany in 1928, the son of anarchists. His father had Jewish roots, and the couple ended up fleeing the Nazis for Paris in 1933. Alexander stayed in Berlin in the care of an acquaintance and would not be reunited with his mother until 1939 (his father was captured by the Vichy regime, handed over to the Germans and interned in Auschwitz, where he was murdered in 1942). After spending the war years mainly in concentration camps for “undesirable foreigners”, the young man entered the French education system, where he discovered a love of mathematics.
In 1950, he joined the University of Nancy, where he wrote his thesis under the guidance of Jean Dieudonnée and Laurent Schwarz (the latter was awarded the Fields Medal that same year). At that time, a long way away, the University of São Paulo was running an intelligent and very consistent policy of attracting some of the best European scientists. After finishing his doctorate in 1953, Grothendieck accepted USP ‘s invitation and traveled to Brazil. To do so, he needed a special passport: having definitively renounced his German citizenship in 1945, he lived as a stateless person until 1971, when he finally agreed to become French.
He stayed at USP until the end of 1954, where he did important work on the theory of topological vector spaces. It was also during this period in Brazil that he became close to Leopoldo Nachbin, one of the founders of the Institute of Pure and Applied Mathematics (IMPA) in Rio de Janeiro and a pioneering leader in our mathematics.
On one of my visits to the Mittag-Leffler Institute in Stockholm, I found one of his monographs in the library. In the preface, Grothendieck explains that it is a very preliminary version of a much more finished work on the theory of topological vector spaces “that I am writing with Leopoldo Nachbin”. Unfortunately, as far as I know, this work never came into existence.
He then moved to Kansas in the United States. In 1957 he was invited to visit Harvard University, but the invitation was withdrawn when he refused to sign a declaration that he would not try to overthrow the US government. The following year he returned to Paris, where he became one of the first professors at the newly created IHES. His most spectacular mathematical work comes from his time there.
Although he continued to be active in research after leaving IHES, religious and mystical themes increasingly attracted his attention. In 1988, I was already a PhD student at IMPA and I well remember the commotion in the mathematical community when Grothendieck turned down the prestigious Crafoord Prize from the Royal Swedish Academy of Sciences. In an open letter to the international community, he declared that established mathematicians like himself didn’t need any more money and attacked what he called “the decline in ethical standards in the scientific community”.