Alexander Grothendieck

Alexander Grothendieck (Berlin, Free State of Prussia, March 28, 1928-Saint-Girons, Ariège, November 13, 2014) was a stateless mathematician, nationalized French in the years 1980. During the second half of the XX century, he carried out an extraordinary process of unifying arithmetic, algebraic geometry and topology, giving great impetus to the development of these three fundamental branches of mathematics. He is considered by many to be the most important mathematician of the XX century.

Family history

His father, Aleksandr Petrovich Shapiro or Sasha Shapiro (Novozíbkov, August 6, 1890 - Auschwitz, 1942?), was a Russian anarchist Jew. He was sentenced to death by the tsarist regime in 1907, but his sentence was commuted to life imprisonment because of his youth. Released by the 1917 revolution, he was sentenced to death by the communist regime; he emigrated clandestinely to Berlin, where he met the occasional journalist Hanka Grothendieck (Hamburg, August 21, 1900-Montpellier, December 16, 1957) in anarchist circles. These events are narrated in her unpublished autobiographical novel Eine Frau until the conception of the only child she had with Shapiro: Alexander Grothendieck.

Between 1934 and 1939, Grothendieck lived in Hamburg with an adoptive family, while his parents were in France and participated in the Spanish Civil War alongside the anarchists. In 1939, he joined her mother Hanka in France. In 1940, being German, he was interned in the Rieucros camp together with his mother, and studied at the nearby Mende Institute. Meanwhile, his father was interned in the Le Vernet camp and deported by the Nazis in 1942 to Auschwitz - he appears under the name of Alexandre Tanaroff on the list of victims of the Holocaust.

In 1942, Grothendieck was welcomed at La Guespy, the Swiss Aid children's home for refugees in Le Chambon-sur-Lignon, and finished his baccalaureate at Collège Cévénol.

First works

Between 1945 and 1948, Alexander Grothendieck studied mathematics at the University of Montpellier and from there he went to Paris, where he attended Henri Cartan's seminar. Laurent Schwartz directed his doctoral thesis on functional analysis in Nancy. Upon meeting him, they gave their new student a list of fourteen problems that they considered a vast program of work for several years, and asked him to choose one of them. Some months later, Alexander went to see the directors of him having solved the fourteen problems: the legend had just begun. Later, Grothendieck became part of the Bourbaki group. In that group, he was interested in knowing what the natural concepts that serve as a basis for geometry should be. Between 1957 and 1962 he presented at the Bourbaki Seminar a total renewal of the fundamentals of algebraic geometry, and in 1958 he introduced K-theory. Within that work, he stated and proved the Riemann-Roch-Grothendieck theorem, a result that would give him worldwide fame as a mathematician.

Mature works

In 1959, the Institute for Higher Scientific Studies (IHES) was created in Bures-sur-Yvette, near Paris, and he was offered a place in mathematics. There, he developed an intense work until 1970, renewing algebraic geometry from start to finish. His Elementos de geometría algebraica, of which he wrote four volumes out of the 12 planned, and the series of seven Seminars on Algebraic Geometry, make a synthesis with arithmetic and topology around the two crucial concepts of "scheme" and "topos" (one of the largest foundational works ever done in mathematics). Central inspiration of this stage were Weil's conjectures, which he largely demonstrated, finishing his work by his most brilliant student Pierre Deligne. In 1966, at the International Mathematical Congress in Moscow, which he did not attend in rejection of the Soviet Union, he received the Fields Medal. In those years, he also unraveled (though did not publish) the theory of motifs, a fantastic insight into a closer union of arithmetic and geometry that still remains largely unproven, and set forth in so-called "standard conjectures" the principles that would allow the development of the theory of motives.^{[citation required]}

Political positions and last years

In November 1967, during the Vietnam War, he traveled to Hanoi to give a lecture on category theory, in protest against the war.

In 1970, he left the IHES, because this institution accepted funds from military institutions, and works in pacifist and environmental circles. Faced with the spiritual stagnation caused by his absorbing dedication to mathematics, he also abandoned all traditional mathematical activities. ^{[citation needed ]}

In 1972, he became a professor at the University of Montpellier, in whose Faculty of Sciences he taught and continued his mathematical research outside of "official circuits." In 1984, he applied for a position at the CNRS, for which he wrote the report Esquisse d'un Program , an outline of the mathematical subjects he studied in recent years and a program to continue them. in the future. At this time, he wrote thousands of pages with mathematical and non-mathematical meditations, including Eloge (lost?), Récoltes et Semailles, where he reviews his career vital in the mathematical world, and La Clef des Songes, where he explains his discovery of God (both works still unpublished).

In 1988, he retired and, together with his student Pierre Deligne, received the Crafoord Prize of the Royal Swedish Academy of Sciences. Despite his large financial endowment, he rejected it because "given the decline in scientific ethics, participating in the prize game means endorsing a spirit that seems to me insane" and because "my pension is more than enough to meet my material needs and those who depend on me".

In 1990, he moved his residence to the town of Lasserre (Ariège), next to the French Pyrenees, and only accepted direct human contact with his closest friends, neighbors and sporadic visitors, while he continued his reflections.^{[ citation required]}

In 2004 he developed the proposal Esquisse d'un programme.

In January 2010, he sent a letter clearly expressing his desire that his writings not be published or disseminated.

He passed away on November 13, 2014, at the Ariège Couserans Hospital in Saint-Girons.

Anecdotes

When asked, for some reason, to offer a random prime number, Grothendieck gave the answer 57, which is not a prime number, with which since then this number has been jokingly known as &# 34;Grothendieck's cousin".