His father, Alexander "Sascha" Schapiro (also known as Alexander Tanaroff), had Hasidic Jewish roots and had been imprisoned in Russia before moving to Germany in 1922, while his mother, Johanna "Hanka" Grothendieck, came from a Protestant family in Hamburg and worked as a journalist.

Alexander Grothendieck (; ; ; 28 March 1928 – 13 November 2014) was a mathematician who became the leading figure in the creation of modern algebraic geometry.

At the time of his birth, Grothendieck's mother was married to the journalist Johannes Raddatz and his birth name was initially recorded as "Alexander Raddatz." The marriage was dissolved in 1929 and Schapiro/Tanaroff acknowledged his paternity, but never married Hanka. Grothendieck lived with his parents in Berlin until the end of 1933, when his father moved to Paris to evade Nazism, followed soon thereafter by his mother.

At the time of his birth, Grothendieck's mother was married to the journalist Johannes Raddatz and his birth name was initially recorded as "Alexander Raddatz." The marriage was dissolved in 1929 and Schapiro/Tanaroff acknowledged his paternity, but never married Hanka. Grothendieck lived with his parents in Berlin until the end of 1933, when his father moved to Paris to evade Nazism, followed soon thereafter by his mother.

In Chambon, Grothendieck attended the Collège Cévenol (now known as the Le Collège-Lycée Cévenol International), a unique secondary school founded in 1938 by local Protestant pacifists and anti-war activists.

In 1938, aged ten, he moved to France as a refugee.

During this time, his parents took part in the Spanish Civil War, according to Winfried Scharlau, as non-combatant auxiliaries, though others state that Sascha fought in the anarchist militia. ===World War II=== In May 1939, Grothendieck was put on a train in Hamburg for France.

He and his mother were then interned in various camps from 1940 to 1942 as "undesirable dangerous foreigners".

As part of this project, his creation of topos theory, a category-theoretic generalization of point-set topology, has influenced the fields of set theory and mathematical logic. The Weil conjectures were formulated in the later 1940s as a set of mathematical problems in arithmetic geometry.

He and his mother were then interned in various camps from 1940 to 1942 as "undesirable dangerous foreigners".

His father was arrested under the Vichy anti-Jewish legislation, and sent to the Drancy, and then handed over by the French Vichy government to the Germans to be sent to be murdered at the Auschwitz concentration camp in 1942.

Records of his nationality were destroyed in the fall of Germany in 1945 and he did not apply for French citizenship after the war.

After three years of increasingly independent studies there, he went to continue his studies in Paris in 1948. Initially, Grothendieck attended Henri Cartan's Seminar at École Normale Supérieure, but he lacked the necessary background to follow the high-powered seminar.

As he consistently spelled his first name "Alexander" rather than "Alexandre" and his surname, taken from his mother, was the Dutch-like Low German "Grothendieck", he was sometimes mistakenly believed to be of Dutch origin. Grothendieck began his productive and public career as a mathematician in 1949.

Between 1949 and 1953 he worked on his doctoral thesis in this subject at Nancy, supervised by Jean Dieudonné and Laurent Schwartz.

Grothendieck introduced new methods, which allowed him to solve all these problems within a few months. In Nancy, he wrote his dissertation under those two professors on functional analysis, from 1950 to 1953.

Grothendieck introduced new methods, which allowed him to solve all these problems within a few months. In Nancy, he wrote his dissertation under those two professors on functional analysis, from 1950 to 1953.

From 1953 to 1955 he moved to the University of São Paulo in Brazil, where he immigrated by means of a Nansen passport, given that he refused to take French Nationality.

Between 1949 and 1953 he worked on his doctoral thesis in this subject at Nancy, supervised by Jean Dieudonné and Laurent Schwartz.

From 1953 to 1955 he moved to the University of São Paulo in Brazil, where he immigrated by means of a Nansen passport, given that he refused to take French Nationality.

The first major application was the relative version of Serre's theorem showing that the cohomology of a coherent sheaf on a complete variety is finite-dimensional; Grothendieck's theorem shows that the [direct image]s of coherent sheaves under a proper map are coherent; this reduces to Serre's theorem over a one-point space. In 1956, he applied the same thinking to the Riemann–Roch theorem, which had already recently been generalized to any dimension by Hirzebruch.

By 1957, he set this subject aside in order to work in algebraic geometry and [algebra].

She died in 1957 from the tuberculosis that she contracted in camps for displaced persons.

The Grothendieck–Riemann–Roch theorem was announced by Grothendieck at the initial Mathematische Arbeitstagung in Bonn, in 1957.

In 1958, he was appointed a research professor at the Institut des hautes études scientifiques (IHÉS) and remained there until 1970, when, driven by personal and political convictions, he left following a dispute over military funding.

Then, following the programme he outlined in his talk at the 1958 International Congress of Mathematicians, he introduced the theory of schemes, developing it in detail in his Éléments de géométrie algébrique (EGA) and providing the new more flexible and general foundations for algebraic geometry that has been adopted in the field since that time.

He went on to plan and execute a programme for rebuilding the foundations of algebraic geometry, which were then in a state of flux and under discussion in Claude Chevalley's seminar; he outlined his programme in his talk at the 1958 International Congress of Mathematicians. His foundational work on algebraic geometry is at a higher level of abstraction than all prior versions.

By the late 1960s, he had started to become interested in scientific areas outside mathematics.

Relatively little of his work after 1960 was published by the conventional route of the learned journal, circulating initially in duplicated volumes of seminar notes; his influence was to a considerable extent personal.

David Ruelle, a physicist who joined the IHÉS faculty in 1964, said that Grothendieck came to talk to him a few times about physics.

He received his Fields Medal in 1966 for advances in algebraic geometry, [algebra], and K-theory.

In 1958, he was appointed a research professor at the Institut des hautes études scientifiques (IHÉS) and remained there until 1970, when, driven by personal and political convictions, he left following a dispute over military funding.

He retired from scientific life around 1970, having found out that IHÉS was partly funded by the military.

Biology interested Grothendieck much more than physics, and he organized some seminars on biological topics. In 1970, Grothendieck, with two other mathematicians, Claude Chevalley and Pierre Samuel, created a political group called Survivre—the name later changed to Survivre et vivre.

He had five children: a son with his landlady during his time in Nancy, three children, Johanna (1959), Alexander (1961) and Mathieu (1965) with his wife Mireille Dufour, and one child with Justine Skalba, with whom he lived in a commune in the early 1970s. == Mathematical work == Grothendieck's early mathematical work was in functional analysis.

Grothendieck's discovery of the ℓ-adic étale cohomology, the first example of a Weil cohomology theory, opened the way for a proof of the Weil conjectures, ultimately completed in the 1970s by his student Pierre Deligne.

He eventually applied for French citizenship in the early 1980s, well past the age that exempted him from military service. ===Family=== Grothendieck was very close to his mother to whom he dedicated his dissertation.

It also includes a study of Teichmüller theory. In 1983, stimulated by correspondence with Ronald Brown and Tim Porter at Bangor University, Grothendieck wrote a 600-page manuscript titled Pursuing Stacks, starting with a letter addressed to Daniel Quillen.

Much of this work anticipated the subsequent development of the motivic homotopy theory of Fabien Morel and Vladimir Voevodsky in the mid-1990s. In 1984, Grothendieck wrote the proposal Esquisse d'un Programme ("Sketch of a Programme") for a position at the Centre National de la Recherche Scientifique (CNRS).

Grothendieck added however that his views are "in no way meant as a criticism of the Royal Academy's aims in the administration of its funds" and added "I regret the inconvenience that my refusal to accept the Crafoord prize may have caused you and the Royal Academy." La Clef des Songes, a 315-page manuscript written in 1987, is Grothendieck's account of how his consideration of the source of dreams led him to conclude that God exists.

The Grothendieck Festschrift, published in 1990, was a three-volume collection of research papers to mark his sixtieth birthday in 1988. In it, Cartier notes that as the son of an antimilitary anarchist and one who grew up among the disenfranchised, Grothendieck always had a deep compassion for the poor and the downtrodden.

Parts of Récoltes et semailles have been translated into Spanish and into Russian and published in Moscow. In 1988 Grothendieck declined the Crafoord Prize with an open letter to the media.

Influenced by the Catholic mystic Marthe Robin who was claimed to survive on the Holy Eucharist alone, Grothendieck almost starved himself to death in 1988.

The Grothendieck Festschrift, published in 1990, was a three-volume collection of research papers to mark his sixtieth birthday in 1988. In it, Cartier notes that as the son of an antimilitary anarchist and one who grew up among the disenfranchised, Grothendieck always had a deep compassion for the poor and the downtrodden.

His growing preoccupation with spiritual matters was also evident in a letter titled Lettre de la Bonne Nouvelle sent to 250 friends in January 1990.

In 1991, he moved to the French village of Lasserre in the Pyrenees, where he lived in seclusion, still working tirelessly on mathematics until his death in 2014. == Life == ===Family and childhood=== Grothendieck was born in Berlin to anarchist parents.

Written in 1991, this latter opus of about 2000 pages further developed the homotopical ideas begun in Pursuing Stacks.

They have been digitized for preservation and are freely available in open access through the Institut Montpelliérain Alexander Grothendieck portal. ===Retirement into reclusion and death=== In 1991, Grothendieck moved to a new address which he did not provide to his previous contacts in the mathematical community.

In it, he described his encounters with a deity and announced that a "New Age" would commence on 14 October 1996. Over 20,000 pages of Grothendieck's mathematical and other writings, held at the University of Montpellier, remain unpublished.

Written in 1991, this latter opus of about 2000 pages further developed the homotopical ideas begun in Pursuing Stacks.

After his death, it was revealed that he lived alone in a house in Lasserre, Ariège, a small village at the foot of the Pyrenees. In January 2010, Grothendieck wrote the letter "Déclaration d'intention de non-publication" to Luc Illusie, claiming that all materials published in his absence have been published without his permission.

A website devoted to his work was called "an abomination." This order may have been reversed later in 2010. On 13 November 2014, aged 86, Grothendieck died in the hospital of Saint-Girons, Ariège. ===Citizenship=== Grothendieck was born in Weimar Germany.

Alexander Grothendieck (; ; ; 28 March 1928 – 13 November 2014) was a mathematician who became the leading figure in the creation of modern algebraic geometry.

In 1991, he moved to the French village of Lasserre in the Pyrenees, where he lived in seclusion, still working tirelessly on mathematics until his death in 2014. == Life == ===Family and childhood=== Grothendieck was born in Berlin to anarchist parents.

A website devoted to his work was called "an abomination." This order may have been reversed later in 2010. On 13 November 2014, aged 86, Grothendieck died in the hospital of Saint-Girons, Ariège. ===Citizenship=== Grothendieck was born in Weimar Germany.

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