1. Alexander Grothendieck's research extended the scope of the field and added elements of commutative algebra, homological algebra, sheaf theory, and category theory to its foundations, while his so-called "relative" perspective led to revolutionary advances in many areas of pure mathematics.
Alexander Grothendieck is considered by many to be the greatest mathematician of the twentieth century.
Alexander Grothendieck received the Fields Medal in 1966 for advances in algebraic geometry, homological algebra, and K-theory.
Alexander Grothendieck later became professor at the University of Montpellier and, while still producing relevant mathematical work, he withdrew from the mathematical community and devoted himself to political and religious pursuits.
Alexander Grothendieck lived with his parents in Berlin until the end of 1933, when his father moved to Paris to evade Nazism.
Alexander Grothendieck was left in the care of Wilhelm Heydorn, a Lutheran pastor and teacher in Hamburg.
In May 1939, Alexander Grothendieck was put on a train in Hamburg for France.
Alexander Grothendieck's father was arrested under the Vichy anti-Jewish legislation, and sent to the Drancy internment camp, 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.
In Le Chambon, Alexander Grothendieck attended the College Cevenol, a unique secondary school founded in 1938 by local Protestant pacifists and anti-war activists.
Alexander Grothendieck introduced new mathematical methods that enabled him to solve all of these problems within a few months.
Alexander Grothendieck stayed in Sao Paulo until the end of 1954.
Alexander Grothendieck moved to Lawrence, Kansas at the beginning of 1955, and there he set his old subject aside in order to work in algebraic topology and homological algebra, and increasingly in algebraic geometry.
In 1958, Alexander Grothendieck was installed at the Institut des hautes etudes scientifiques, a new privately funded research institute that, in effect, had been created for Jean Dieudonne and Alexander Grothendieck.
Alexander Grothendieck attracted attention by an intense and highly productive activity of seminars there.
Alexander Grothendieck practically ceased publication of papers through the conventional, learned journal route.
Alexander Grothendieck went on to introduce the etale cohomology theory of schemes, providing the key tools for proving the Weil conjectures, as well as crystalline cohomology and algebraic de Rham cohomology to complement it.
Alexander Grothendieck provided, by means of a categorical Galois theory, an algebraic definition of fundamental groups of schemes giving birth to the now famous etale fundamental group and he then conjectured the existence of a further generalization of it, which is known as the fundamental group scheme.
Alexander Grothendieck strongly opposed both United States intervention in Vietnam and Soviet military expansionism.
Alexander Grothendieck retired from scientific life around 1970 after he had found out that IHES was partly funded by the military.
Alexander Grothendieck returned to academia a few years later as a professor at the University of Montpellier.
In that publication, Cartier notes that as the son of an antimilitary anarchist and one who grew up among the disenfranchised, Alexander Grothendieck always had a deep compassion for the poor and the downtrodden.
David Ruelle, a physicist who joined the IHES faculty in 1964, said that Alexander Grothendieck came to talk to him a few times about physics.
Alexander Grothendieck devoted the next three years to this group and served as the main editor of its bulletin.
Alexander Grothendieck then became a professor at the University of Montpellier, where he became increasingly estranged from the mathematical community.
Alexander Grothendieck formally retired in 1988, a few years after having accepted a research position at the CNRS.
In 1983, stimulated by correspondence with Ronald Brown and Tim Porter at Bangor University, Alexander Grothendieck wrote a 600-page manuscript entitled Pursuing Stacks.
In 1984, Alexander Grothendieck wrote the proposal Esquisse d'un Programme for a position at the Centre National de la Recherche Scientifique.
Alexander Grothendieck complains about what he saw as the "burial" of his work and betrayal by his former students and colleagues after he had left the community.
Alexander Grothendieck helped with the translation and wrote a preface for it, in which he called Tsuji his "first true collaborator".
In 1988, Alexander Grothendieck declined the Crafoord Prize with an open letter to the media.
Alexander Grothendieck wrote that he and other established mathematicians had no need for additional financial support and criticized what he saw as the declining ethics of the scientific community that was characterized by outright scientific theft that he believed had become commonplace and tolerated.
Alexander Grothendieck's growing preoccupation with spiritual matters was evident in a letter entitled Lettre de la Bonne Nouvelle sent to 250 friends in January 1990.
The Alexander Grothendieck Festschrift, published in 1990, was a three-volume collection of research papers to mark his sixtieth birthday in 1988.
In 1991, Alexander Grothendieck moved to a new address that he did not share with his previous contacts in the mathematical community.
In January 2010, Alexander Grothendieck wrote the letter entitled "Declaration d'intention de non-publication" to Luc Illusie, claiming that all materials published in his absence had been published without his permission.
Alexander Grothendieck asked that none of his work be reproduced in whole or in part and that copies of this work be removed from libraries.
Alexander Grothendieck characterized a website devoted to his work as "an abomination".
On 13 November 2014, aged 86, Alexander Grothendieck died in the hospital of Saint-Lizier or Saint-Girons, Ariege.
Alexander Grothendieck eventually applied for French citizenship in the early 1980s, after he was well past the age that would have required him to do military service.
Alexander Grothendieck was very close to his mother, to whom he dedicated his dissertation.
Alexander Grothendieck died in 1957 from tuberculosis that she contracted in camps for displaced persons.
Alexander Grothendieck had five children: a son with his landlady during his time in Nancy; three children, Johanna, Alexander, and Mathieu with his wife Mireille Dufour; and one child with Justine Skalba, with whom he lived in a commune in the early 1970s.
Alexander Grothendieck took them to a higher level of abstraction and turned them into a key organising principle of his theory.
Alexander Grothendieck shifted attention from the study of individual varieties to his relative point of view, allowing a broad generalization of many classical theorems.
Alexander Grothendieck went on to plan and execute a programme for rebuilding the foundations of algebraic geometry, which at the time were in a state of flux and under discussion in Claude Chevalley's seminar.
Alexander Grothendieck outlined his programme in his talk at the 1958 International Congress of Mathematicians.
Alexander Grothendieck adapted the use of non-closed generic points, which led to the theory of schemes.
Alexander Grothendieck is noted for his mastery of abstract approaches to mathematics and his perfectionism in matters of formulation and presentation.
Alexander Grothendieck's influence spilled over into many other branches of mathematics, for example the contemporary theory of D-modules.
The bulk of Alexander Grothendieck's published work is collected in the monumental, yet incomplete, Elements de geometrie algebrique and Seminaire de geometrie algebrique.
Alexander Grothendieck's work includes the invention of the etale and l-adic cohomology theories, which explain an observation made by Andre Weil that argued for a connection between the topological characteristics of a variety and its diophantine properties.
Alexander Grothendieck wrote that, of these themes, the largest in scope was topoi, as they synthesized algebraic geometry, topology, and arithmetic.
Alexander Grothendieck wrote that the first and last themes, topological tensor products and regular configurations, were of more modest size than the others.
Alexander Grothendieck is considered by many to be the greatest mathematician of the twentieth century.
Alexander Grothendieck approached algebraic geometry by clarifying the foundations of the field, and by developing mathematical tools intended to prove a number of notable conjectures.
Alexander Grothendieck laid a new foundation for algebraic geometry by making intrinsic spaces and associated rings the primary objects of study.
The Benjamin Labatut book When We Cease to Understand the World dedicates one chapter to the work and life of Alexander Grothendieck, introducing his story by reference to the Japanese mathematician Shinichi Mochizuki.