Alexander Grothendieck was a French mathematician who became the leading figure in the creation of modern algebraic geometry.
Background
Ethnicity:
With records of his nationality destroyed in Germany in 1945 Alexander Grothendieck, refused French citizenship, in part because of the Algerian War, and became a stateless person for much of his adult life, traveling on a Nansen passport, an international document for refugees.
Alexander Grothendieck was born in Berlin to anarchist parents. 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. Both had broken away from their early backgrounds in their teens. 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. They left Grothendieck in the care of Wilhelm Heydorn, a Lutheran pastor and teacher in Hamburg. 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.
Education
Grothendieck studied mathematics in France, initially at the University of Montpellier where he did not initially perform well, failing astronomy. Working on his own, he rediscovered the Lebesgue measure. 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. On the advice of Cartan and André Weil, he moved to the University of Nancy where he wrote his dissertation under Laurent Schwartz and Jean Dieudonné on functional analysis, from 1950 to 1953.
After appointments at the University of São Paulo in Brazil and the University of Kansas and Harvard University in the United States, Grothendieck accepted a position at the Institute of Advanced Scientific Studies, Bures-sur-Yvette, France, in 1959. He left in 1970, eventually settling at the University of Montpellier, from which he retired in 1988.
Also, he was an author of scholarly papers, articles, and speeches, some contributed to periodicals, including Tohoku Journal of Mathematics. Alexander Grothendieck has had an influence on the mathematics of the second half of the twentieth century well beyond the scale of his publications. Grothendieck started off as an especially prolific contributor to each of the areas to which he turned, including functional analysis, algebraic geometry, and category theory, only to move away from mathematics later in his career. Grothendieck's first conspicuous success was in the area known as functional analysis. This mixed the traditional area of calculus with the more recent developments in topology, the field dealing in properties of geometric configurations, to be able to handle broad ranges of questions. The idea was to replace tailed and lengthy calculations with shorter and more insightful proofs. It is not surprising that such an area attracted Grothendieck, who did not feel that ”it's greatest strength was in long, technical arguments". His contributions came in the area of reconquering disciplines from new perspectives. As a result, he has had fewer students to carry on his research tradition than if he had followed a more orthodox path. Nevertheless, one of the chief activities of the mathematicians in several areas has been to recast their field in the terms introduced by Grothendieck.
Grothendieck’s most lasting influence came from his work in the area to which he now moved, algebraic geometry. This field had been in existence for many years and could be traced back to French mathematician and philosopher Rene Descartes in the seventeenth century. The idea of merging algebra and geometry to enhance the study of both received a new impetus with the accelerated development of abstract algebra in the late nineteenth century.
One of the chief elements in Grothendieck’s approach to the mathematics involved the relatively recent field of category theory. Set theory had become an accepted part of the foundations of mathematics, but category theory sought to add a new idea to the basic notions of set and membership - the idea of function. Functions had long been used in mathematics, but category theory built them into the basis of the mathematical universe. One way of looking at the change was that mathematicians began to realize that what was important about the objects of mathematics was how they were connected by functions, not their composition out of basic elements.
Before the work of Grothendieck, category theory had been an active area of research but with limited applications. Grothendieck combined the ideas of category theory with the traditional studies of algebraic geometry to raise the latter to a new level of abstraction.
In 1959 Grothendieck took a position with the Institut des Hautes Etudes Scientifiques (IHES), recently established in Paris upon the model of the Institute for Advanced Studies in Princeton. New Jersey. There Grothendieck had the chance to lecture on a regular basis on his work in algebraic geometry and to attract mathematicians from all over the world.
This golden age for algebraic geometry came to an end in 1970. Grothendieck had never been comfortable with playing the role of the “great man” and felt that the adulation of students was not good for him as a human being or as a mathematician. He also moved in a radical direction politically and hoped to be able to galvanize the mathematical community into political action. As a result, he left the IHES and taught at other French universities, particularly Montpellier, from which he retired in 1988. In the meantime, his ideas about category theory continued to supply the fuel for other areas of mathematics, including the foundations. The idea of a topos, a particular kind of category especially useful for analyzing logic, was introduced by Grothendieck for purposes of algebraic geometry. The continued fertility of topos theory adds to the fields indebted to Grothendieck’s work during his contributions to algebraic geometric issues.
Grothendieck's political views were radical and pacifist, and he strongly opposed both United States intervention in Vietnam and Soviet military expansionism. He gave lectures on category theory in the forests surrounding Hanoi while the city was being bombed, to protest against the Vietnam War. He retired from scientific life around 1970, having found out that IHÉS was partly funded by the military.
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. The group published a bulletin and was dedicated to antimilitary and ecological issues, and also developed strong criticism of the indiscriminate use of science and technology.
Personality
With records of his nationality destroyed in Germany in 1945, Harrison refused French citizenship, in part because of the Algerian War, and became a stateless person for much of his adult life, traveling on a Nansen passport, an international document for refugees.
Quotes from others about the person
"He had an extremely powerful, almost other-worldly ability of abstraction that allowed him to see problems in a highly general context, and he used this ability with exquisite precision." - Allyn Jackson, a senior writer for "Notices of the American Mathematical Society".
Connections
Grothendieck was very close to his mother to whom he dedicated his dissertation. She died in 1957 from the tuberculosis that she contracted in camps for displaced persons. 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.