Alexander Grothendieck is one of the major mathematicians of 20th century, known for his groundbreaking theories in mathematics. Read through the article to know more about his profile, childhood, life and timeline.

Alexander Grothendieck

Alexander Grothendieck

Also Listed In: Mathematicians

Famous as: Mathematician

Nationality: French

Born on: 28 March 1928 AD    Famous 28th March Birthdays

Zodiac Sign: Aries    Famous Arians

Born in: Berlin, Prussia, Germany

father: Alexander "Sascha" Shapiro aka Tanaroff

mother: Johanna "Hanka" Grothendieck

education: University of Montpellier, Nancy-Université

Works & Achievements: Alexander Grothendieck is a prominent mathematician who is well known for his theories in algebraic geometry, homological algebra and functional analysis.

awards: Fields Medal (1966)
Crafoord Prize (1988)

  Alexander Grothendieck.  2 People do.
Jihye Priya

One of the foremost mathematicians of 20th century, Alexander Grothendieck is a pioneer of modern algebraic geometry. His contributions to algebraic geometry, homological algebra and functional analysis are so huge and vast, that it antagonised even his most ardent followers who envied him for his achievements. His genius was honoured by 'Fields medal' and the Crafoord prize (co-awarded) though he refused both on ethical grounds. During his long career in the Institute of Advanced Scientific Studies in Paris, his biggest achievements were not only his theorems and concepts, but also a huge bunch of students and a strong school of thought that, helped him come up with groundbreaking theories in mathematics. The world owes a great deal to this great French mathematician for the increased generalization and formalisation of mathematics in 20th century. Though leading a secluded life since his retirement in 1988, Grothendieck's achievements are well remembered and acknowledged by the mathematical community even now.

Early Life And Childhood 
Alexander Grothendieck was born on March 28, 1928 in Berlin to Russian-born, Jewish father, Alexander Sascha Shapiro, and German protestant mother, Johanna Hanka Grothendieck. Alexander Grothendieck was born out of wedlock, though the couple stayed together all their lives. Grothendieck’s mother was briefly married to a German journalist, Johannes Raddatz and hence, his birth name was Alexander Raddatz. Grothendieck lived with his biological parents until 1933 after which they moved to Paris leaving him with Wilhelm Heydorn, a pastor and teacher in Hamburg where he attended school. In the meantime, his parents became part of Spanish Civil war.
 
Education And Career
During the Second World War, Grothendieck lived in France, with Heydorn, hidden in a village. In 1942, his Jewish father was deported to Auschwitz, where he died in a concentration camp. During the war, Grothendieck attended a secondary school in Chambon (France), from where he discovered his fascination with mathematics. Once the war ended, he attended the University of Montpellier in France, hoping to pursue a career as a mathematics teacher. After completing three years of studies, he received a scholarship in 1948, to carry on with his studies in Paris. Grothendieck then moved to the University of Nancy, where he did a dissertation on Functional Analysis under Laurent Schwartz during 1950-1953. By this time, he had become an expert on topological vector verses. In 1957, he started working on algebraic geometry and homological algebra.
 
Golden Age In Institute of Advanced Scientific Studies (IHES)
Institute of Advanced Scientific Studies, a reputed institution in France, hired Grothendieck who made his years productive by organising seminars and inspiring young talents. As a mathematician, the years in IHES were very productive for Grothendieck and he discovered the subject of K-theory and wrote proof for Grothendieck–Hirzebruch–Riemann–Roch theorem in algebraic geometry. In the meantime, from 1953 to 1955, Grothendieck visited the University of Sao Paulo and came back to France in 1956 to rejoin the institute. In 1960, he visited the University of Kansas and started working on geometry and topology. In 1966, he was honoured with Fields medal, renowned as the ‘Nobel Prize of Mathematics’, for his immense contributions to this field. However, he skipped the ceremony which was held in Moscow as a protest against the subjugation in Eastern Europe. The time Grothendieck spent in IHES is referred to as his golden age. It was during this time that a new school of thought took shape under him, making IHES the epicentre of algebraic geometry. This strong school of thought and the huge bunch of students he taught are considered Grothendieck’s biggest assets. His student list included names such as Michel Demazure (worked on SGA3 and group schemes), Michel Raynaud, Jean-Louis Verdier (co-founded derived category theory), Luc Illusie (cotangent complex), Mike Artin (étale cohomology), Nick Katz (monodromy theory and Lefschetz pencils) and so on. There were also plenty of concepts named after him such as Grothendieck group, the Grothendieck category, Grothendieck universe and Grothendieck topology.

The twelve years of his career at IHES also witnessed Grothendieck leading an apparently bourgeois life. He got married to Mireille Dufour with whom he had three children. He did not allow his children to have conventional education nor did they attend public schools. He always believed that finding one’s own way is more important than attending schools. Grothendieck also travelled extensively over Eastern Europe and even delivered a lecture at the School of Mathematics in Bucharest. As a person, he was a pacifist with plenty of ideals and goals and was vehemently against the nuclear-missile build-up of soviets; this was also a key reason why he refused to visit Moscow to receive his Fields Medal. 

Later Years
In 1970’s, Grothendieck became a visiting professor in College De France. In 1985, he published his autobiography ‘Récoltes et Semailles’ (Reaping and Sowing) which portrayed his life other than his mathematical career. In 1988, he was awarded Crafoord Prize, one of the most reputed awards in mathematics which had a cash award of 1.5M French francs, which he refused. The reasons for the refusal cited were his lack of requirement for money and his dislike for such honours. In 1988, he announced retirement from the University of Montpellier and presently lives in France. Since 1991, he has been leading a secluded life in Pyrenean village.

ALEXANDER GROTHENDIECK TIMELINE

1928:

Alexander Grothendieck was born on March 28, in Berlin to Russian-born, Jewish father, Alexander Sascha Shapiro, and German protestant mother, Johanna Hanka Grothendieck.

1933:

His parents moved to Paris, leaving him with Wilhelm Heydorn, a pastor and teacher in Hamburg, where he attended school.

1942:

Grothendieck’s father was deported to and died in Auschwitz concentration camp.

1950-1953:

He attended the University of Nancy where he did a dissertation on Functional Analysis under Laurent Schwartz.

1953-1955:

Grothendieck visited the University of Sao Paulo and came back to France in 1956 to work in Institute of Advanced Scientific Studies.

1957:

Grothendieck started working on algebraic geometry and homological algebra.

1960:

He visited the University of Kansas, thus working in geometry and topology.

1966:

He was honoured with Fields medal for his immense contributions to Mathematics though he rejected it.

1985:

Grothendieck published his autobiography, Récoltes et Semailles (Reaping and Sowing), which concentrated more on his life other than his mathematical career.

1988:

He was awarded with Crafoord Prize though he rejected it.

1988:

He announced retirement from the University of Montpellier and presently lives in France.

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Books by Alexander Grothendieck

    Cohomologie Locale Des Faisceaux Coherents (Sga 2): Seminaire De Geometrie Algebrique Du Bois Marie 1962 (French Edition)

    by Alexander Grothendieck

Books About Alexander Grothendieck

    Who is Alexander Grothendieck? Part 1: Anarchy

    by Winfried Scharlau

    Biography - Grothendieck, Alexander (1928-): An article from: Contemporary Authors

    by Gale Reference Team

    By Pierre Cartier - The Grothendieck Festschrift, Volume I: A Collection of Articles Written in Honor of the 60th Birthday of Alexander Grothendieck

    by Luc Illusie (Editor), Nicholas M. Katz (Editor), Gerard Laumon (Editor), Yuri I. Manin (Editor) Pierre Cartier