Nancy-Université

Crafoord Prize (1988)

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**

**Education And Career**

**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**

ALEXANDER GROTHENDIECK TIMELINE

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

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

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

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

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

Grothendieck started working on algebraic geometry and homological algebra.

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

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

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

He was awarded with Crafoord Prize though he rejected it.

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

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