A. Grothendieck

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Alexander Grothendieck, 1928 was born in a Jewish family in Berlin, Germany on March 28th. His father was killed by the Nazis during World War II. After the war, Grothendieck went to France to study mathematics, and successively studied under dieudonne, an analyst of Bourbaki School, and Laurent Schwartz, a famous master of functional analysis. In his twenties, Grothendieck became the authority of the popular topological vector space theory at that time. But from 1957, Grothendieck's research mainly turned to algebraic geometry and homology algebra. Starting from 1959, he became the chairman of the newly established Paris Institute for Advanced Science. His work has developed the homology method and layer theory of Leray and Serre's algebraic geometry to a new height. The schema theory he founded laid the foundation of modern algebraic geometry. Because of his pioneering work, algebraic geometry, an ancient branch of mathematics, was endowed with new vitality, which eventually led to Deligne's complete proof of Weil conjecture, which was considered as one of the most significant achievements of pure mathematics in the 20th century. Thanks to Grothendieck's leadership, the Paris Institute for Advanced Studies was recognized as the research center of algebra and geometry in the world at that time, and he also won the Fields Prize 1966, the highest prize in international mathematics. Perhaps because of his wartime experience when he was young, Grothendieck was a radical pacifist. male

You can give up your math research for the war. During the Vietnam War, he taught category theory to local scholars in the forest of Hanoi. 1970, he was only 42 years old. At the peak of his research, he gave up mathematics completely and left the Paris Institute for Advanced Studies. Later, he taught at Montpellier University in France until he retired at the age of 60. He also said that he would go to the Pyrenees in southwest Europe to be a reclusive Buddhist. On the occasion of his 60th birthday in 1988, Grothendieck unexpectedly turned down the Crawford Prize and the Royal Swedish Academy Science Prize of $250,000. The reason is that he thinks money should be spent on young and promising mathematicians. Although Grothendieck has been away from academia for a long time, he is still considered as one of the greatest and most influential mathematicians in modern times. The great changes brought about by his extensive and profound theoretical system of modern algebraic geometry can be felt in almost all the core branches of mathematics.

Open any modern algebra and geometry textbook or monograph, you will frequently see nouns such as gross. Topology, hair, homology, hair. Rings and so on. At this point, I thought of Grothendieck,

This great mathematician whom we admire most may be living in obscurity in a small town in Europe at the moment, but the great wealth he left to mankind will undoubtedly go down in history forever!

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"For these' pure' mathematicians, the material world is just an illusion, and only the spiritual world is eternal. All they need is a pencil and a few sheets of white paper, and they can count purely with their clever minds.

Open up a splendid world in the ivory tower of knowledge. "The 1960s was a rather unsettled era. At this time, the idols worshipped by young students are Mao Zedong and ernesto guevara. They will wear red armbands, carry portraits of Guevara and take to the streets to confront the armed police. At this time, university professors are not obedient because they have more contact with students. For example, Smale, an American mathematician and winner of the 1966 Fields Prize, has repeatedly publicly criticized the hegemonic policies of the United States and the Soviet Union. Because of this, he was taken care of by the CIA. During the 1966 International Congress of Mathematicians held in Moscow, the KGB only "invited" him to a car for a while. However, compared with Grothendieck, what Smale did was not out of line.

Bourbaki is a school founded by a group of young French mathematicians in 1930s. The first batch of its members all graduated from higher normal schools, including A.Weil, H.Cartan, J. Dieudonné, C.Chevalley, J.Delsarte and others. Grothendieck was in its prime when he joined the school. At that time, the Bourbaki school included not only the masters of the older generation, but also talented young people like L. Schwartz and J.-P. Searle. Here, Grothendieck came into contact with the frontier of mathematics, and then grew into a leader among the new generation of mathematicians. Grothendieck first studied functional analysis, and he profoundly changed the face of this subject. Dieudonne said that Grothendieck's work, like Barnach's, left the deepest impression in functional analysis. However, Grothendieck's most important work is algebraic geometry. Algebraic geometry studies the graphs represented by the solutions of algebraic equations (groups). Nearly 400 years have passed since Descartes invented analytic geometry. In 1930s, O.Zariski and B.L.van der Waerden introduced commutative algebra into algebraic geometry. In the mid-1940s, Weil thoroughly established algebraic geometry on the basis of abstract algebra and put forward the famous Weil conjecture. Later, Kodaira, F.Hirzebruch, J.-P.Serre and others also made great breakthroughs in this subject. In 1950s and 1960s, Grothendieck innovated algebraic geometry, published more than a dozen masterpieces and established a grand and complete "probability theory". Grothendieck's works are the pinnacle of algebraic geometry, and his works are known as "Grothendieck Bible". Grothendieck's theory came into play. On the basis of probability theory, mathematicians have made remarkable achievements one after another: Grothendieck gave the algebraic proof of the famous Riemann-Roach theorem for the first time.

It also caused the following events:

1973, P.Deligne proved Weil conjecture (won 1978 Fields Prize);

1983, G.Faltings proved the Mordell conjecture (won the Fields Prize1986);

1995, wiles (A.Wiles) proved the Taniyama-Zhicun conjecture, and then solved Fermat's last theorem with a history of more than 350 years (1996 won the Fields Special Prize).

These achievements represent the highest level of contemporary mathematics, enough to shine through the ages.

There were many geniuses and Fields Prizes in algebraic geometry in the 20th century, but there was only one God, and that was Grothendieck. His series of monographs "EGA" is recognized as the Bible of algebraic geometry.

Grothendieck was a thorough anarchist and pacifist. He often gives political propaganda to those who ask him for advice on mathematics. In the 1960s, he was hired as the director of the French Institute of Advanced Science.

Institut (Institut des Hautes etudes Scientifiques), but when he found that this institution was funded and supported by NATO (North Atlantic Treaty Organization), he resolutely resigned and returned to his hometown to farm. 1970

At the International Congress of Mathematicians, L Pontrjagin, a blind mathematician from the Soviet Union, gave a report on "differential countermeasures", which talked about the problem of tracking aircraft with missiles. Grothendieck angrily took to the stage and grabbed the microphone to protest his existence.

Military affairs were mentioned at the math meeting. G. Hardy once said: "Real mathematics has no influence on war ... it is a' harmless and innocent' profession". Maybe that's why Grothendieck chose mathematics. However, Grothendieck was gradually disappointed to find that mathematics was often used in the military. For example, his research on algebraic geometry was used for coding, and most of the mathematical research was directly or indirectly supported by the military. This obviously runs counter to his ideal. So at 1970, he left his beloved mathematics career forever and turned to disarmament activities and farm management. In the 1980s, he simply disappeared into this dirty world. Only a few of his friends knew his address, but these friends kept their mouths shut. Up to now, Grothendieck is still missing. Hermits have existed since ancient times, but Grothendieck, who did not love glory and retired after success, was rare in ancient times.