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A mad day’s work: from Grothendieck to Connes and Kontsevich The evolution of concepts of space and symmetry

2001; American Mathematical Society; Volume: 38; Issue: 4 Linguagem: Inglês

10.1090/s0273-0979-01-00913-2

1088-9485

Pierre Cartier,

Philosophy and History of Science

CARTIERthat they are necessarily central to any serious scientific reflection.Mathematicians as influential as Bernhard Riemann or Hermann Weyl, to name only a few, have undertaken to analyze these concepts on the dual levels of mathematics and physics. A brief biography of GrothendieckGrothendieck wrote a long, very personal memoir, Harvesting and Sowing (which remains to date unpublished), but it would be difficult to find a narrative of his life in it, especially his childhood.In the three volumes of the Grothendieck Festschrift that I published on the occasion of his sixtieth birthday there is a brief introduction and a rather long analysis by Dieudonné of Grothendieck's work.The narrative of his life there is rather cursory, besides being abridged in relation to his early projects.In his autobiography [10] Laurent Schwartz mentions his student Grothendieck, but only in passing and with many inaccuracies.What I know of his life comes from Grothendieck himself, and that, supplemented by some other testimony, forms the basis of the following narrative.First of all, I should mention the remarkable personality of his parents.His father's name was Shapiro-I don't know his first name.He was born around 1890 in a small town close to the point where Russia, Ukraine, and Belarus now meet.All the Shapiros (there are numerous spellings of the name: Shapira, Szpiro, . . . ) are descended from a group in a very small geographical region.Alexander Grothendieck's grandfather was probably a member of the community of Hasidic Jews to which the Shapiros belonged.These were very pious Jews, who would nowadays be called fundamentalists.Some of them were so "enamored of God" that they had themselves walled into a small tower with a window where the faithful came to offer them alms of food.While visiting Grothendieck I have seen a portrait of his father, done by a co-detainee in the French camp of Vernet in 1942.It bears a strong resemblance to the photograph of the son that we put at the front of the Festschrift, the head shaved, with a fiery expression of the eyes.As Alexander told me, his father's political career constitutes a Who's Who of the European revolution from 1900 to 1940.Because of the borders that existed at the time, he was born a Russian citizen.He participated in the abortive 1905 revolution against the tsar, along with the revolutionary currents of the period.After the quashing of the revolution he was deported to Siberia, and spent more than ten years in jail.He was released in 1917, when the exiles returned to Russia to work for the overthrow of the Russian monarchy.Two revolutions occurred in St. Petersburg: the Menshevik Revolution of February 1917 and the Bolshevik Revolution of October 1917.Shapiro was one of the leaders of the "Socialist-Revolutionary of the Left" Party.Allied at first with the Bolsheviks in October 1917, they soon clashed with Lenin and formed part of the many revolutionaries-Bolsheviks and non-Bolsheviks alike-purged by Lenin. 1 After the collapse of the two central empires, Europe was agitated by a number of revolutionary movements: Rosa Luxemburg and the Spartakists in Berlin in 1919, the Munich Soviets, Bela Kun's revolution in Hungary.To these we may add the various events of the Russian Civil War, one of them being the Makhno movement 2 in Ukraine.Grothendieck's father participated in all these movements.