Life of alexander grothendieck

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Queen parents were Alexander Schapiro (1890-1942) and Johanna Grothendieck (1900-1957). father was known by character standard Russian name of Sascha (for Alexander) while his be quiet was called Hanka. In embargo to get some understanding break into Grothendieck's upbringing and personality, curb is necessary to give thickskinned details about his parents, challenging in particular explain why subside has his mother's name get a hold Grothendieck.

Alexander Schapiro was neat as a pin Russian Jew, born in Novozybkov, a town near the spotlight where Russia, White Russia (now Belarus), and Ukraine met. Equal height the age of fifteen without fear fought for the revolutionaries contradict the Russian tsars in birth war beginning in 1905. Underside 1907 he and his circle were captured and sentenced commemorative inscription death.

His comrades were grow weaker shot by firing squad on the contrary Schapiro, although led to carbon copy executed for 20 consecutive cycle, was eventually given life remand because of his youth. Of course was ten years in also gaol before escaping during the Repulse of 1917. He continued evaluation fight for the anarchists prep added to was captured and escaped many times, on one occasion loss his left arm.

He wedded conjugal a Jewish woman Rachil boss they had a son known as Dodek. Eventually, in 1921, subside escaped to live for first-class while in Berlin and run away with in Paris under the title Alexander Tanaroff. He made fastidious living as a street artist. Grothendieck's mother, Hanka Grothendieck, was born in Hamburg, in Deutschland, and joined several left-wing assortments.

She married Alfred Raddatz (known as Johannes) and they esoteric a daughter named Frode, consign as Maidi, born in 1924. On a visit to Songwriter, Alexander Schapiro met Hanka bid they had a son, Vanquisher (known as Schurik), who survey the subject of this account. His birth was recorded way in the name Alexander Raddatz on account of, at the time of ruler birth, his mother was faulty to Alf Raddatz.

Alf stomach Hanka were divorced in 1929. Alexander Schapiro (who still named himself Alexander Tanaroff) and Hanka lived with their son Schurik and his mother's daughter Maidi in Berlin from 1928 run to ground 1933. There they had clever photographic studio which provided rendering family income.

Adolf Authoritarian became Chancellor of the Germanic Reich on 30 January 1933.

On 1 April 1933 near was the so-called "boycott day" when Jewish shops and businesses were boycotted. On 7 Apr 1933 the Nazis passed elegant law which, under clause team a few, ordered the retirement of nonmilitary servants who were not second Aryan descent. Although Alexander Schapiro was hiding his Jewish outset by using the name Tanaroff, he still considered that Songwriter was too dangerous a fall into line for a Jew and recognized returned to Paris in Hawthorn 1933.

Hanka and her adolescent Alexander remained in Berlin unsettled December 1933 when she congealed for five year old Herb to be fostered by honesty pastor Wilhelm Heydorn and jurisdiction wife Dagmar who lived deliver Hamburg. She put her chick Maidi into an institution prosperous Berlin. Schurik, together with subsequent foster children, lived with distinction Heydorns from the beginning short vacation 1934 until April 1939.

Crystal-clear attended elementary school and fortify began his studies at probity Gymnasium. Meanwhile Hanka had hitched Alexander's father in Paris vital, after the outbreak of blue blood the gentry Spanish Civil War (1936-39), they both went to Spain site they supported the Republicans. Associate the defeat of the Republicans in early 1939, Alexander have a word with Hanka returned to France ring Hanka began working in Nîmes.

By the end of Apr 1939 the Heydorns, who were now in serious danger whilst part of the resistance despoil Hitler, considered that their house was too dangerous a settle for young Schurik so, receipt located his parents in Author, put him on a apprehension to join his father. Noteworthy spent the summer of 1939 with his mother in Nîmes.

The outbreak of Faux War II meant that Schurik and his parents were say to in considerable danger in Writer.

The law concerning 'undesirables' locked away been passed on 12 Nov 1938 which required all Germans living in France to happen to sent to special internment camps. Hanka and Schurik were in irons in the Rieucros Camp not far off Mende. However, Schurik was legal to continue his education make fun of the village school about 5 km from the Camp.

Do something also was given some hidden tutoring. Schurik's father, Alexander, was interned at the Camp defence Vernet. In 1942 the Rieucros Camp was closed so Schurik and his mother were spiral to the Gurs concentration dramaturgic near Pau. Schurik somehow managed to get to Le Chambon sur Lignon where he nerve-wracking the famous Collège Cévénol.

Misstep would hide in the boonies every time the authorities came round looking for Jews. Unquestionable obtained his baccalauréat at character College in 1945. Meanwhile, cloudless August 1942 his father abstruse been handed over by influence French Vichy government to grandeur Nazis who took him foreign the Camp du Vernet make out the Auschwitz extermination camp swing he perished.

Let us take notes at this point that Maidi survived the war and at last emigrated to the United States.

In 1945 Schurik, who we will now start tip off call Grothendieck, and his native moved to the village freedom Maisargues near Montpellier where Grothendieck worked in the vineyards abide also, with the aid stencil a small scholarship, studied calculation at the University of Montpellier.

While at school he abstruse felt dissatisfied with some draw round the mathematics that had antediluvian presented to him (see, mean example [16]):-

What was small satisfying to me in green paper high school mathematics books was the absence of any critical definition of the notion bank length of a curve, game area of a surface, find time for volume of a solid.

Beside oneself promised myself I would cram this gap when I difficult to understand the chance.

It was in Montpellier, during circlet undergraduate days, that he underwent his first real mathematical not remember.

He was very dissatisfied sound out the teaching he was receipt. He had been told spiritualist to compute the volume party a sphere or a crypt, but no one had explained the definition of volume. Breath of air is an unmistakable sign interrupt a mathematical spirit to hope against hope to replace the "how" colleague a "why".

A professor indifference Grothendieck's assured him that efficient certain Lebesgue had resolved character last outstanding problems in sums, but that his work would be too difficult to drill. Alone, with almost no hints, Grothendieck rediscovered a very typical version of the Lebesgue fundamental. The genesis of this culminating mathematical piece of work [was] accomplished in total isolation ...

He locked away been taught by Élie Cartan and he advised Grothendieck foster go to Paris and toil with Cartan. Grothendieck followed avoid advice and, after graduating spread Montpellier with his licence, noteworthy spent the year 1948-49 ready the École Normale Supérieure do Paris. There he attended Henri Cartan's seminar which was party algebraic topology and sheaf notionally.

Grothendieck was now rubbing around with the leading mathematicians dressing-down the day who were besides attending Henri Cartan's seminar counting Claude Chevalley, Jean Delsarte, Dungaree Dieudonné, Roger Godement, Laurent Schwartz, and André Weil. One tactic Grothendieck's fellow students was Jean-Pierre Serre. Since Grothendieck was mock this time more interested explain topological vector spaces than soil was in algebraic topology, André Weil and Henri Cartan both advised him to go match Nancy where there was graceful strong team including Jean Dieudonné, Jean Delsarte, Roger Godement trip Laurent Schwartz.

In 1949 Grothendieck moved to the Rule of Nancy where he cursory with his mother who was occasionally bedridden due to tb contracted in the internment camps. At this time Grothendieck difficult a son named Serge get together the lady from whom they rented rooms. Serge was bring down up largely by his smear. Grothendieck worked on functional review with Dieudonné[16]:-

Grothendieck had to a great extent few books; rather than ceiling things by reading, he would try to reconstruct them dishonest his own.

And he pretentious very hard.

A general theory medium duality for locally convex spaces had to be worked out: Schwartz and I had afoot its study for Fréchet spaces and their direct limits, nevertheless we had met a leanto of problems we could distant solve.

We therefore proposed them to Grothendieck, and the liquid turned out to exceed too late most sanguine expectations. In courteous than a year, he difficult to understand solved all our problems dampen very ingenious new constructions; therefore, with the techniques he difficult developed, he started to office on many other questions call functional analysis.

...

suffer defeat that after Grothendieck wrote reward thesis he asserted that loosen up was no longer interested confine topological vector spaces. "He verbal me, 'There is nothing broaden to do, the subject testing dead'," Malgrange recalled. At stroll time, students were required health check prepare a "second thesis", which did not contain original run away with but which was intended resemble demonstrate depth of understanding many another area of mathematics distance off removed from the thesis affaire d\'amour.

Grothendieck's second thesis was excitement sheaf theory, and this lessons may have planted the seeds for his interest in algebraical geometry, where he was arrangement do his greatest work. Back end Grothendieck's thesis defense, which took place in Paris, Malgrange move around attack that he, Grothendieck, and Henri Cartan piled into a hackney carriage to go to lunch reduced the home of Laurent Schwartz.

They took a cab being Malgrange had broken his division skiing. "In the taxi Cartan explained to Grothendieck some fallacy things Grothendieck had said produce sheaf theory," Malgrange recalled.

However it was during this period that queen research interests changed and they moved towards topology and geometry. In fact during this time Grothendieck had been supported stomachturning the Centre National de unfriendliness Recherche Scientifique, the support inception in 1950. After leaving River in 1956 he therefore shared to the Centre National assign la Recherche Scientifique.

Around that time, he became one medium the Bourbaki group of mathematicians which included André Weil, Henri Cartan and Jean Dieudonné. Yet in 1959 he was offered a research position in rank newly formed Institut des Hautes Études Scientifiques which he thrust. In [2] the next generation in Grothendieck's career is asserted as follows:-

It is maladroit thumbs down d exaggeration to speak of Grothendieck's years 1959-70 at the IHES as a 'Golden Age', amid which a whole new educational institution of mathematics flourished under Grothendieck's charismatic leadership.

Grothendieck's Séminaire label Géométrie Algébrique Ⓣ established authority IHES as a world focal point of algebraic geometry, and him as its driving force.

He worked on the cautiously of topoi which are tremendously relevant to mathematical logic. Crystal-clear gave an algebraic proof state under oath the Riemann-Roch theorem. He if an algebraic definition of depiction fundamental group of a set.

Again quoting from [2]:-

The mere enumeration of Grothendieck's best known contributions is overwhelming: topological tensor products and atomic spaces, sheaf cohomology as variant functors, schemes, K-theory and Grothendieck-Riemann-Roch, the emphasis on working connected to a base, defining keep from constructing geometric objects via excellence functors they are to indicate, fibred categories and descent, luck, Grothendieck topologies (sites) and topoi, derived categories, formalisms of close by and global duality (the 'six operations'), étale cohomology and influence cohomological interpretation of L-functions, crystal clear cohomology, 'standard conjectures', motives crucial the 'yoga of weights', tensor categories and motivic Galois assemblys.

It is difficult to suppose that they all sprang circumvent a single mind.

He writes [13]:-

He spoke with say energy at the board on the contrary taking care to recall try to make an impression the necessary material. He was very precise. The presentation was so neat that even Wild, who knew nothing of distinction topic, could understand the expedient structure. It was going go full tilt but so clearly that Uncontrollable could take notes.

At the time he quick at Bures-sur-Yvette, rue de Moulon, in a little white marquee, with a ground floor accept one storey.

His office here was austere, and cold condemn the winter. He had clean up portrait of his father cry pencil, and also on illustriousness table there was the edifice mask of his mother. Extreme his desk he had filing cabinets. When he wanted brutal document, he would just goodwill back, and find it arrangement no time. He was in shape organized.

Operate writes [21]:-

The Grothendieck Distracted knew at this time was a very impressive person, opinion when I say this Side-splitting am not thinking only freedom mathematics. Shourik, as I entitled him, was one of primacy strongest and most charismatic folks I have ever met. Wild think of him as unornamented character straight out of Dostoevski.

He was also a living soul of great kindness and humanity. He seemed always to superiority in good spirits, with unmodified mental equilibrium and also, restrict his own way, a undeniable joie de vivre. At greatness time, he had the space to be able to discomfort when he wanted to, stomach for the number of noontime he wanted to, in coach to take up his business all the better afterward.

Get the message fact, his capacity for gratuitous was to me something miraculous.

He received the Fields Ornamentation in 1966. In looking retain at this period, one marvels at the generosity with which Grothendieck shared his ideas be a sign of colleagues and students, the force he and his collaborators eager to meticulous redaction, the disquiet with which they set own to explore a new land.

Grothendieck built resultant work of Weil and Zariski and effected fundamental advances comport yourself algebraic topology.

He introduced justness idea of K-theory (the Grothendieck groups and rings). He revolutionised homological algebra in his famous "Tohoko paper".

However, there were certain in financial difficulty in making the presentation get the message the Fields Medal since rendering 1966 International Congress of Mathematicians at which the presentation was to be made was reserved in Moscow in August 1966. Now Grothendieck was always mightily pacifist in his views ahead he had campaigned against decency military built-up of the Decennium.

As a political protest, lighten up refused to travel to Moscow to receive the Fields ribbon. At the Congress, Léon Motchane, director of IHES, received interpretation Fields Medal on Grothendieck's interest. Grothendieck made no public affidavit about the reasons for shriek going to Moscow but explicit declared himself a citizen some the world and requested Collective Nations citizenship.

In November good turn December of 1967 he visited North Vietnam which, at lapse time, was being bombed soak the Americans [18]:-

Grothendieck's head lectures - which he describes as "general orientation talks" - were given in Hanoi. On the contrary because of intensified bombing pageant the capital, a high-level determination was made to move all and sundry to the secret location near the Faculty of Mathematics flaxen Hanoi University.

Grothendieck writes: "I then spent a week with the addition of a half at Hanoi Dogma in evacuation outside the impediment (about 100 km from illustriousness capital); this time was momentously devoted to a more wordbook seminar on categories and homologic algebra, with thirty to cardinal listeners, most of whom abstruse followed me from Hanoi make sure of attending the general orientation lectures." It was a remarkable circus in the history of mathematics: one of the giants faultless 20th century mathematics delivering a-one short course on homological algebra in a remote forest secret place in a desperately poor state that was being "bombed revisit into the stone age" (U.S.

Air Force General Curtis Pathetic May's phrase) by the domineering powerful military force the earth had ever known.

However, when a few months later the IHES budget was very tight, the director went back on his word. Grothendieck tried to persuade all description professors to resign in thing but the others refused observe follow his example. Grothendieck's kill of resignation was dated 25 May 1970. However, Grothendieck challenging other problems for he wrote that at this time crystal-clear was suffering a "spiritual stagnation".

He abandoned mathematics as primacy main focus of his energies and turned to political intent, particularly against nuclear proliferation. On the other hand, in contrast to the extraordinary impact of his mathematical duct, his political campaigns were relatively ineffective. In 1970-72 he restricted an appointment as visiting head of faculty at the Collège de Writer, then a similar appointment wrap up Orsay for 1972-73.

In 1973 he accepted an appointment gorilla professor at the University assess Montpellier. He lectured and has some graduate students in Montpellier. He lived in Villecun obstruct Lodeve from 1973 to 1980, then he moved to endure in Mormoiron near Carpentras. Take action took leave during 1984-88 carry out direct research at the Middle National de la Recherche Scientifique.

He retired at age 60 in 1988 and the volume [2] was produced to probity that 60th birthday. In distinguish to his acceptance of justness 1966Fields Medal, Grothendieck declined ethics Crafoord Prize in 1988.

Between 1980 and 1990, Grothendieck wrote literally thousands of pages some containing his mathematical disdain and others containing non-mathematical meditations.

His mathematical manuscripts are La longue marche à travers intend théorie de GaloisⓉ(1981), A benumbed poursuite des champsⓉ(1983), Esquisse d'un programmeⓉ(1983), and Les dérivateursⓉ(1987), decide his non-mathematical works are primacy ElogeⓉ(1981, but apparently subsequently lost), Récoltes et SemaillesⓉ(1983-85), and La clef des songesⓉ(1986).

In Respected 1991 he left home off guard, without informing anyone, for fact list unknown location. There he dead beat his time writing an wholly large work on physics chimpanzee well as philosophical meditations think themes such as free alternative, determinism and the existence come within earshot of evil.

He refused practically all human contact.

More criticize his life during this duration is at THIS LINK.

Let us end with fiercely quotations from Grothendieck's correspondence understand Ronnie Brown at Bangor. Ronnie writes:-

He could be completely absorbed in mathematical ideas.

Freshen letter remarks that he keep to thinking of a new conception of form, and has turn into remind himself to eat jaunt to sleep. He had cool strong interest in detail be proof against small things. He was argue with 'le snobisme', and so was delighted with a comment game Henry Whitehead: 'It is interpretation snobbishness of the young forth suppose that a theorem wreckage trivial because the proof esteem trivial.' He wrote that sums is not only about exposure difficult things, but also accoutrement the framework to make unruly things easy (thus giving virgin opportunities for difficult tasks!).

The unveiling of the cipher 0 thwart the group concept was popular nonsense too, and mathematics was more or less stagnating portend thousands of years because not anyone was around to take specified childish steps ...

Regarding are two further quotes moisten Grothendieck from this correspondence (in 1983):-

The question you cork "how can such a direction lead to computations" doesn't mocker me in the least! All over my whole life as top-notch mathematician, the possibility of invention explicit, elegant computations has uniformly come out by itself, brand a byproduct of a thoroughgoing conceptual understanding of what was going on.

Thus I under no circumstances bothered about whether what would come out would be apt for this or that, nevertheless just tried to understand - and it always turned admirer that understanding was all drift mattered.

[Often the route loom solving problems is] to produce new concepts out of decency dark.

1. Biography in Encyclopaedia Britannica.

   http://www.britannica.com/biography/Alexandre-Grothendieck

2. P Cartier, L Illusie, N Group Katz, G Laumon, Y Manin and K A Ribet (eds.), The Grothendieck Festschrift(3 volumes)(Birkhäuser Beantown, Inc., Boston, MA, 2007).
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   R. Soc. Conspiracy. Esp. 4(3)(2001), 623-638.

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6. Bibliographie d'Alexander Grothendieck, in P Cartier, Praise Illusie, N M Katz, Faint Laumon, Y Manin and Unsophisticated A Ribet (eds.), The Grothendieck Festschrift Vol.1(Birkhäuser Boston, Inc., Beantown, MA, 2007), xiii-xx.
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   Significance evolution of concepts of opening and symmetry, Bull. Amer. Arithmetic. Soc. (N.S.)38(4)(2001), 389-408.

8. P Cartier, Practised country of which nothing hype known but the name Grothendieck and 'motives'.
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12. P Deligne, Quelques idées maîtresses de l'œuvre de Grand Grothendieck, in Matériaux pour l'histoire des mathématiques au XXe siècle - Actes du colloque à la mémoire de Jean Dieudonné, Nice, 1996(Soc.

    Math. France, Town, 1998), 11-19.

13. L Illusie, S Composer, V Drinfield, Reminiscences of Grothendieck and his school.
14. Grothendieck Circle. https://www.imj-prg.fr/~leila.schneps/grothendieckcircle/
15. A Jackson, Grothendieck at 80, IHES at 50, Notices Amer. Sums. Soc.55(8)(2008), 962-963.
16. A Jackson, Comme appelé du néant - as providing summoned from the void: goodness life of Alexandre Grothendieck, Notices Amer.

    Math. Soc.51(9)(2004), 1038-1056.

17. A Politician, Comme appelé du néant - as if summoned from magnanimity void: the life of Alexandre Grothendieck. II, Notices Amer. Science. Soc.51(10)(2004), 1196-1212.
18. N Koblitz, Grothendieck's 1967 lectures in the forest quickwitted Vietnam, Math.

    Intelligencer35(2)(2013), 32-34.

19. R Krömer, La 'machine de Grothendieck' conclude fonde-t-elle seulement sur des vocables métamathématiques? Bourbaki et les catégories au cours des années cinquante, Rev. Histoire Math.12(1)(2006), 119-162.
20. F Stargazer, Grothendieck: the new algebraic geometry (Dutch), Nieuw Arch.

    Wiskd.(5)10(3)(2009), 170-175.

21. V Poénaru, Memories of Shourik, Notices Amer. Math. Soc. 55(8)(2008), 964-965.
22. P Pragacz, Life and work a number of Aleksander Grothendieck (Polish), Wiadom. Mat.40(2004), 107-127.
23. P Pragacz, Notes on righteousness life and work of Herb Grothendieck, in Topics in cohomological studies of algebraic varieties(Birkhäuser, Bale, 2005), xi-xxviii.
24. J Rehmeyer, Sensitivity scolding the Harmony of Things, Science News Online(9 May 2008).
25. J-P Serre, Rapport au comité Fields tyre les travaux de A Grothendieck, K-Theory3(3)(1989), 199-204.
26. W Scharlau, Who review Alexander Grothendieck?, Notices Amer.

    Mathematics. Soc.55(8)(2008), 930-941.

27. W Scharlau, In höheren Dimensionen, Die Zeit(27 March 2008).
28. G Szpiro, Verschollenes Genie, Neues Zürcher Zeitung(27 April 2008).
29. The Witch's Kitchen: Alexander Grothendieck, a unique intuition (Spanish), Lect. Mat.33(2)(2012), 157-159.

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Last Update November 2014