## Comme Appelé du Néant— As If Summoned from the Void: The Life of Alexandre

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@MISC{Jackson_commeappelé,

author = {Allyn Jackson},

title = {Comme Appelé du Néant— As If Summoned from the Void: The Life of Alexandre},

year = {}

}

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### Abstract

part of the article will appear in the next issue of the Notices. Et toute science, quand nous l’entendons non comme un instrument de pouvoir et de domination, mais comme aventure de connaissance de notre espèce à travers les âges, n’est autre chose que cette harmonie, plus ou moins vaste et plus ou moins riche d’une époque à l’autre, qui se déploie au cours des générations et des siècles, par le délicat contrepoint de tous les thèmes apparus tour à tour, comme appelés du néant. And every science, when we understand it not as an instrument of power and domination but as an adventure in knowledge pursued by our species across the ages, is nothing but this harmony, more or less vast, more or less rich from one epoch to another, which unfurls over the course of generations and centuries, by the delicate counterpoint of all the themes appearing in turn, as if summoned from the void. —Récoltes et Semailles, page P20 Alexandre Grothendieck is a mathematician of immense sensitivity to things mathematical, of profound perception of the intricate and elegant lines of their architecture. A couple of high points from his biography—he was a founding member of Allyn Jackson is senior writer and deputy editor of the Notices. Her email address is axj@ams.org. the Institut des Hautes Études Scientifiques (IHÉS)

### Citations

202 |
Sur quelques points d’algèbre homologique
- Grothendieck
- 1957
(Show Context)
Citation Context ...r quelques points d’algèbre homologique,” which came to be known informally among specialists as the “Tôhoku paper” after the name of the journal in which it appeared, the Tôhoku Mathematical Journal =-=[To]-=-. This paper, which became a classic in homological algebra, extended the work of Cartan and Eilenberg on modules. Also while he was in Kansas, Grothendieck wrote “A general theory of fiber spaces wit... |

133 |
Produits tensoriels topologiques et espaces nucléaires
- Grothendieck
- 1955
(Show Context)
Citation Context ...d’après Grothendieck,” published in 1954 [Schwartz]. In addition, Grothendieck’s thesis appeared as a monograph in 1955 in the Memoirs of the AMS series; it was reprinted for the seventh time in 1990 =-=[Gthesis]-=-. Grothendieck’s work in functional analysis “was quite remarkable,” commented Edward G. Effros of the University of California at Los Angeles. “He was arguably the first to realize that the algebraic... |

71 |
Residues and duality, Lecture notes of a seminar on the work of A. Grothendieck, given at Harvard 1963/64. With an appendix by P. Deligne
- Hartshorne
- 1966
(Show Context)
Citation Context ... red ink.” After realizing that this was a potentially endless process, Hartshorne decided one day to send the manuscript off to be published; it appeared in the Springer Lecture Notes series in 1966 =-=[Hartshorne]-=-. 1054 NOTICES OF THE AMS VOLUME 51, NUMBER 9Grothendieck “had so many ideas that he kept basically all the serious people working in algebraic geometry in the world busy during that time,” Hartshorn... |

49 |
Foundations of algebraic geometry
- Weil
- 1962
(Show Context)
Citation Context ...use of the lack of rigor of the Italian school of algebraic geometry, it was necessary to build new foundations for the field. This is what Weil did in his 1946 book Foundations of Algebraic Geometry =-=[Weil1]-=-. Weil’s conjectures appeared in his 1949 paper [Weil2]. Motivated by problems in number theory, Weil studied a certain zeta function that had been introduced in special cases by Emil Artin; it is cal... |

46 |
Le theoreme de Riemann-Roch
- Borel, Serre
- 1958
(Show Context)
Citation Context ... first Arbeitstagung in July 1957 that Grothendieck spoke about his work on Riemann-Roch. But in a curious twist, the result was not published under his name; it appears in a paper by Borel and Serre =-=[BS]-=- (the proof also appeared later as an exposé in volume 6 of Séminaire de Géometrie Algébrique du Bois Marie from 196667). While visiting the IAS in the fall of 1957, Serre received a letter from Groth... |

42 |
Contributions to the theory of Ramanujan’s function τ(n)and similar functions. II. The order of the Fourier coefficients of integral modular forms
- Rankin
- 1939
(Show Context)
Citation Context ...ay, the standard conjectures remain inaccessible. Deligne found a clever way to circumvent them when he proved the last Weil conjecture. One of the key ideas he used came from a paper by R. A. Rankin =-=[Rankin]-=-, which is about the classical theory of modular forms and of which Grothendieck was unaware. As John Tate put it, “For the proof of the last Weil conjecture, you needed another ingredient that was mo... |

42 | Automorphic representations, Shimura varieties, and motives. Ein Märchen. Automorphic forms, representations and L-functions (Proc
- Langlands
- 1977
(Show Context)
Citation Context ... Robert Langlands of the IAS conjectured precise relationships between motives and automorphic representations. This conjecture, now part of the socalled Langlands Program, first appeared in print in =-=[Langlands]-=-. James Arthur of the University of Toronto said that proving this conjecture in full generality is decades away. But, he pointed out, what Andrew Wiles did in the proof of Fermat’s Last Theorem was e... |

38 | A mad day’s work: from Grothendieck to Connes and Kontsevich. The evolution of concepts of space and symmetry [in Les relations entre les mathématiques et la physique théorique
- Cartier
- 1998
(Show Context)
Citation Context ...triking portrait of his father, painted by a fellow detainee in the Le Vernet camp. As Pierre Cartier described it, the portrait showed a man with his head shaved and a “fiery expression” in the eyes =-=[Cartier1]-=-; for many years Grothendieck also shaved his head. According to Ribenboim, Hanka Grothendieck was very proud of her brilliant son, and he in turn had an extremely deep attachment to his mother. After... |

10 |
The cohomology theory of abstract algebraic varieties
- Grothendieck
- 1958
(Show Context)
Citation Context ...orphosis, yet more profound, of the notion of space). —Récoltes et Semailles, page P23 In August 1958, Grothendieck gave a plenary lecture at the International Congress of Mathematicians in Edinburgh =-=[Edin]-=-. The talk outlined, with a remarkable prescience, many of the main themes that he was to work on for the next dozen years. It was clear by this time that he was aiming to prove the famous conjectures... |

8 |
A beautiful mind, Simon and
- Nasar
- 1998
(Show Context)
Citation Context ...s with that of another great mathematician of the time, John Nash. In his mathematical prime, Nash searched out specific problems considered by his colleagues to be the most important and challenging =-=[Nasar]-=-. “Nash was like an Olympian athlete,” remarked Hyman Bass of the University of Michigan. “He was interested in enormous 1048 NOTICES OF THE AMS VOLUME 51, NUMBER 9personal challenges.” If Nash is an... |

7 | Récoltes et Semailles, Réflexions et témoignages sur un passé de mathématicien, IReprint - Grothendieck - 1985 |

5 |
Faisceaux algébriques cohérents, Ann. of Math. (2) 61
- Serre
- 1955
(Show Context)
Citation Context ...ohomology.” The notion of a sheaf was conceived by Jean Leray and further developed by Henri Cartan and Jean-Pierre Serre. In his groundbreaking paper known as FAC (“Faisceaux algébriques cohérents”, =-=[FAC]-=-), Serre showed how sheaves could be used in algebraic geometry. Without saying exactly what a sheaf is, Grothendieck described in Récoltes et Semailles how this notion changed the landscape: When the... |

4 |
Twenty-five years with Nicolas Bourbaki
- BOREL
- 1998
(Show Context)
Citation Context ... of view. Borel, who was a member of Bourbaki for 25 years, wrote that this collaboration 1050 NOTICES OF THE AMS VOLUME 51, NUMBER 9may have been “a unique occurrence in the history of mathematics” =-=[Borel]-=-. Bourbaki pooled the efforts of some of the top mathematicians of the day, who unselfishly and anonymously devoted a good deal of time and energy to writing texts that would make a wide swath of the ... |

3 |
1998]: A Cultural History of Catastrophes and Chaos: Around the ‘Institut des Hautes Études Scientifiques
- Aubin
(Show Context)
Citation Context ...late 1969, Grothendieck became embroiled in a conflict with the founder and director of the IHÉS, Léon Motchane, over military funding for the institute. As historian of science David Aubin explained =-=[Aubin]-=-, during the 1960s, the IHÉS finances were rather precarious, and in some years the institute received a small portion of its budget, never more than about 5 percent, from sources within the French mi... |

2 |
longue marche a travers la theorie de Galois, Tome I, Transcription d'un manuscrit inedit, par
- Grothendieck, La
- 1995
(Show Context)
Citation Context ...e Long March through Galois Theory), completed in 1981. Grothendieck did not publish La Longue Marche, but through Malgoire’s efforts part of it was published in 1995 by the Université de Montpellier =-=[Marche]-=-. There was also a small working seminar in which Ladegaillerie gave some lectures on William Thurston’s work on Teichmüller spaces, which stimulated Grothendieck’s interest in this subject. By the 19... |

1 |
Société Mathématique de France, 2001
- Grothendieck-Serre
(Show Context)
Citation Context ...e the work that you had undertaken and largely completed. But you do not ask the most obvious question, the one every reader expects you to answer: and you, why did you abandon the work in question?” =-=[Corr]-=-. Contents of Récoltes et Semailles Présentation des Themes—ou Prélude en Quatre Mouvements •En guise d’avant-propos (January 1986: pages A1–A6) •Promenade à travers une oeuvre—ou l’enfant et la mère ... |

1 |
by Alexandre Grothendieck, edited by
- Dérivateurs
(Show Context)
Citation Context ...ring the 1990s he wrote a 2,000-page mathematical work on the foundations of homotopy theory called Les Dérivateurs, which he gave to Malgoire in 1995 and which is now being made available on the Web =-=[Deriv]-=-. While he was at Montpellier, Grothendieck’s uncompromising, “anti-establishment” bent seems to have become more pronounced. After Ladegaillerie’s thesis was finished, Grothendieck wrote to Springer-... |

1 | Découvrir et transmettre: La dimension collective des mathématiques dans Récoltes et Semailles d’Alexandre Grothendieck, Prépublications de l’IHÉS, 2000. Available at http:// name.math.univ-rennes1.fr/alain.herreman - HERREMAN |

1 |
Whom the Gods Love. The Story of Évariste Galois
- INFELD
- 1948
(Show Context)
Citation Context ...s; indeed, in various places in Récoltes et Semailles Grothendieck wrote that he strongly identified with Galois. He also mentioned that as a young man he read a biography of Galois by Leopold Infeld =-=[Infeld]-=- (page P63). Ultimately, the wellspring of Grothendieck’s achievement in mathematics is something quite humble: his love for the mathematical objects he studied. A Spirit in Stagnation [P]endant vingt... |

1 |
Alexandre Grothendieck après
- LADEGAILLERIE
- 1970
(Show Context)
Citation Context ... extra-terrestrial. Rather than translating things into another language, he thought and spoke directly in the language of modern structural mathematics, to whose creation he had contributed greatly” =-=[Ladegaillerie]-=-. Once, in order to verify a certain algebraic computation involving braids, Ladegaillerie made a little model using some string and a small plank with holes. This made Grothendieck laugh out of sheer... |

1 |
à l’Académie Royale des Sciences de Suède: Le mathématicien français Alexandre Grothendieck refuse le prix Crafoord, Le Monde
- Lettre
- 1988
(Show Context)
Citation Context ... of Récoltes et Semailles. The academy had awarded the prize of around US$200,000 to him and Pierre Deligne. Grothendieck’s letter became widely known when it was published in Le Monde on May 4, 1988 =-=[LeMonde]-=-. To play into the game of accepting prizes and honors, Grothendieck wrote, would be to validate “a spirit and an evolution in the scientific world that I see as profoundly unhealthy, and condemned to... |

1 |
La vie mathématique en République Democratique du Vietnam, text of a lecture presented
- GROTHENDIECK
- 1967
(Show Context)
Citation Context ...hendieck refused to attend as a protest against the Soviet government. In 1967 Grothendieck made a three-week trip to Vietnam, which clearly left an impression on him. His written account of the trip =-=[Vietnam]-=- described the many air raid alerts and a bombing that left two mathematics teachers dead, as well as the valiant efforts of the Vietnamese to cultivate a mathematical life in their country. A friends... |

1 |
Trois quarts de siècle avec Henri Cartan, Gazette des
- CERF
(Show Context)
Citation Context ...birthday, Jean Cerf recalled seeing in the Cartan seminar around this time “a stranger (it was Grothendieck) who took the liberty of speaking to Cartan, as if to his equal, from the back of the room” =-=[Cerf]-=-. Grothendieck felt free to ask questions, and yet, he wrote, he also found himself struggling to learn things that those around him seemed to grasp instantly and play with “like they had known them f... |

1 |
Société Mathématique de France, 2001. (Published in a bilingual French-English version by
- Grothendieck-Serre
(Show Context)
Citation Context ... things Grothendieck had said about sheaf theory,” Malgrange recalled. After leaving Brazil Grothendieck spent the year of 1955 at the University of Kansas, probably at the invitation of N. Aronszajn =-=[Corr]-=-. There Grothendieck began to immerse himself in homological algebra. It was while he was at Kansas that he wrote “Sur quelques points d’algèbre homologique,” which came to be known informally among s... |

1 | Grothendieck’s early work (19501960 - DIEUDENNÉ, A - 1989 |

1 |
Nur Mensch Sein!, Memoirs from 1873
- HEYDORN
- 1999
(Show Context)
Citation Context ...capped children in Berlin, although she was not handicapped (R&S, pages 472–473). The foster family was headed by Wilhelm Heydorn, whose remarkable life is outlined in his biography, Nur Mensch Sein! =-=[Heydorn]-=-; the book contains a photograph of Alexandre Grothendieck from 1934, and he is mentioned briefly. Heydorn had been a Lutheran priest and army officer, then left the church and worked as an elementary... |

1 |
Science et Vie
- Ikonicoff, Grothendieck
- 1995
(Show Context)
Citation Context ...ving finished his Licenceès Sciences at Montpellier, Grothendieck went to Paris, the main center for mathematics in France. In an article about Grothendieck that appeared in a French magazine in 1995 =-=[Ikonicoff]-=-, a French education official, André Magnier, recalled Grothendieck’s application for a scholarship to go to Paris. Magnier asked him to describe the project he had been working on at Montpellier. “I ... |

1 |
Les produits tensoriels d’après Grothendieck, Séminaire Secrétariat mathématique
- SCHWARTZ
- 1954
(Show Context)
Citation Context ...s, which has had wide applications, was first proposed in this paper. Schwartz popularized Grothendieck’s results in a Paris seminar, “Les produits tensoriels d’après Grothendieck,” published in 1954 =-=[Schwartz]-=-. In addition, Grothendieck’s thesis appeared as a monograph in 1955 in the Memoirs of the AMS series; it was reprinted for the seventh time in 1990 [Gthesis]. Grothendieck’s work in functional analys... |

1 |
Geometric syzygies
- WASHNITZER
- 1959
(Show Context)
Citation Context ...ht have been others who would have been able to prove it. But the statement itself was ten years ahead of anybody else.” This theorem, which was also proved independently by Gerard Washnitzer in 1959 =-=[Washnitzer]-=-, applies not just to a complex algebraic variety—the case where the ground field has characteristic zero—but to any proper smooth algebraic variety regardless of the ground field. The HirzebruchRiema... |