Alexander Grothendieck

1932:" for eight of the other themes (all but 1, 5, and 12). Grothendieck wrote that the first and last themes, topological tensor products and regular configurations, were of more modest size than the others. Topological tensor products had played the role of a tool rather than of a source of inspiration for further developments; but he expected that regular configurations could not be exhausted within the lifetime of a mathematician who devoted oneself to it. He believed that the deepest themes were motives, anabelian geometry, and Galois–Teichmüller theory. 1358:

commonplace and tolerated. The letter also expressed his belief that totally unforeseen events before the end of the century would lead to an unprecedented collapse of civilization. Grothendieck added however that his views were "in no way meant as a criticism of the Royal Academy's aims in the administration of its funds" and he added, "I regret the inconvenience that my refusal to accept the Crafoord prize may have caused you and the Royal Academy."

735:, given that he had refused to take French nationality (as that would have entailed military service against his convictions). He stayed in São Paulo (apart from a lengthy visit in France from October 1953 - March 1954) until the end of 1954. His published work from the time spent in Brazil is still in the theory of topological vector spaces; it is there that he completed his last major work on that topic (on "metric" theory of 1328:('Harvests and Sowings', 1986), Grothendieck describes his approach to mathematics and his experiences in the mathematical community, a community that initially accepted him in an open and welcoming manner, but which he progressively perceived to be governed by competition and status. He complains about what he saw as the "burial" of his work and betrayal by his former students and colleagues after he had left the community. 6319: 6329: 1124:("long-term guest") at the IHÉS, wrote a piece about Grothendieck for a special volume published on the occasion of the IHÉS's fortieth anniversary. In that publication, Cartier notes that as the son of an antimilitary anarchist and one who grew up among the disenfranchised, Grothendieck always had a deep compassion for the poor and the downtrodden. As Cartier puts it, Grothendieck came to find 1430:, claiming that all materials published in his absence had been published without his permission. He asked that none of his work be reproduced in whole or in part and that copies of this work be removed from libraries. He characterized a website devoted to his work as "an abomination". His dictate may have been reversed in 2010. 558:

and worked as a journalist. As teenagers, both of his parents had broken away from their early backgrounds. At the time of his birth, Grothendieck's mother was married to the journalist Johannes Raddatz and initially, his birth name was recorded as "Alexander Raddatz." That marriage was dissolved in

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while the city was being bombed. In 1966, he had declined to attend the International Congress of Mathematicians (ICM) in Moscow, where he was to receive the Fields Medal. He retired from scientific life around 1970 after he had found out that IHÉS was partly funded by the military. He returned to

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He was so completely unknown to this group and to their professors, came from such a deprived and chaotic background, and was, compared to them, so ignorant at the start of his research career, that his fulgurating ascent to sudden stardom is all the more incredible; quite unique in the history of

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Although mathematics became more and more abstract and general throughout the 20th century, it was Alexander Grothendieck who was the greatest master of this trend. His unique skill was to eliminate all unnecessary hypotheses and burrow into an area so deeply that its inner patterns on the most

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was heating up, and Cartier suggests that this also reinforced Grothendieck's distaste at having become a mandarin of the scientific world. In addition, after several years at the IHÉS, Grothendieck seemed to cast about for new intellectual interests. By the late 1960s, he had started to become

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period. The first three volumes (corresponding to Parts 0 to III of the book) were published between 1989 and 1993, while the fourth volume (Part IV) was completed and, although unpublished, copies of it as a typed manuscript are circulated. Grothendieck helped with the translation and wrote a

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with an open letter to the media. He wrote that he and other established mathematicians had no need for additional financial support and criticized what he saw as the declining ethics of the scientific community that was characterized by outright scientific theft that he believed had become

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More than 20,000 pages of Grothendieck's mathematical and other writings are held at the University of Montpellier and remain unpublished. They have been digitized for preservation and are freely available in open access through the Institut Montpelliérain Alexander Grothendieck portal.

1168:. The group published a bulletin and was dedicated to antimilitary and ecological issues. It also developed strong criticism of the indiscriminate use of science and technology. Grothendieck devoted the next three years to this group and served as the main editor of its bulletin. 777:, but the offer fell through when he refused to sign a pledge promising not to work to overthrow the United States government—a refusal which, he was warned, threatened to land him in prison. The prospect of prison did not worry him, so long as he could have access to books. 658:), a unique secondary school founded in 1938 by local Protestant pacifists and anti-war activists. Many of the refugee children hidden in Le Chambon attended Collège Cévenol, and it was at this school that Grothendieck apparently first became fascinated with mathematics. 44: 1977:

Grothendieck approached algebraic geometry by clarifying the foundations of the field, and by developing mathematical tools intended to prove a number of notable conjectures. Algebraic geometry has traditionally meant the understanding of geometric objects, such as

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In 1991, Grothendieck moved to a new address that he did not share with his previous contacts in the mathematical community. Very few people visited him afterward. Local villagers helped sustain him with a more varied diet after he tried to live on a staple of

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and, while still producing relevant mathematical work, he withdrew from the mathematical community and devoted himself to political and religious pursuits (first Buddhism and later, a more Catholic Christian vision). In 1991, he moved to the French village of

2375: – Weil cohomology theory for schemes over a base field, whose values are modules over the ring of Witt vectors over the base field, that replaces Zariski open sets by infinitesimal thickenings of Zariski open sets with divided power structures 1986:. In this approach, the properties of a geometric object are related to the properties of an associated ring. The space (e.g., real, complex, or projective) in which the object is defined, is extrinsic to the object, while the ring is intrinsic. 2155:

into the mainstream as an organizing principle for mathematics in general. Among its uses, category theory creates a common language for describing similar structures and techniques seen in many different mathematical systems. His notion of

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with Serre. This result was his first work in algebraic geometry. Grothendieck went on to plan and execute a programme for rebuilding the foundations of algebraic geometry, which at the time were in a state of flux and under discussion in

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Kleinert, Werner (2007). "Wer ist Alexander Grothendieck? Anarchie, Mathematik, Spiritualität. Eine Biographie. Teil 1: Anarchie" [Who is Alexander Grothendieck? Anarchy, mathematics, spirituality. A biography. Part 1: Anarchy.].

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for two years. He then became a professor at the University of Montpellier, where he became increasingly estranged from the mathematical community. He formally retired in 1988, a few years after having accepted a research position at the

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exists. As part of the notes to this manuscript, Grothendieck described the life and the work of 18 "mutants", people whom he admired as visionaries far ahead of their time and heralding a new age. The only mathematician on his list was

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is associated to every open subset of the space. Schemes have become the basic objects of study for practitioners of modern algebraic geometry. Their use as a foundation allowed geometry to absorb technical advances from other fields.

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Grothendieck is noted for his mastery of abstract approaches to mathematics and his perfectionism in matters of formulation and presentation. Relatively little of his work after 1960 was published by the conventional route of the

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Grothendieck wrote that, of these themes, the largest in scope was topoi, as they synthesized algebraic geometry, topology, and arithmetic. The theme that had been most extensively developed was schemes, which were the framework

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located him, then carried on a brief correspondence. Thus they became among "the last members of the mathematical establishment to come into contact with him". After his death, it was revealed that he lived alone in a house in

435: 1704:, circulating initially in duplicated volumes of seminar notes; his influence was to a considerable extent personal. His influence spilled over into many other branches of mathematics, for example the contemporary theory of 1544:

in studying linear maps between topological vector spaces. In a few years, he had become a leading authority on this area of functional analysis—to the extent that Dieudonné compares his impact in this field to that of

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By the 1970s, Grothendieck's work was seen as influential, not only in algebraic geometry and the allied fields of sheaf theory and homological algebra, but influenced logic, in the field of categorical logic.

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working groups drafting into foundational work some of the ablest French and other mathematicians of the younger generation). Grothendieck practically ceased publication of papers through the conventional,

1783:. Weil had realized that to prove such a connection, one needed a new cohomology theory, but neither he nor any other expert saw how to accomplish this until such a theory was expressed by Grothendieck. 1377:

who was claimed to have survived on the Holy Eucharist alone, Grothendieck almost starved himself to death in 1988. His growing preoccupation with spiritual matters was also evident in a letter entitled

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in 2025. A partial English translation can be found on the Internet. A Japanese translation of the whole book in four volumes was completed by Tsuji Yuichi (1938–2002), a friend of Grothendieck from the

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While not publishing mathematical research in conventional ways during the 1980s, he produced several influential manuscripts with limited distribution, with both mathematical and biographical content.

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was intended to be the "ℓ-adic" theory but without the choice of "ℓ", a prime number. It did not provide the intended route to the Weil conjectures, but has been behind modern developments in

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that argued for a connection between the topological characteristics of a variety and its diophantine (number theoretic) properties. For example, the number of solutions of an equation over a

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While the issue of military funding was perhaps the most obvious explanation for Grothendieck's departure from the IHÉS, those who knew him say that the causes of the rupture ran more deeply.

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Grothendieck laid a new foundation for algebraic geometry by making intrinsic spaces ("spectra") and associated rings the primary objects of study. To that end, he developed the theory of

1599:. Grothendieck took them to a higher level of abstraction and turned them into a key organising principle of his theory. He shifted attention from the study of individual varieties to his 1496:

during his time in Nancy; three children, Johanna (1959), Alexander (1961), and Mathieu (1965) with his wife Mireille Dufour; and one child with Justine Skalba, with whom he lived in a

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In September 2014, almost totally deaf and blind, he asked a neighbour to buy him a revolver so he could kill himself.On 13 November 2014, aged 86, Grothendieck died in the hospital of

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to their algebraic structure and now bears his name, being called "the Grothendieck–Hirzebruch–Riemann–Roch theorem". The tools he developed to prove this theorem started the study of

1965:, "Whole fields of mathematics speak the language that he set up. We live in this big structure that he built. We take it for granted—the architect is gone". In the same article, 1953:

abstract level revealed themselves–and then, like a magician, show how the solution of old problems fell out in straightforward ways now that their real nature had been revealed.

2104:. Grothendieck's large-scale approach has been called a "visionary program". The ℓ-adic cohomology then became a fundamental tool for number theorists, with applications to the 3022: 1171:

Although Grothendieck continued with mathematical enquiries, his standard mathematical career mostly ended when he left the IHÉS. After leaving the IHÉS, Grothendieck became a

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of complex curves. Although Grothendieck never published his work in this area, the proposal inspired other mathematicians to work in the area by becoming the source of

165: 1609:), allowing a broad generalization of many classical theorems. The first major application was the relative version of Serre's theorem showing that the cohomology of a 6398: 4352: 4287: 1708:. Although lauded as "the Einstein of mathematics", his work also provoked adverse reactions, with many mathematicians seeking out more concrete areas and problems. 1007:) and providing the new more flexible and general foundations for algebraic geometry that has been adopted in the field since that time. He went on to introduce the 1728: 999: 655: 6378: 4847: 1676:

has become established as the best universal foundation for this field, because of its expressiveness as well as its technical depth. In that setting one can use

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was finally published in 2022 by Gallimard and, thanks to French science historian Alain Herreman, is also available on the Internet. An English translation by

5026: 5800: 5782: 3127: 605:, where his mother contracted the tuberculosis that would eventually cause her death in 1957. While there, Grothendieck managed to attend the local school, at 1738: 1064: 5500: 4970: 4916: 1285: 1181: 488:(IHÉS) and remained there until 1970, when, driven by personal and political convictions, he left following a dispute over military funding. He received the 5233: 1982:

and surfaces, through the study of the algebraic equations for those objects. Properties of algebraic equations are in turn studied using the techniques of

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sent to 250 friends in January 1990. In it, he described his encounters with a deity and announced that a "New Age" would commence on 14 October 1996.

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His first works on topological vector spaces in 1953 have been successfully applied to physics and computer science, culminating in a relation between

4862: 4989: 4935: 2599: 1650: 1601: 1473:(1954–62). He eventually applied for French citizenship in the early 1980s, after he was well past the age that exempted him from military service. 990: 982: 474: 4270: 2992: 5664: 4051: 2164:. The emergence of a separate mathematical discipline of category theory has been attributed to Grothendieck's influence, although unintentional. 716:. The latter had recently won a Fields Medal. He showed his new student his latest paper; it ended with a list of 14 open questions, relevant for 559:

1929 and Schapiro acknowledged his paternity, but never married Hanka Grothendieck. Grothendieck had a maternal sibling, his half sister Maidi.

1364:, a 315-page manuscript written in 1987, is Grothendieck's account of how his consideration of the source of dreams led him to conclude that a 4088: 1239:

below). Within these, in an informal, diary-like manner, Grothendieck explained and developed his ideas on the relationship between algebraic

5587: 5163: 5130: 4831: 4755: 4696: 4645: 4618: 4584: 4547: 4514: 3554: 2287: 2245: 2025:, which explores the topological properties of objects by associating them with rings. After direct contact with Grothendieck's ideas at the 4219: 1656:

His foundational work on algebraic geometry is at a higher level of abstraction than all prior versions. He adapted the use of non-closed

1469:. Part of his reluctance to hold French nationality is attributed to not wishing to serve in the French military, particularly due to the 632:, although he occasionally had to seek refuge in the woods during Nazi raids, surviving at times without food or water for several days. 3302:

Peixoto, Tatiana; Bietenholza, Wolfgang (2016). "To the Memory of Alexander Grothendieck: a Great and Mysterious Genius of Mathematics".

6403: 601:. He and his mother were then interned in various camps from 1940 to 1942 as "undesirable dangerous foreigners." The first camp was the 4140: 5439: 5409: 5264: 5222: 3015: 2634: 484:

Grothendieck began his productive and public career as a mathematician in 1949. In 1958, he was appointed a research professor at the

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Luca Barbieri Viale, 'Alexander Grothendieck:entusiasmo e creatività,' in C. Bartocci, R. Betti, A. Guerraggio, R. Lucchetti (eds.,)

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Alexander Grothendieck's work during what is described as the "Golden Age" period at the IHÉS established several unifying themes in

4487: 4120: 3929: 3339: 2462: 763: 4271:‘He was in mystic delirium’: was this hermit mathematician a forgotten genius whose ideas could transform AI – or a lonely madman? 3969: 1903: 517:, where he lived in seclusion, still working on mathematics and his philosophical and religious thoughts until his death in 2014. 1556:

and related fields where Grothendieck did his most important and influential work. From approximately 1955 he started to work on

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The Grothendieck Festschrift, Volume I: A Collection of Articles Written in Honor of the 60th Birthday of Alexander Grothendieck

4424: 3782: 6418: 5346: 5326: 727:, from 1950 to 1953. At this time he was a leading expert in the theory of topological vector spaces. In 1953 he moved to the 5974: 5820: 5096: 5056: 5014: 5000: 4345: 2660: 2209: 2193:

dedicates one chapter to the work and life of Grothendieck, introducing his story by reference to the Japanese mathematician

1117: 783: 691: 5699:: This is an account of how 'Pursuing Stacks' was written in response to a correspondence in English with Ronnie Brown and 4291: 3568: 2232:(1955). "Produits Tensoriels Topologiques et Espaces Nucléaires" [Topological Tensor Products and Nuclear Spaces]. 1806:, he identified twelve of his contributions that he believed qualified as "great ideas". In chronological order, they are: 6295: 5787: 5679: 5513: 4576: 4037: 3589: 1255:. The manuscript, which is being edited for publication by G. Maltsiniotis, later led to another of his monumental works, 870:

route. However, he was able to play a dominant role in mathematics for approximately a decade, gathering a strong school.

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Matériaux pour l'histoire des mathématiques au XXe siècle – Actes du colloque à la mémoire de Jean Dieudonné (Nice 1996)

5071: 1828: 1218: 1020: 720:. Grothendieck introduced new mathematical methods that enabled him to solve all of these problems within a few months. 648: 3069: 2420: 6413: 5018: 3410: 2619: 2517: 2112: 1866: 1633: 1573: 922: 662: 338: 3469: 5732: 5003:(1998), "La folle journée, de Grothendieck à Connes et Kontsevich – Évolution des notions d'espace et de symétrie", 5964: 5696: 5401: 5242: 2614: 2604: 2584: 1810: 1525: 1280: 1206: 1040: 861:

and Grothendieck. Grothendieck attracted attention by an intense and highly productive activity of seminars there (

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where at first he did not perform well, failing such classes as astronomy. Working on his own, he rediscovered the

261: 5545: 1259:. Written in 1991, this latter opus of approximately 2000 pages, further developed the homotopical ideas begun in 6423: 6408: 6388: 6383: 6322: 5813: 5746: 5006:

Les relations entre les mathématiques et la physique théorique – Festschrift for the 40th anniversary of the IHÉS

4958: 4904: 4571: 2883: 2639: 2538: 2092:, of the number of points on an algebraic curve or variety of higher dimension. Grothendieck's discovery of the 1945: 1110: 681:. After three years of increasingly independent studies there, he went to continue his studies in Paris in 1948. 674: 597:

In May 1939, Grothendieck was put on a train in Hamburg for France. Shortly afterward his father was interned in

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asserts that his mother was of Jewish German descent: "what I know of his life comes from Grothendieck himself".

2010: 1621: 1301: 1141:, a physicist who joined the IHÉS faculty in 1964, said that Grothendieck came to talk to him a few times about 5669: 5569: 5509: 3491: 2533: 2483: 2451: 1529: 1044: 705: 428: 5700: 5019:"A mad day's work: from Grothendieck to Connes and Kontsevich The evolution of concepts of space and symmetry" 2353: 358: 5555: 2100:

theory, opened the way for a proof of the Weil conjectures, ultimately completed in the 1970s by his student

1940:

Grothendieck is considered by many to be the greatest mathematician of the twentieth century. In an obituary

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of coherent sheaves under a proper map are coherent; this reduces to Serre's theorem over a one-point space.

1389:, published in 1990, was a three-volume collection of research papers to mark his sixtieth birthday in 1988. 2624: 2197:. The book is a lightly fictionalized account of the world of scientific inquiry and was a finalist for the 2050: 1438: 834: 6209: 6116: 4962: 4908: 3696: 3161:, p. 2: "Beide beteiligten sich am Spanischen Bürgerkrieg, nicht aktiv kämpfend, aber unterstützend." 3130:[Scientific treasure or unreadable old paper? The mysterious archives of Alexandre Grothendieck]. 2372: 2347: 1877: 1016: 640: 99: 3735: 2049:

theories, which use algebraic techniques to study topological objects, has influenced the development of

696:, but he lacked the necessary background to follow the high-powered seminar. On the advice of Cartan and 2984: 2558: 2401: 2363: 2058: 1820: 1537: 1497: 1481:

Grothendieck was very close to his mother, to whom he dedicated his dissertation. She died in 1957 from

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In January 2010, Grothendieck wrote the letter entitled "Déclaration d'intention de non-publication" to

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have been translated into Spanish, as well as into a Russian translation that was published in Moscow.

930: 625: 277: 71: 4713: 1757: 1453:. In 1938, aged ten, he moved to France as a refugee. Records of his nationality were destroyed in the 1264: 754:, and increasingly in algebraic geometry. It was in Lawrence that Grothendieck developed his theory of 191: 5790: 5738: 5659: 4660:

R. P. Langlands, Modular forms and l-adic representations, Lecture Notes in Math. 349. (1973), 361—500

2967: 6373: 6358: 6353: 3128:"Trésor scientifique ou vieux papiers illisibles? Les mystérieuses archives d'Alexandre Grothendieck" 2899: 2574: 2446: 2215: 2034: 2022: 1990: 1870: 1847: 1661: 1625: 1211: 1176: 1149:

interested Grothendieck much more than physics, and he organized some seminars on biological topics.

1081: 994: 717: 614: 5655: 5546:"Who is Alexander Grothendieck? Anarchy, Mathematics, Spirituality, Solitude. Part 3: Spirituality" 4950: 4896: 4148: 2609: 2594: 2478: 2441: 2332: 2198: 2186: 2161: 2136: 2124: 2093: 2089: 2085: 1969:

said, "Lots of people today live in Grothendieck’s house, unaware that it’s Grothendieck’s house."

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During this period, Grothendieck also gave his consent to publishing some of his drafts for EGA on

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as non-combatant auxiliaries. However, others state that Schapiro fought in the anarchist militia.

510: 497: 462: 458: 235: 227: 139: 6328: 5556:"Who is Alexander Grothendieck? Anarchy, Mathematics, Spirituality, Solitude. Part 2: Mathematics" 4189: 6332: 6285: 6204: 6165: 6148: 6111: 5620: 4841: 3303: 2579: 2425: 2337: 2194: 2148: 2120: 2116: 2074: 2066: 2054: 2026: 2018: 1909: 1899: 1693: 1553: 1458: 1310: 1297: 1272: 1244: 958: 890: 770: 755: 747: 547: 493: 454: 363: 231: 153: 5295: 5275: 4539: 4401:: " mathematician of staggering accomplishment... a legendary figure in the mathematical world." 4215: 1293: 1043:

and he then conjectured the existence a further generalization of it, which is now known as the

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Piotr Pragacz, 'Notes on the Life and Work of Alexander Grothendieck,' in Piotr Pragacz (ed.),

570:. His mother followed soon thereafter. Grothendieck was left in the care of Wilhelm Heydorn, a 6246: 6219: 6214: 6160: 6133: 6079: 6013: 5920: 5891: 5751: 5583: 5563: 5525: 5517: 5445: 5435: 5405: 5260: 5254: 5218: 5159: 5140: 5126: 4827: 4751: 4745: 4692: 4641: 4635: 4614: 4608: 4580: 4543: 4510: 4504: 4483: 4471: 4116: 4110: 4066: 3550: 3429: 3284: 3223: 2948: 2925: 2917: 2673: 2293: 2283: 2259: 2241: 2179:

in English), a novel by Puerto Rican–Costa Rican writer Carlos Fonseca is about Grothendieck.

2105: 1994: 1861: 1768: 1592: 1517: 1486: 1222: 1036: 1028: 858: 817: 813: 709: 629: 586: 582: 562:

Grothendieck lived with his parents in Berlin until the end of 1933, when his father moved to

302: 5296:"Comme Appelé du Néant – As If Summoned from the Void: The Life of Alexandre Grothendieck II" 3241: 3205: 3190: 6300: 6273: 6182: 6143: 6067: 6040: 6018: 5979: 5969: 5886: 5869: 5770: 5612: 5476: 5377: 5276:"Comme Appelé du Néant – As If Summoned from the Void: The Life of Alexandre Grothendieck I" 5108: 5035: 4979: 4925: 4686: 4566: 3721: 3542: 3419: 3354: 2907: 2863: 2741: 2677: 2629: 2589: 2523: 2503: 2497: 2395: 2327: 2157: 2081: 1998: 1824: 1787: 1646: 1581: 1577: 1521: 1370: 1365: 1153: 1125: 1052: 1048: 1012: 974: 938: 918: 914: 894: 759: 743: 713: 678: 606: 546:

roots and had been imprisoned in Russia before moving to Germany in 1922, while his mother,

478: 388: 318: 297: 289: 5715: 5632: 4594: 4174:[Alexandre Grothendieck, the greatest mathematician of the 20th century, is dead]. 3564: 3541:. Lecture Notes in Mathematics. Vol. 1960. New York: Springer-Verlag. pp. 1–259. 3441: 3321: 3319: 2255: 6263: 6236: 6192: 6177: 6057: 5991: 5628: 5480: 5361: 4771: 4590: 4387:

Alexandre Grothendieck is arguably the most important mathematician of the 20th century...

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The bulk of Grothendieck's published work is collected in the monumental, yet incomplete,

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Homological methods and sheaf theory had already been introduced in algebraic geometry by

1585: 1466: 1450: 1240: 1227: 1101: 970: 874: 867: 842: 801: 732: 543: 539: 470: 445: 348: 328: 75: 5193: 3936: 3860:] (in Japanese). Translated by Tsuji Yuichi (2nd ed.). Kyoto: Gendai Sūgaku-sha. 3841:] (in Japanese). Translated by Tsuji Yuichi (2nd ed.). Kyoto: Gendai Sūgaku-sha. 3822:] (in Japanese). Translated by Tsuji Yuichi (2nd ed.). Kyoto: Gendai Sūgaku-sha. 3820:

The Solitary Adventures of a Mathematician: A Journey into Mathematics and Self-Discovery

3667: 2312: 1565: 5693:, collection of mathematical and biographical information, photos, links to his writings 5459: 4378: 4007: 3962: 2903: 857:(IHÉS), a new privately funded research institute that, in effect, had been created for 6258: 6138: 6089: 6045: 6023: 6008: 5937: 5173: 5004: 4532: 2473: 2430: 2276: 2128: 2101: 2030: 1921: 1791: 1780: 1610: 1354: 1263:. Much of this work anticipated the subsequent development during the mid-1990s of the 1248: 1232: 946: 898: 886: 793: 661:

In 1990, for risking their lives to rescue Jews, the entire village was recognized as "

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After the war, the young Grothendieck studied mathematics in France, initially at the

481:. He is considered by many to be the greatest mathematician of the twentieth century. 6347: 6268: 6241: 6121: 6106: 6094: 6084: 6062: 5996: 5952: 5857: 5742: 5550:

Third part of planned four-volume biography; crowd-financed translation into English.

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writes the other terms "Ariadne's thread" and "philosophy" as effective equivalents.

1893: 1814: 1772: 1685: 1681: 1669: 1657: 1546: 1533: 1513: 1462: 1407: 1333: 1204:) is a 1600-page handwritten manuscript containing many of the ideas that led to the 1157: 1093: 1032: 962: 934: 902: 821: 809: 789: 774: 746:

at the beginning of 1955, and there he set his old subject aside in order to work in

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Récoltes et Semailles : réflexions et témoignage sur un passé de mathématicien

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Récoltes et Semailles : réflexions et témoignage sur un passé de mathématicien

4274: 2486: – cohomology theory for algebraic varieties introduced by Grothendieck (1966) 2322: 2062: 1776: 1641: 1613:

on a complete variety is finite-dimensional; Grothendieck's theorem shows that the

1482: 1470: 1434: 1411: 1374: 1289: 1268: 1138: 878: 736: 685: 644: 618: 610: 489: 466: 182: 95: 5908: 5574:

First 4 chapters from the incomplete second part of planned four-volume biography.

5040: 2546: – in algebraic geometry, an analogue of a proper map for algebraic varieties 2406: 2282:. Translated by Chaljub, Orlando. New York: Gordon and Breach Science Publishers. 1317: V, published in Ulam Quarterly in 1992–1993 and later made available on the 797: 5727: 5395: 5120: 3531: 2888:"Alexander Grothendieck (1928–2014) Mathematician who rebuilt algebraic geometry" 1346:

preface for it, in which he called Tsuji his "first true collaborator". Parts of

6231: 6187: 5925: 5735:

with photos from Grothendieck's life, given by Winfried Scharlau at IHES in 2009

5100: 2563: 2358: 2132: 1983: 1454: 1427: 1133: 1097: 1089: 942: 882: 838: 598: 343: 223: 17: 5942: 5903: 5112: 5084:"A country of which nothing is known but the name: Grothendieck and "motives"" 4245: 3546: 3207:

Topics in Cohomological Studies of Algebraic Varieties: Impanga Lecture Notes,

2685: 2182:

The band Stone Hill All Stars have a song named after Alexander Grothendieck.

2070: 2046: 1962: 1794:

in the early 1970s after Grothendieck had largely withdrawn from mathematics.

1596: 551: 5521: 5449: 5323:

Topics in Cohomological Studies of Algebraic Varieties: Impanga Lecture Notes

4172:"Alexandre Grothendieck, le plus grand mathématicien du XXe siècle, est mort" 3433: 3424: 3016:"Who is Alexander Grothendieck? Anarchy, Mathematics, Spirituality, Solitude" 2921: 1023:

to complement it. Closely linked to these cohomology theories, he originated

5675: 5529: 5214: 5143:. "De L'analyse fonctionelle aux fondements de la géométrie algébrique". In 5116: 5104: 5061:"Un pays dont on ne connaîtrait que le nom (Grothendieck et les " motifs ")" 4136: 3258:"Alexandre Grothendieck, ou la mort d'un génie qui voulait se faire oublier" 3073: 2386: 1884: 1665: 1512:. Between 1949 and 1953 he worked on his doctoral thesis in this subject at 1403: 1337: 910: 805: 535: 5721: 4712:

Marquis, Jean-Pierre (2015). "Category Theory". In Zalta, Edward N. (ed.).

3890: 2929: 2317: 2263: 1132:" ("a gilded cage"). While Grothendieck was at the IHÉS, opposition to the 704:

where two leading experts were working on Grothendieck's area of interest,

654:

In Le Chambon, Grothendieck attended the Collège Cévenol (now known as the

5420: 4796: 3760: 2297: 1465:

person for at least the majority of his working life and he traveled on a

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Loving and Hating Mathematics: Challenging the Myths of Mathematical Life

5009:, vol. S88, Institut des Hautes Études Scientifiques, pp. 11–19 3879:] (Unpublished manuscript) (in Japanese). Translated by Tsuji Yuichi. 3132: 2468: 2411: 1838: 1705: 1606: 1541: 1493: 1420: 1085: 986: 966: 571: 514: 501: 161: 2084:

were formulated in the later 1940s as a set of mathematical problems in

1058:

The results of his work on these and other topics were published in the

5624: 4009:

Die Mutanten – Les Mutants – eine Meditation von Alexander Grothendieck

3287:[Alexander Grothendieck: A journey in pursuit of the obvious]. 3285:"Alexandre Grothendieck: Un voyage à la poursuite des choses évidentes" 2970:

David Mumford at Brown and Harvard Universities: Archive for Reprints:

2792: 2790: 1146: 1142: 578: 555: 4718:(Winter 2015 ed.). Metaphysics Research Lab, Stanford University. 3816:

Suugakusha no kodokuna bōken : suugaku to jiko no hakken eno tabi

5687:

is a peripatetic seminar on Grothendieck view not just on mathematics

5650:

is a website devoted to the life and works of Alexandre Grothendieck.

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Mathematics and the Naked King: A Dream and the Burial of Mathematics

3252: 3250: 1318: 1235:. This letter and successive parts were distributed from Bangor (see 926: 574: 567: 531: 457:. His research extended the scope of the field and added elements of 271: 67: 5616: 5422:

Wer ist Alexander Grothendieck?: Anarchie, Mathematik, Spiritualität

2912: 2887: 989:. Then, following the programme he outlined in his talk at the 1958 5805: 5776: 4480:

Sheaves in Geometry and Logic: a First Introduction to Topos Theory

3452: 3450: 3308: 609:

Once, he managed to escape from the camp, intending to assassinate

449:; 28 March 1928 – 13 November 2014) was a German-born French 3492:"1953 : un « Résumé » aux développements illimités" 1852: 1105: 1024: 723:

In Nancy, he wrote his dissertation under those two professors on

563: 5582:, Somerville Massachusetts: International Press of Boston, Inc., 3477:

Who Is Alexandre Grothendieck: Anarchy, Mathematics, Spirituality

1668:. As 'functions' these can take only the value 0, but they carry 621:. Grothendieck was permitted to live separated from his mother. 2571: – Conditions for a divisor of a local ring to be principal 1920:

denotes a kind of "meta-theory" that may be used heuristically;

1637: 5809: 3210:

Springer Science & Business Media, 2006 pp-xi-xxviii p.xii.

977:. His first (pre-IHÉS) discovery in algebraic geometry was the 5796:

Alexandre-Grothendieck-une-mathematique-en-cathedrale-gothique

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A Dream and the Burial of Mathematics: The Key to Yin and Yang

2968:

Alexander Grothendieck obituary by David Mumford and John Tate

1649:'s seminar. He outlined his programme in his talk at the 1958 412: 406: 4346:"The Rising Sea: Grothendieck on simplicity and generality I" 3228:

Springer Science & Business Media, 2007 pp.237–249 p.237.

2511: – a moduli space that exists in the category of schemes 4747:

Tool and Object: A History and Philosophy of Category Theory

4052:

Les «gribouillis» d'Alexandre Grothendieck enfin sauvegardés

3225:

Vite matematiche: Protagonisti del '900, da Hilbert a Wiles,

1887:; cohomological formalism of topoi as inspiration for a new 5158:. AMS and the Société Mathématique de France. p. 600. 3539:

Foundations of Grothendieck Duality for Diagrams of Schemes

1011:

theory of schemes, providing the key tools for proving the

400: 4089:"The Mysterious Disappearance revolutionary mathematician" 2088:. They describe properties of analytic invariants, called 1790:, the last of which was settled by Grothendieck's student 1779:

reflects the topological nature of its solutions over the

1624:, which recently had been generalized to any dimension by 628:, he was sheltered and hidden in local boarding houses or 5368:

The Grothendieck I Knew: Telling, Not Hiding, Not Judging

5178:"Quelques idées maîtresses de l'œuvre de A. Grothendieck" 4503:

Dov M. Gabbay; Akihiro Kanamori; John Woods, Jr. (2012).

4112:

Unknown Quantity: A Real and Imaginary History of Algebra

3494:[1953: a "Summary" with unlimited developments]. 1880:, yoga of "de Rham coefficients", "Hodge coefficients"... 1027:

theory as a generalisation of topology (relevant also in

985:

proved algebraically; in this context he also introduced

394: 5144: 4750:. Springer Science & Business Media. pp. 158–. 4640:. Springer Science & Business Media. pp. 156–. 4025: 3325: 2737: 2465: – 1957 mathematics paper by Alexander Grothendieck 2366: – Cartesian sections of certain fibered categories 453:

who became the leading figure in the creation of modern

4691:. Springer Science & Business Media. p. viii. 3109: 3107: 3105: 3103: 3101: 3099: 3097: 3095: 3093: 3091: 5791:

Rebellious Genius: In Memory of Alexander Grothendieck

5316:"Notes on the life and work of Alexander Grothendieck" 3835:

Sūgaku to hadaka no ōsama: Aru yume to sūgaku no maisō

3647: 3645: 3643: 3641: 3639: 3637: 3532:"Notes on derived categories and Grothendieck duality" 3049: 3047: 2832: 2830: 2828: 2826: 2824: 2822: 2809: 2807: 2805: 2721: 2719: 2717: 2715: 2713: 2711: 2709: 2707: 2705: 1640:, in 1957. It appeared in print in a paper written by 1300:. Later, it was published in two-volumes and entitled 1152:

In 1970, Grothendieck, with two other mathematicians,

278:

Produits tensoriels topologiques et espaces nucléaires

4170:

Stéphane Foucart; Philippe Pajot (14 November 2014).

3408:(1957), "Sur quelques points d'algèbre homologique", 2777: 2775: 2773: 2760: 2758: 2756: 2754: 2752: 2750: 780:

Comparing Grothendieck during his Nancy years to the

415: 5801:

Les-archives-insaisissables-d-alexandre-grothendieck

5783:

Les-archives-insaisissables-d-alexandre-grothendieck

5765:

Alexander Grothendieck: A Country Known Only by Name

5760:, Winfried Scharlau, Notices of the AMS 55(8), 2008. 5156:

Grothendieck-Serre Correspondence: Bilingual Edition

3340:"Topological vector spaces, by A. Grothendieck, ..." 2548: