Alexander Grothendieck
Manuscripts written in the 1980s

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.

Produced during 1980 and 1981, La Longue Marche à travers la théorie de Galois (The Long March Through Galois Theory) is a 1600-page handwritten manuscript containing many of the ideas that led to the Esquisse d'un programme. It also includes a study of Teichmüller theory.

In 1983, stimulated by correspondence with Ronald Brown and Tim Porter at Bangor University, Grothendieck wrote a 600-page manuscript entitled Pursuing Stacks. It began with a letter addressed to Daniel Quillen. This letter and successive parts were distributed from Bangor (see External links below). Within these, in an informal, diary-like manner, Grothendieck explained and developed his ideas on the relationship between algebraic homotopy theory and algebraic geometry and prospects for a noncommutative theory of stacks. The manuscript, which is being edited for publication by G. Maltsiniotis, later led to another of his monumental works, Les Dérivateurs. Written in 1991, this latter opus of approximately 2000 pages, further developed the homotopical ideas begun in Pursuing Stacks. Much of this work anticipated the subsequent development during the mid-1990s of the motivic homotopy theory of Fabien Morel and Vladimir Voevodsky.

In 1984, Grothendieck wrote the proposal Esquisse d'un Programme ("Sketch of a Programme") for a position at the Centre National de la Recherche Scientifique (CNRS). It describes new ideas for studying the moduli space 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 dessin d'enfant theory and anabelian geometry. Later, it was published in two-volumes and entitled Geometric Galois Actions (Cambridge University Press, 1997).

During this period, Grothendieck also gave his consent to publishing some of his drafts for EGA on Bertini-type theorems (EGA V, published in Ulam Quarterly in 1992–1993 and later made available on the Grothendieck Circle web site in 2004).

In the 1,000-page autobiographical manuscript, Récoltes et semailles (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. The Récoltes et semailles work is now available on the internet in the French original, and an English translation is underway. A Japanese translation of the whole book in four volumes was completed by Tsuji Yuichi (1938–2002), a friend of Grothendieck from the Survivre 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 preface for it, in which he called Tsuji his "first true collaborator". Parts of Récoltes et semailles have been translated into Spanish, as well as into a Russian translation that was published in Moscow. The French original was finally published in two volumes in January 2022, with additional texts by people of various professions who discuss certain aspects of the book.

In 1988, Grothendieck declined the Crafoord Prize 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 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."

La Clef des Songes, 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 deity 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 Bernhard Riemann. Influenced by the Catholic mystic Marthe Robin 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 Lettre de la Bonne Nouvelle 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.

The Grothendieck Festschrift, published in 1990, was a three-volume collection of research papers to mark his sixtieth birthday in 1988.

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.
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