Unpublished works

The introduction of the cipher 0 or the group concept was general nonsense, too,
and for a thousand years or two mathematics was more or less stagnating,
because nobody was around to make such childish steps . . .

When addressing the substantial body of unpublished works by A. Grothendieck, two main aspects come to light. Firstly, in his active years, it was a recognizable pattern of his methodology that he had to think about so many ideas that sprung into his mind, that he often left to colleagues or students the details of their consequences, leaving an important body of notes that would serve for these needs. Secondly, a notable facet of Grothendieck’s life and work is his gradual withdrawal from the world. This successive isolation began with his departure from the main institution of his active years, namely the IHÉS in 1970, at just 42. It continued with his distancing from the mathematical community, and ultimately culminated in his detachment from society and family. By 1991, he had isolated himself, adopting a hermit-like existence until his passing in 2014. This self-imposed isolation bequeathed us an extensive collection of intermittent, both lengthy and concise, mathematical reflections and literary meditations. These two main aspects are even more essential when we recognize the importance Grothendieck gave to writing. 

Among the wealth of materials, there are discernible documents that, in a sense, stand as finished works. Below, you will find a selection of these. They have been organized into two helpful categories: scientific and literary works, for ease of reference. They have been chosen from original sources or the archives presented in the next section. While we are committed to expanding this selection with other clearly referentially items, we also extend an open invitation for collaborations to publish, digitize, scan, and more.

  • Title: Quelques remarques d’Algèbre homologique
  • Language: French
  • Written date: July, 1955
  • Bibliographical data: [scan], Rédaction Bourbaki [No. 222] Fonds du secrétariat Bourbaki (ENS-ULM)
  • TitleAlgèbre chap VIII. Modules et anneaux semi-simples. §§ 7 et 8 (état 7)
  • Language: French
  • Written date: June, 1956
  • Bibliographical data: [scan], Rédaction Bourbaki [No. 245] Fonds Jean Delsarte (Institut Élie Cartan)
  • Title: Généralités sur les Espaces fibrés
  • Language: French
  • Written date: July, 1956
  • Bibliographical data: [scan], Rédaction Bourbaki [No. 243] Fonds du secrétariat Bourbaki (ENS-ULM)
  • TitlePréliminaires au livre des variétés. Catégories de variétés
  • Language: French
  • Written date: April, 1957
  • Bibliographical data: [scan], Rédaction Bourbaki [No. 262] Fonds du secrétariat Bourbaki (ENS-ULM)
  • TitleVariétés différentiables. Chapitre I. Le formalisme différentiel (état 0)
  • Language: French
  • Written date: June, 1957
  • Bibliographical data: [scan], Rédaction Bourbaki [No. 270] Fonds du secrétariat Bourbaki (ENS-ULM)
  • TitleContre-rédaction pour la réédition de Topologie générale. chap. 10
  • Language: French
  • Written date: June, 1958
  • Bibliographical data: [scan], Rédaction Bourbaki [No. 288] Fonds Jean Delsarte (Institut Élie Cartan) 
  • TitleSur la formalisation des catégories et foncteurs
  • Language: French
  • Written date: 11.1958
  • Bibliographical data: [scan], Rédaction Bourbaki [No. 307] Fonds Pierre Cartier (Archives Henri Poincaré)
  • TitleAlgèbre commutative
  • Language: French
  • Written date: 9.1959
  • Bibliographical data: [scan], Rédaction Bourbaki [No. 326bis] Fonds du secrétariat Bourbaki (ENS-ULM)
  • Title: Anneaux adiques
  • Language: French
  • Written date: 9.1959
  • Bibliographical data: [scan], Rédaction Bourbaki [No. 327] Fonds Pierre Cartier (Archives Henri Poincaré)
  • Title: Modules projectifs de type fini, idéaux fractionnaires inversibles
  • Language: French
  • Written date: 9.1960
  • Bibliographical data: [scan], Rédaction Bourbaki [No. 346] Fonds Pierre Cartier (Archives Henri Poincaré)
  • Title: Suggestion sur les Gries et Algoupes de Lebres
  • Language: French
  • Written date: ca. 1960
  • Bibliographical data: [scan], Rédaction Bourbaki [No. 383bis] Fonds Pierre Cartier (Archives Henri Poincaré)
  • Title: Catégories tannakiennes
  • Language: French
  • Written date: Uncertain (c. 1960s)
  • Bibliographical data: Montpellier archive [Cote No. 10]
  • Title: Filtrations sur foncteurs fibres pour catégories tensorielles
  • Language: French
  • Written date: Uncertain (c. 1960s)
  • Bibliographical data: Montpellier archive [Cote No. 10]
  • Title: Quelques exemples de catégories tensorielles
  • Language: French
  • Written date: Uncertain (c. 1960s)
  • Bibliographical data: Montpellier archive [Cote No. 10]
  • TitleLocal Picard schemes
  • Language: French
  • Written date: Uncertain (c. 1960s)
  • Bibliographical data: Montpellier archive [Cote No. 57]
  • Title: Motifs
  • Language: French
  • Written date: Uncertain (c. 1960s)
  • Bibliographical data: Montpellier archive [Cote No. 12]
  • Title: Travaux de thèses
  • Language: French
  • Written date: 1964
  • Bibliographical data: Montpellier archive [Cote n 66]
  • Notes: Selected topics of research for students
  • TitleFormules de Künneth pour la cohomologie à supports quelconques
  • Author: L. Illusie (d’après des papiers secrets de A. Grothendieck)
  • Language: French
  • Written date: 1965/66
  • Bibliographical data: [scan]
  • Title: Introduction au langage fonctoriel
  • Author: Rédigé par M. Karoubi d’après un cours de Monsieur A. Grothendieck
  • Language: French
  • Written date: 1965
  • Bibliographical data: [scan]
  • Notes: This notes, taken by Max Karoubi, were the result of a series of talks on the functorial language that Grothendieck gave during the month of November 1965 in the “Faculté des Sciences d’Alger. Département de Mathématiques”.
  • Title: Esquisse d’une théorie des motifs
  • Language: French
  • Written date: 1968 (?)
  • Bibliographical data: Montpellier archive [Cote No. 12]
  • Title: Tapis de Quillen I, II
  • Language: French
  • Written date: 1968
  • Bibliographical data: [scan I], Montpellier archive [Cote No. 162-5]
  • Title: Résumé de quelques résultats de Kostant
  • Language: French
  • Written date: 1969
  • Bibliographical data: Montpellier archive [Cote No. 123]
  • Title: Réflexions sur le plan des EGA
  • Language: French
  • Written date: 1960’s
  • Bibliographical data: [scan]
  • TitleNotice sur les travaux de Mr. Pierre Deligne. Parties I et II
  • Language: French
  • Written date: 1968/69
  • Bibliographical data: [scan I], [scan II]
  • Notes: Report on Deligne’s scientific activity in Bures under Grothendieck’s direction
  • Title: Rapport sur l’oeuvre mathématique de David Mumford
  • Authors: A. Grothendieck and M. Raynaud
  • Language: French
  • Written date: 1969
  • Bibliographical data: [scan]
  • TitleRapport de mission de Mr. A. Grothendieck
  • Authors: A. Grothendieck
  • Language: French
  • Written date: 1969
  • Bibliographical data: [scan]
  • Title: Introductory notes on group schemes
  • Language: English
  • Author: Leslie Roberts
  • Written date: January – March, 1971
  • Bibliographical data: [scan]
  • Notes: Introductory notes by L. Roberts on a series of lectures Grothendieck gave at Kingston, Canada.
  • TitleTorseur relativement universel
  • Language: French
  • Bibliographical data: [scan]
  • Title: Esquisse thématique des principaux travaux mathématiques
  • Language: French
  • Written date: 1972
  • Bibliographical data: [scan I], [scan II] Montpellier archive [Cote No. 119]
  • Notes: Written in 1972 on the occasion of an application for a professorship at the Collège de France.
  • Title: Fonctions holomorphes I, II
  • Language: French
  • Written date: 1973/74
  • Bibliographical data: Montpellier archive [Cote No. 119]
  • Title: Introduction to functorial algebraic geometry
  • Subtitle: Part 1, affine Algebraic geometry
  • Language: English
  • Written date: 1973
  • Bibliographical data: [scan]
  • Notes: The following notes were written by Federico Gaeta, and printed by the university in 1984 in the form of mimeographed notes. These are not based on prenotes by Grothendieck and to some extent represent Gaeta’s personal understanding of what was taught. For more on this, see the foreword in the introduction
  • Title: Complexe de De Rham à puissance divisée et ombres des modules
  • Language: French
  • Written date: 1975/76
  • Bibliographical data: Montpellier archive [Cote No. 136]
  • Notes: Last public lecture by Grothendieck. I.H.É.S, 1976
  • Title: Notations semi-simpliciaux. Constructions universelles
  • Language: French
  • Written date: 1975/76
  • Bibliographical data: Montpellier archive [Cote No. 137]
  • Notes: See “Complexe de De Rham à puissance divisée et ombres des modules”
  • TitleFaisceautisation du topos de De Rham
  • Language: French
  • Written date: Uncertain (c. 1970s)
  • Bibliographical data: Montpellier archive [Cote No. 136]
  • TitlePolyèdres réguliers
  • Language: French
  • Written date: 1976
  • Bibliographical data: Montpellier archive [Cote No. 69]
  • Notes: Extrait de la présentation du cours de D.E.U.G. A Première année sur les polyèdres réguliers (1976).
  • Title: Géométrie de l’icosaèdre
  • Language: French
  • Written date: 1977/78
  • Bibliographical data: Montpellier archive [Cote No. 75]
  • Notes: C4 course 1977/78. Montpellier University
  • Title: Géométrie arithmétique des polygônes réguliers
  • Language: French
  • Written date: 1977/78
  • Bibliographical data: Montpellier archive [Cote No. 75]
  • Notes: DEA course 1977/78. Montpellier University
  • Title: Structure à l’infini des Mg,v
  • Language: French
  • Written date: c. 1978
  • Bibliographical data: Montpellier archive [Cote No. 147]
  • Title: Structures Stratifiées
  • Language: French
  • Written date: 1981
  • Bibliographical data: Montpellier archive [Cote No. 151]
  • Title: Notes Anabéliennes
  • Language: French
  • Written date: 1983
  • Bibliographical data: Montpellier archive [Cote No. 149]
  • Title: Rapport d’activité
  • Language: French
  • Written date: 1984
  • Bibliographical data: [scan I], [scan II], Montpellier archive [Cote No. 119]
  • Title: Vers une géométrie des formes
  • Language: French
  • Written date: 1986
  • Bibliographical data: Montpellier archive [Cote No. 156 1-9]
  • Notes: This text is the write up of an alternative foundations for “topology”, starting with the “geometrical objects” or “figures”, rather than with a set of “points” and some kind of notion of “limit” or (equivalently) “neighborhoods”. Like the language of topoi (and unlike the so-called “moderate space”), it is a kind of topology “without points” – a direct approach to “shape”.
  • Title: Les Dérivateurs
  • Language: French
  • Written date: Between October 1990 and the middle of 1991
  • Bibliographical data: Montpellier archive [Cote No. 157 1-5]
  • Notes: This manuscript, 1976 pages long, is devoted to the foundations of the theory of derivators as part of his program of topological algebra.
  • Title: Géométrie Élémentaire Schématique
  • Language: French
  • Written date: From August to October, 1992
  • Bibliographical data: As part of ‘[Réflexions sur la Vie et le Cosmos],’ in the BnF archive.
  • Title: Correspondence A Grothendieck – R. Brown
  • Language: English
  • Written date: Between 1982 and 1991
  • Bibliographical data:
  • TitleLa vie mathématique en République Démocratique du Vietnam
  • Language: French
  • Date: 20.12.1967
  • Bibliographical data: [scan]
  • TitleLe congrès international des mathématiciens de Nice (1-10 septembre 1970)
  • Language: French
  • Date: 1970
  • Bibliographical data: [scan]
  • TitlePourquoi encore un autre mouvement ?
  • Language: French
  • Date: Septembre/Octobre 1970
  • Bibliographical data: ‘Survivre’ No’s 2 et 3 [scan]
  • TitleDes adhérents se présentent (C. Chevalley – M. Escuder – A. Grothendieck)
  • Language: French
  • Date: Septembre/Octobre 1970
  • Bibliographical data: ‘Survivre’ No’s 2 et 3, [scan]
  • TitleRemous au Collège de France
  • Language: French
  • Date: August/September 1971
  • Bibliographical data: Survivre et. . . vivre’ No 9 [scan]
  • TitleL’OTAN les matheux et les gens
  • Language: French
  • Date: June 1972
  • Bibliographical data: ‘Survivre et. . . vivre’ No 12 [scan]
  • TitleSur le divorce entre Science et Vie, scientifiques et population
  • Language: French
  • Date: July, 1970
  • Bibliographical data: “Survivre” No. 1 [scan]
  • Notes: “Les réflexions suivantes ont été suscitées par une discussion avec P. Koosis et d’autres collègues pendant le Séminaire de Mathématiques Supérieures à l’Université de Montréal (juillet 1970).”
  • TitleAllons-nous continuer la recherche scientifique ?
  • Authors: A. Grothendieck and D. Guedj
  • Language: French
  • Date: 1971
  • Bibliographical data: [scan], “Survivre et. . . vivre” No 10, October/December 1971 [scan]
  • Title: Hexensküche
  • Language: German
  • Date: 6.12.1971
  • Place: Bielefeld, Germany
  • Bibliographical data: [image]
  • Notes: After a conference at Bielefeld discussing the Riemann-Roch theorem, Grothendieck wrote a short text associated with the proceedings of the colloquium.
  • TitleLe Maître-enseignant et le maître-chercheur dans l’Université d’aujourd’hui et de demain
  • Language: French
  • Date: Uncertain (c. 1970s)
  • Bibliographical data: [scan], Montpellier archive [Cote No. 119]
  • TitleRapport de la commission relative au recrutement des enseignants
  • Language: French
  • Date: Uncertain (c. 1970s)
  • Bibliographical data: Montpellier archive [Cote No. 119]
  • TitleDoctorat d’État en Mathématiques
  • Language: French
  • Date: Uncertain (c. 1970s)
  • Bibliographical data: Montpellier archive [Cote No. 119]
  • Title: En Guise de Programme
  • Language: French
  • Date: 1978-79
  • Bibliographical data: Montpellier archive [Cote No. 119]
  • Notes: Grothendieck was planning to give a course called “Introduction to research” for the fourth-year students in Montpellier, and in October 1978 he prepared an information sheet for the class entitled “En Guise de Programme” where he presented the intentions of the course.
  • Title: L’Éloge de l’Inceste
  • Language: French
  • Date: Between January and July of 1979.
  • Bibliographical data: As far as is known most of this text must be considered lost; for the moment we know only the table of contents and one chapter.
  • Notes: This work holds a special position in that Grothendieck himself regarded it as a poetic work.
  • Title: Kimchi
  • Language: French
  • Date: 15.10. 1983
  • Bibliographical data: [link1], [link2]
  • Notes: A write-up about kimchi, a traditional Korean preparation of fermented vegetables.
  • Title: Lettre de la Bonne Nouvelle
  • Language: French
  • Date: Between January and March 1990
  • Notes: On January 26, 1990, a letter was sent inquiring about the preparations for a ‘New Age’. Subsequently, a series of commentaries, referred to as ‘Développements’, were provided between February and March following the letter.
  • Title: Structures de la Psyché
  • Language: French
  • Date: Between 1992 and 1993
  • Bibliographical data: As part of ‘[Réflexions sur la Vie et le Cosmos],’ in the BnF archive.
  • Notes: Development of combinatorial mathematical structures to study manifestations of an individual’s personality.
  • Title: Esprit et Matière – ou l’Esprit des Lois naturelles
  • Language: French
  • Date: Between 1992 and 1997
  • Bibliographical data: As part of ‘[Réflexions sur la Vie et le Cosmos],’ in the BnF archive.
  • Title: Le problème du Mal
  • Language: French
  • Date: Between 1993 and 1997
  • Bibliographical data: As part of ‘[Réflexions sur la Vie et le Cosmos],’ in the BnF archive.
  • Notes: Metaphysical meditations, introspective dives, and autobiographical narrative
  • TitleDéclaration d’intention de non-publication
  • Language: French
  • Date: 5.2.1986
  • Unpublished
  • Bibliographical data: [link]
  • Notes: Attached to a Letter to L. Illusie the same date

The Montpellier archive

This collection was entrusted by A. Grothendieck to one of his former students, Jean Malgoire, a professor-researcher at the University of Montpellier. It encompassed a wide range of materials, including preprints, extensive mathematical notes and manuscripts in various stages of development and completion, as well as a substantial portion of his meticulously organized scientific and private correspondence, comprising thousands of pages.  The delivery of these materials was carried out in two stages, in June or July 1990 when Grothendieck was preparing his departure from Mormoiron, and on July 28, 1995. Subsequently, Jean Malgoire received explicit permission to deal with the documents he had received as he judged it appropriate. Jean Malgoire kept the Grothendieck archives at his home until 2010, when they were deposited at the University of Montpellier. They were donated from Jean Malgoire to the University in 2012.

Since May 2017, part of this archive, known under the name of Fonds Grothendieck, has been available online and can be accessed at the link below:

The BnF archive

A collection of unpublished manuscripts by A. Grothendieck has been integrated into the National Library of France collections. Bequeathed by Grothendieck to the Library, this collection is complemented by a donation from his children. It consists, on one hand, of a corrected typescript of La Clef des Songes, and on the other hand, of a handwritten work titled Réflexions sur la Vie et le Cosmos, spanning across 41 volumes and composed of Géométrie élémentaire schématique (1992), Structures de la Psyché, developed from 1992 to 1993, Équations de Maxwell (1992-1994), and Le Problème du Mal, a work composed between 1993 and 1997, of almost 15,000 pages. This collection, of major importance for research, joins the Manuscripts department of the BnF alongside those of other eminent scientists.

Since September 2023, access to this archive, known under the name of Fonds Alexandre Grothendieck, has been possible but restricted to in-person visits by researchers. You can consult it at the Richelieu Library – Manuscripts Reading Room.
More information are available at the link below: