Alexander Grothendieck

Life

The lived universe

The lived universe: statelessness, war, migration, institutions, friendship, conflict, activism, withdrawal, and the archive left behind. Preface

A life in twelve Parts

The chapters in the order of the life. Beside each chapter, the years its text names: one mark for each year, larger where the year recurs.

Years named in the text of each chapter

  1. Part IBefore Belonging
  2. 1Before the Name1871: 11872: 11882: 11889: 11890: 11894: 11897: 11900: 21905: 21911: 11914: 11917: 31920: 21921: 121926: 11930: 1
  3. 2A House without Borders1921: 31922: 11924: 21925: 61926: 31927: 91928: 11929: 11933: 1
  4. 3Berlin, 19281927: 11928: 191929: 201930: 21933: 1
  5. 4The Absent Father1929: 31930: 21933: 141979: 21980: 21991: 1
  6. 5The Road South1933: 381934: 61938: 81939: 61979: 11980: 1
  7. 6Stateless1913: 21921: 11922: 11925: 11928: 31929: 31930: 11933: 171934: 21939: 61971: 4
  8. Part IISchooling in Exile
  9. 7Flight1933: 61934: 71936: 41937: 21938: 41939: 191987: 1
  10. 8The Camp1938: 11939: 151940: 71941: 21942: 61944: 1
  11. 9Le Chambon1938: 11940: 31941: 121942: 11944: 41989: 21990: 32013: 12020: 1
  12. 10Lessons in Hiding1943: 11944: 31945: 51948: 2
  13. 11A Child of War1933: 21939: 31940: 21942: 11944: 201945: 21968: 11987: 142017: 1
  14. 12Liberation without Home1933: 21942: 21944: 61945: 71971: 11987: 2
  15. Part IIILearning from First Principles
  16. 13Montpellier1902: 11945: 31948: 61952: 11985: 11986: 1
  17. 14The Measure of Volume1902: 11945: 71948: 5
  18. 15The Solitary Student1945: 21948: 71949: 11952: 1
  19. 16Parisian Thresholds1948: 151949: 171950: 11952: 1
  20. 17Nancy1948: 11949: 71950: 91951: 51952: 21953: 11989: 1
  21. 18The First Harvest1948: 21949: 11950: 11951: 31952: 271953: 131954: 41955: 91956: 41996: 1
  22. Part IVA Language Begins
  23. 19São Paulo1945: 11947: 11950: 11952: 31953: 61954: 111955: 61958: 6
  24. 20Kansas1949: 11955: 211956: 121957: 121958: 7
  25. 21The Homological Turn1945: 11955: 61956: 21957: 91958: 11960: 11966: 1
  26. 22The Language of Functors1955: 61956: 71957: 271958: 3
  27. 23Riemann–Roch Recast1953: 21956: 11957: 121958: 221959: 1
  28. 24Toward Geometry1946: 11953: 11954: 11955: 11957: 21958: 561959: 61960: 31966: 11970: 5
  29. Part VThe Relative World
  30. 25A New Foundation1946: 11954: 11955: 21956: 21957: 11958: 221959: 191960: 151961: 41962: 11970: 2
  31. 26The Scheme1958: 21959: 121960: 11961: 4
  32. 27The Relative View1958: 21959: 111960: 41961: 8
  33. 28Representability1954: 11959: 131960: 91961: 241962: 2
  34. 29The House at Bures1900: 11930: 11933: 11958: 201959: 221960: 111961: 261962: 161970: 41971: 11980: 12007: 1
  35. 30Elements of a Future Geometry1959: 41960: 91961: 271962: 41963: 21964: 11967: 11974: 1
  36. Part VIThe Architecture of Cohomology
  37. 31The Seminar1958: 21959: 11960: 51961: 41962: 71963: 121964: 41965: 51966: 131967: 11968: 21970: 51971: 51972: 41973: 31974: 11977: 3
  38. 32Descent1959: 21960: 81961: 131962: 51971: 3
  39. 33The Étale Site1955: 11956: 11957: 11958: 31960: 11962: 71963: 71964: 71965: 11966: 21969: 21972: 51973: 31974: 11977: 1
  40. 34A Machine for Weil1949: 11958: 21960: 41961: 11963: 11964: 41965: 111966: 201968: 21969: 21972: 11974: 11977: 10
  41. 35Collective Intelligence1961: 21962: 51963: 41964: 21965: 61966: 131970: 21972: 11974: 21977: 5
  42. 36Moscow, Absent1928: 11961: 11963: 31964: 31965: 31966: 651967: 91968: 51970: 71971: 31972: 11974: 31977: 61988: 4
  43. Part VIIThe Summit and the Breach
  44. 37At the Summit1966: 221967: 161968: 51970: 4
  45. 38Motives1964: 61967: 161968: 51969: 31970: 21992: 1
  46. 39The Standard Conjectures1967: 31968: 61969: 31974: 21992: 1
  47. 40The Price of an Institute1958: 11966: 11969: 261970: 22
  48. 41The Ethics of Departure1964: 11965: 11966: 11967: 51968: 51969: 21970: 141972: 21973: 31974: 1
  49. 42The Door Closes1966: 31967: 31968: 71969: 21970: 211971: 22014: 1
  50. Part VIIISurvival
  51. 43Survivre1963: 11968: 51970: 71971: 31972: 1
  52. 44The Living Earth1968: 11970: 31971: 41972: 6
  53. 45Against the Bomb1945: 11967: 11970: 61971: 41972: 9
  54. 46The Lecture as Assembly1971: 51972: 4
  55. 47Mathematics and Refusal1963: 21966: 11967: 11969: 41970: 71971: 121972: 131973: 41985: 2
  56. 48After the Institute1968: 21970: 51971: 21972: 101973: 131975: 1
  57. Part IXTeaching at the Margin
  58. 49Return to Montpellier1945: 11948: 21968: 21969: 61970: 51973: 221974: 21975: 21976: 21977: 21978: 101979: 11980: 21983: 11984: 52014: 62015: 12024: 2
  59. 50Beginning Again1970: 31974: 231975: 111976: 151977: 11979: 101981: 91982: 21983: 31984: 111990: 42007: 1
  60. 51The Classroom and the World1968: 31973: 11975: 11976: 81977: 101978: 161979: 11984: 21998: 12024: 12026: 3
  61. 52A Mathematics outside Fashion1966: 11970: 21977: 21978: 131979: 51980: 91981: 11984: 32017: 1
  62. 53The Hidden Workshop1973: 11975: 91977: 11978: 21981: 201982: 61983: 21984: 81991: 11995: 21996: 21997: 42017: 12019: 12020: 12021: 7
  63. 54The Long Silence1983: 111984: 22022: 7
  64. Part XReaping, Sowing, Pursuing
  65. 55A Sketch of a Programme1970: 21972: 41975: 11977: 11983: 181984: 151986: 11994: 31996: 21997: 7
  66. 56Reaping and Sowing1960: 11970: 21983: 61984: 41985: 111986: 161987: 31989: 31990: 11993: 11998: 12022: 12
  67. 57The Ethics of Credit1965: 21966: 31970: 61974: 11977: 31979: 11980: 11983: 61984: 11985: 21986: 21988: 21991: 1
  68. 58Pursuing Stacks1970: 11982: 21983: 161984: 11986: 11988: 11990: 11991: 12002: 12010: 12022: 10
  69. 59Dreams and Proofs1957: 11970: 21980: 21981: 11982: 11983: 31984: 11985: 11986: 21987: 101988: 41990: 91991: 92022: 1
  70. 60Retirement1966: 11970: 31973: 11983: 21984: 61988: 171989: 11990: 41991: 282011: 12014: 12022: 1
  71. Part XIThe Village and the Invisible Work
  72. 61The Village1942: 11970: 11982: 11984: 11985: 11987: 31988: 21990: 71991: 211992: 71994: 21995: 91997: 31999: 12004: 52010: 72014: 22017: 12023: 12025: 1
  73. 62The Dream Manuscript1968: 11987: 61988: 21990: 21991: 21992: 21999: 12024: 3
  74. 63Letters of Withdrawal1990: 81991: 41995: 22010: 172017: 12023: 1
  75. 64The Unpublished Archive1949: 11987: 11990: 21991: 41992: 101993: 71994: 41995: 41996: 61997: 41998: 61999: 122004: 12010: 32012: 12017: 12023: 22024: 2
  76. 65The Last Boundary1965: 11990: 11991: 11992: 11995: 11999: 102004: 82010: 152014: 42023: 1
  77. 66Saint-Girons, 20141928: 11970: 21991: 21992: 11993: 11999: 12010: 32014: 112017: 12023: 2
  78. Part XIIAfter the Life
  79. 67The Papers Return1949: 21987: 21988: 11990: 21991: 21992: 71993: 41994: 21995: 11997: 21999: 12010: 12014: 32016: 12017: 42022: 12023: 52024: 32025: 42026: 1
  80. 68Montpellier Opens the Boxes1949: 11970: 11973: 41981: 11983: 11984: 21986: 11990: 21991: 41995: 12010: 12016: 12017: 22024: 12025: 32026: 4
  81. 69Mathematics after Grothendieck1970: 11975: 11982: 11983: 21997: 22002: 12012: 12014: 12017: 12021: 12025: 12026: 1
  82. 70The Politics of a Legacy2010: 32014: 12021: 12022: 22023: 12024: 12026: 1
  83. 71The Biographer’s Limit1973: 11984: 11990: 21991: 21995: 11999: 12010: 22014: 1
  84. 72The Rising Sea1949: 11973: 11990: 21991: 21995: 12010: 42014: 22017: 22022: 12023: 12024: 12025: 22026: 3

The Parts, their chapters and sections

Part I

Before Belonging

6Stateless

Part II

Schooling in Exile

7Flight

The regions and départements of France.The département of Ariège in France.The Camp du Vernet, Ariège: aerial photograph, 1945.

8The Camp

Carved rock at the site of the Rieucros camp, Mende (photographed 2008).Street map of Mende.Mende, Lozère, seen from the Mont Mimat (photographed 2006).The Gurs internment camp, around 1939.Gurs in the arrondissement of Oloron-Sainte-Marie, Pyrénées-Atlantiques.

9Le Chambon

The town hall of Le Chambon-sur-Lignon (photographed 2010).

10Lessons in Hiding

11A Child of War

The Drancy internment camp, August 1941.Auschwitz I, the main camp (photographed 2010).

Part III

Learning from First Principles

13Montpellier

The medical school of Montpellier, on an early postcard.

14The Measure of Volume

15The Solitary Student

16Parisian Thresholds

Henri Cartan, 1968.Jean Leray at Oberwolfach, 1961.Jean Dieudonné, 1970.The entrance of the École normale supérieure, Paris (photographed 2013).Jean-Pierre Serre, Lille, October 2003.

17Nancy

Roger Godement, 1984.The Place Stanislas, Nancy (photographed 2013).The University of Nancy (photographed 2006).

18The First Harvest

Part IV

A Language Begins

19São Paulo

The campus of the University of São Paulo (photographed 2016).

20Kansas

The main campus of the University of Kansas, Lawrence (photographed 2007).

21The Homological Turn

Saunders Mac Lane (left) and Samuel Eilenberg at the Isle of Thorns meeting on category theory, 1992.

22The Language of Functors

23Riemann–Roch Recast

Armand Borel, Berkeley, 1975.The integers as a Grothendieck group: the sum (−2) + 1 = −1.Friedrich Hirzebruch at Berkeley, 1973.

24Toward Geometry

The Togliatti surface.The Tschirnhausen cubic.Bézout’s theorem: two plane curves and their points of intersection.The Riemann surface of the logarithm.

Part V

The Relative World

25A New Foundation

26The Scheme

27The Relative View

28Representability

29The House at Bures

The town hall of Bures-sur-Yvette (photographed 2009).

30Elements of a Future Geometry

Part VI

The Architecture of Cohomology

31The Seminar

Jean-Louis Verdier (right) with Emma Previato, Oberwolfach, 1984.Luc Illusie lecturing at the IHÉS, 2014 (still from a video).

32Descent

The Möbius strip as a fibre bundle.The connection form of a principal bundle as a projection.

33The Étale Site

34A Machine for Weil

The elliptic curve y² = x³ − x.Homology cycles on a torus.

35Collective Intelligence

Jacques Tits, Oslo, May 2008.Barry Mazur, Berkeley, April 1992.Michel Demazure, Bures-sur-Yvette, 2007.Pierre Deligne, October 2005.Pierre Cartier, Oberwolfach, 2009.

36Moscow, Absent

Soviet stamp for the International Congress of Mathematicians, Moscow, 1966.Moscow State University from the air (photographed 2015).The obverse of the Fields Medal.

Part VII

The Summit and the Breach

38Motives

A catalogue of real elliptic curves.

39The Standard Conjectures

40The Price of an Institute

41The Ethics of Departure

Demonstrators in the Place du Capitole, Toulouse, June 1968.

42The Door Closes

Part VIII

Survival

44The Living Earth

Demonstration against nuclear power, Bonn, 14 October 1979.

46The Lecture as Assembly

47Mathematics and Refusal

48After the Institute

Part IX

Teaching at the Margin

50Beginning Again

A Möbius band cut once along its length.

51The Classroom and the World

The entrance of the Université Montpellier 2 (photographed 2008).

53The Hidden Workshop

The hyperelliptic curve y² = x⁴ − x² + 1.

Part X

Reaping, Sowing, Pursuing

56Reaping and Sowing

57The Ethics of Credit

58Pursuing Stacks

59Dreams and Proofs

60Retirement

The hamlet of Ussau, Montégut-en-Couserans, Ariège (photographed 2011).

Part XI

The Village and the Invisible Work

Part XII

After the Life

71The Biographer’s Limit

72The Rising Sea