亚历山大·格罗滕迪克

生活

生活的宇宙

生活的宇宙：无国籍、战争、迁徙、机构、友谊、冲突、社会运动、退隐，以及身后留下的档案。序言

十二部中的一生

各章按人生的先后排列。每章旁边是它的正文所提到的年份：每个年份一道刻线，出现得越多，刻线越长。

各章正文所提到的年份

各部、各章与各节

第 I 部

归属之前

1名字之前Before the Name

Hamburg within the German Empire of 1871.

2没有边界的家A House without Borders

3柏林，1928Berlin, 1928

Stolperstein for Alexander Grothendieck, Brunnenstraße 165, Berlin-Mitte (photographed 2017).

Map of Berlin-Mitte.

Stolperstein for Johanna (Hanka) Grothendieck, Brunnenstraße 165, Berlin-Mitte (photographed 2017).

4缺席的父亲The Absent Father

Stolperstein for Alexander Schapiro, Brunnenstraße 165, Berlin-Mitte (photographed 2017).

5南下之路The Road South

6无国籍Stateless

第 II 部

流亡中的学业

7出逃Flight

The regions and départements of France.

The département of Ariège in France.

The Camp du Vernet, Ariège: aerial photograph, 1945.

8拘留营The 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.

9勒尚邦Le Chambon

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

10藏身中的功课Lessons in Hiding

11战争中的孩子A Child of War

The Drancy internment camp, August 1941.

Auschwitz I, the main camp (photographed 2010).

12没有家园的解放Liberation without Home

第 III 部

从第一原理学起

13蒙彼利埃Montpellier

The medical school of Montpellier, on an early postcard.

14体积的测度The Measure of Volume

15孤独的学生The Solitary Student

16巴黎的门槛Parisian 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.

17南锡Nancy

Roger Godement, 1984.

The Place Stanislas, Nancy (photographed 2013).

The University of Nancy (photographed 2006).

18最初的收获The First Harvest

第 IV 部

一种语言的开端

19圣保罗São Paulo

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

20堪萨斯Kansas

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

21同调的转向The Homological Turn

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

22函子的语言The Language of Functors

23重铸 Riemann–RochRiemann–Roch Recast

Armand Borel, Berkeley, 1975.

The integers as a Grothendieck group: the sum (−2) + 1 = −1.

Friedrich Hirzebruch at Berkeley, 1973.

24走向几何Toward Geometry

The Togliatti surface.

The Tschirnhausen cubic.

Bézout’s theorem: two plane curves and their points of intersection.

The Riemann surface of the logarithm.

第 V 部

相对的世界

25新的基础A New Foundation

26概形The Scheme

27相对的观点The Relative View

28可表性Representability

29Bures 的房子The House at Bures

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

30一门未来几何的原理Elements of a Future Geometry

第 VI 部

上同调的建筑

31讨论班The Seminar

Jean-Louis Verdier (right) with Emma Previato, Oberwolfach, 1984.

Luc Illusie lecturing at the IHÉS, 2014 (still from a video).

32下降Descent

The Möbius strip as a fibre bundle.

The connection form of a principal bundle as a projection.

33平展景The Étale Site

34为 Weil 而造的机器A Machine for Weil

The elliptic curve y² = x³ − x.

Homology cycles on a torus.

35集体的智慧Collective 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.

36莫斯科，缺席Moscow, 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.

第 VII 部

顶峰与决裂

37在顶峰At the Summit

Stephen Smale, 2008.

Michael Atiyah at a symposium in honour of Shiing-Shen Chern, Berkeley, April 1996.

Composite numbers arranged as rectangles; the primes cannot be.

Lars Hörmander, Tokyo, 1969.

René Thom, Nice, 1970.

38动机Motives

A catalogue of real elliptic curves.

39标准猜想The Standard Conjectures

40一所研究所的代价The Price of an Institute

41离去的伦理The Ethics of Departure

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

42门关上了The Door Closes

第 VIII 部

生存

43SurvivreSurvivre

The main building of Bielefeld University (photographed 2012).

44有生命的地球The Living Earth

Demonstration against nuclear power, Bonn, 14 October 1979.

45反对核弹Against the Bomb

South Vietnamese troops airlifted by U.S. Army helicopters near Khâm Đức, July 1970.

46作为集会的讲座The Lecture as Assembly

47数学与拒绝Mathematics and Refusal

48研究所之后After the Institute

第 IX 部

边缘处的教学

49回到蒙彼利埃Return to Montpellier

The Place de la Comédie, Montpellier (photographed 2008).

50重新开始Beginning Again

A Möbius band cut once along its length.

51课堂与世界The Classroom and the World

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

52潮流之外的数学A Mathematics outside Fashion

The sheets of a covering space.

53隐藏的工作坊The Hidden Workshop

The hyperelliptic curve y² = x⁴ − x² + 1.

54漫长的沉默The Long Silence

第 X 部

收获、播种、追寻

55一份纲领的概要A Sketch of a Programme

The headquarters of the CNRS, rue Michel-Ange, Paris (photographed 2018).

56收获与播种Reaping and Sowing

57功劳的伦理The Ethics of Credit

58Pursuing StacksPursuing Stacks

59梦与证明Dreams and Proofs

60退休Retirement

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

第 XI 部

村庄与看不见的工作

61村庄The Village

62梦的手稿The Dream Manuscript

Lasserre, Ariège (photographed 2023).

63退隐的书信Letters of Withdrawal

Saint-Girons seen from the Cap du Garrié (photographed 2024).

64未出版的档案The Unpublished Archive

65最后的边界The Last Boundary

66圣吉龙，2014Saint-Girons, 2014

Saint-Girons and the Sourroque mountain (photographed 2009).

Alexander Grothendieck’s grave, Lasserre (photographed 2025).

第 XII 部

身后

67文稿归来The Papers Return

Leila Schneps, 2011.

68蒙彼利埃打开档案箱Montpellier Opens the Boxes

69格罗滕迪克之后的数学Mathematics after Grothendieck

Nicholas Katz, Oberwolfach, 2004.

Gérard Laumon, Oberwolfach, 2004.

70一份遗产的政治The Politics of a Legacy

71传记作者的界限The Biographer’s Limit

72涨潮的海The Rising Sea