Alexander Grothendieck

The Biography

Alexander Grothendieck

The book online: the Preface and seventy-two chapters in twelve Parts, the notes beside the text, then the bibliography, the illustration credits and the index of names.

A Life in Three Universes

Vincent Liu · Lives of Mathematical Thought · 1

72chapters
12Parts
1,436pages
2,707notes
86figures
244works cited
Begin with the Preface Begin with Chapter 1

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The front cover of Alexander Grothendieck: A Life in Three Universes

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DOI 10.5281/zenodo.24013028 · All versions 10.5281/zenodo.24013027 · Licence CC BY-NC-ND 4.0

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Liu, Vincent. Alexander Grothendieck: A Life in Three Universes. Lives of Mathematical Thought · 1. First Edition, version 1.0.0. WiseMotif.ai, 2026. https://doi.org/10.5281/zenodo.24013028.

@book{liu2026grothendieck,
  author    = {Liu, Vincent},
  title     = {Alexander Grothendieck: A Life in Three Universes},
  series    = {Lives of Mathematical Thought},
  number    = {1},
  edition   = {First Edition},
  publisher = {WiseMotif.ai},
  year      = {2026},
  version   = {1.0.0},
  doi       = {10.5281/zenodo.24013028}
}

Contents

Preface

Part I

Before Belonging

  1. 1Before the Name
  2. 2A House without Borders
  3. 3Berlin, 1928
  4. 4The Absent Father
  5. 5The Road South
  6. 6Stateless

Part II

Schooling in Exile

  1. 7Flight
  2. 8The Camp
  3. 9Le Chambon
  4. 10Lessons in Hiding
  5. 11A Child of War
  6. 12Liberation without Home

Part III

Learning from First Principles

  1. 13Montpellier
  2. 14The Measure of Volume
  3. 15The Solitary Student
  4. 16Parisian Thresholds
  5. 17Nancy
  6. 18The First Harvest

Part IV

A Language Begins

  1. 19São Paulo
  2. 20Kansas
  3. 21The Homological Turn
  4. 22The Language of Functors
  5. 23Riemann–Roch Recast
  6. 24Toward Geometry

Part V

The Relative World

  1. 25A New Foundation
  2. 26The Scheme
  3. 27The Relative View
  4. 28Representability
  5. 29The House at Bures
  6. 30Elements of a Future Geometry

Part VI

The Architecture of Cohomology

  1. 31The Seminar
  2. 32Descent
  3. 33The Étale Site
  4. 34A Machine for Weil
  5. 35Collective Intelligence
  6. 36Moscow, Absent

Part VII

The Summit and the Breach

  1. 37At the Summit
  2. 38Motives
  3. 39The Standard Conjectures
  4. 40The Price of an Institute
  5. 41The Ethics of Departure
  6. 42The Door Closes

Part VIII

Survival

  1. 43Survivre
  2. 44The Living Earth
  3. 45Against the Bomb
  4. 46The Lecture as Assembly
  5. 47Mathematics and Refusal
  6. 48After the Institute

Part IX

Teaching at the Margin

  1. 49Return to Montpellier
  2. 50Beginning Again
  3. 51The Classroom and the World
  4. 52A Mathematics outside Fashion
  5. 53The Hidden Workshop
  6. 54The Long Silence

Part X

Reaping, Sowing, Pursuing

  1. 55A Sketch of a Programme
  2. 56Reaping and Sowing
  3. 57The Ethics of Credit
  4. 58Pursuing Stacks
  5. 59Dreams and Proofs
  6. 60Retirement

Part XI

The Village and the Invisible Work

  1. 61The Village
  2. 62The Dream Manuscript
  3. 63Letters of Withdrawal
  4. 64The Unpublished Archive
  5. 65The Last Boundary
  6. 66Saint-Girons, 2014

Part XII

After the Life

  1. 67The Papers Return
  2. 68Montpellier Opens the Boxes
  3. 69Mathematics after Grothendieck
  4. 70The Politics of a Legacy
  5. 71The Biographer’s Limit
  6. 72The Rising Sea

Back matter

Back matter

Bibliography

244 worksBack matter

Illustration Credits

86 figuresBack matter

Index of Names

105 names