edited by Sir Michael Atiyah (University of Edinburgh, UK) & Daniel Iagolnitzer (CEA-Saclay, France)

Table of Contents (57k)
Preface to the First Edition (47k)
Chapter 1: Lars Valerian Ahlfors (98k)

Although the Fields Medal does not have the same public recognition as the Nobel Prizes, they share a similar intellectual standing. It is restricted to one field — that of mathematics — and an age limit of 40 has become an accepted tradition. Mathematics has in the main been interpreted as pure mathematics, and this is not so unreasonable since major contributions in some applied areas can be (and have been) recognized with Nobel Prizes.

A list of Fields Medallists and their contributions provides a bird's-eye view of mathematics over the past 60 years. It highlights the areas in which, at various times, greatest progress has been made. This volume does not pretend to be comprehensive, nor is it a historical document. On the other hand, it presents contributions from Fields Medallists and so provides a highly interesting and varied picture.

The second edition of Fields Medallists' Lectures features additional contributions from the following Medallists: Kunihiko Kodaira (1954), Richard E Borcherds (1998), William T Gowers (1998), Maxim Kontsevich (1998), Curtis T McMullen (1998) and Vladimir Voevodsky (2002).

• 1936
  • L V Ahlfors:
    • Quasiconformal Mappings, Teichmüller Spaces, and Kleinian Groups
• 1950
  • L Schwartz:
    • The Work of L Schwartz by H Bohr
    • Calcul Infinitesimal Stochastique
• 1954
  • K Kodaira:
    • Obituary: Kunihiko Kodaira
    • On Kähler Varieties of Rrestricted Type
• 1958
  • K F Roth:
    • The Work of K F Roth by H Davenport
    • Rational Approximations to Algebraic Numbers
  • R Thom:
    • The Work of R Thom by H Hopf
• 1962
  • L Hörmanjder:
    • Hörmanjder's Work on Linear Differential Operators by L Gårding
    • Looking Forward from ICM 1962
• 1966
  • M F Atiyah:
    • L'oeuvre de Michael F Atiyah by H Cartan
    • The Index of Elliptic Operators
  • S Smale:
    • Sur Les Travaux de Stephen Smale by R Thom
    • A Survey of Some Recent Developments in Differential Topology
• 1970
  • A Baker:
    • The Work of Alan Baker by P Turán
    • Effective Methods in the Theory of Numbers
    • Effective Methods in Diophantine Problems
    • Effective Methods in the Theory of Numbers/Diophantine Problems
  • S Novikov:
    • The Work of Serge Novikov by M F Atiyah
    • Rôle of Integrable Models in the Development of Mathematics
• 1974
  • D Mumford:
    • The Work of David Mumford by J Tate
    • Pattern Theory: A Unifying Perspective
• 1978
  • G A Margulis:
    • The Work of Gregory Aleksandrovitch Margulis by J Tits
    • Oppenheim Conjecture
• 1982
  • A Connes:
    • The Work of Alain Connes by H Araki
    • Brisure de Symétrie Spontanée et Géométrie du Point de vue Spectral
  • W P Thurston:
    • The Work of W Thurston by C T C Wall
• 1986
  • S K Donaldson:
    • The Work of Simon Donaldson by M F Atiyah
    • Remarks on Gauge Theory, Complex Geometry and 4-Manifold Topology
  • M H Freedman:
    • The Work of M H Freedman by J Milnor
    • Betti Number Estimates for Nilpotent Groups
• 1990
  • V F R Jones:
    • The Work of Vaughan F R Jones by J S Birman
    • A Polynomial Invariant for Knots via von Neumann Algebras
  • S Mori:
    • The Work of Shigefumi Mori by H Hironaka
    • Birational Classification of Algebraic Threefolds
  • E Witten:
    • The Work of E Witten by L D Faddeev
    • The Work of Edward Witten by M F Atiyah
    • Geometry and Quantum Field Theory
• 1994
  • J Bourgain:
    • The Work of Jean Bourgain by L Caffarelli
    • Hamiltonian Methods in Nonlinear Evolution Equations
  • P L Lions:
    • The Work of Pierre-Louis Lions by S R S Varadhan
    • On Some Recent Methods for Nonlinear Partial Differential Equations
  • J C Yoccoz:
    • Présentation de Jean-Christophe Yoccoz by A Douady
    • Recent Developments in Dynamics
  • E I Zelmanov:
    • The Work of Efim Zelmanov by W Feit
    • On the Restricted Burnside Problem
• 1998
  • R E Borcherds:
    • The Work of Richard Ewen Borcherds by P Goddard
    • What is Moonshine?
  • W T Gowers:
    • The Work of William Timothy Gowers by B Bollobás
    • A New Proof of Szemerédi's Theorem for Arithmetic Progressions of Length Four
  • M Kontsevich:
    • The Work of Maxim Kontsevich by C H Taubes
    • Formal (Non)-Commutative Symplectic Geometry
    • Comments on “Formal (Non)-Commutative Symplectic Geometry”
  • C T McMullen:
    • The Work of Curtis T McMullen by J Milnor
    • Rigidity and Inflexibility in Conformal Dynamics
• 2002
  • L Lafforgue:
    • The Work of Laurent Lafforgue by G Laumon
  • V Voevodsky:
    • The Work of Vladimir Voevodsky by C Soulé
    • Open Problems in the Motive Style Homotopy Theory, I