Fields Medallists' Lectures

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. The medal is awarded to the best mathematicians who are 40 or younger, every four years.

A list of Fields Medallists and their contributions provides a bird's-eye view of the major developments in mathematics over the past 80 years. It highlights the areas in which, at various times, the greatest progress has been made.

The third edition of Fields Medallists' Lectures features additional contributions from: John W Milnor (1962), Enrico Bombieri (1974), Gerd Faltings (1986), Andrei Okounkov (2006), Terence Tao (2006), Cédric Villani (2010), Elon Lindenstrauss (2010), Ngô Bao Châu (2010), Stanislav Smirnov (2010).

• 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
• J W Milnor:
  • The Work of John W Milnor by H Whitney
  • Topological Manifolds and Smooth Manifolds
• 1966 M F Atiyah:
  • The Work of Michael F Atiyah by H Cartan
  • The Index of Elliptic Operators
• Paul J Cohen:
  • The Continuum Problem by A Church
• Alexander Grothendieck:
  • The Works of Alexander Grothendieck by Jean Dieudonné
• S Smale:
  • On the Works of 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 Diophantine Problems. II
  • 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 E Bombieri:
  • The Work of Enrico Bombieri by K Chandrasekharan
  • Variational Problems and Elliptic Equations
• 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
• 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
• G Faltings:
  • On Some of the Mathematical Contributions of Gerd Faltings by B Mazur
  • Neuere Entwicklungen in der Arithmetischen Algebraischen Geometrie
• 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
  • Index for Subfactors
• 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:
  • Presentation 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 Stable Homotopy Theory, I
• 2006 A Okounkov:
  • The Work of Andrei Okounkov by G Felder
• Terence Tao:
  • The Work of Terence Tao by C Fefferman
  • The Dichotomy between Structure and Randomness, Arithmetic Progressions, and the Primes
• 2010 Ngô Bao Châu:
  • The Work of Ngô Bao Châu by J Arthur
  • Endoscopy Theory of Automorphic Forms
• E Lindenstrauss:
  • The Work of Elon Lindenstrauss by H Furstenberg
  • Equidistribution in Homogeneous Spaces and Number Theory
• S Smirnov:
  • The Work of Stanislav Smirnov by H Kesten
  • Discrete Complex Analysis and Probability
• C Villani:
  • The Work of Cédric Villani by H-T Yau, Landau Damping