# Colloquium Lectures

In 1894 the American Mathematical Society, known as the The New York Mathematical Society, held its first meeting in Brooklyn under its new name. At this meeting G W Hill was elected President.

Two summer meetings were held in conjunction with the American Association for the Advancement of Science while Hill was President. The first was held in Springfield, Massachusetts in the summer of 1895, the second at Buffalo, New York in the summer of 1896.

T S Fiske writes —

The summer meeting at Buffalo in 1896 is memorable for the first colloquium of the Society. The colloquium was the idea of Professor H S White, then at Northwestern University, who had been one of the leading spirits in the organisation of the colloquium held at Evanston in connection with the World's Fair at Chicago.

The Colloquium of the American Mathematical Society was born and continues today with the lectures through the years listed below.

## Upcoming lecture:

The 2024 Colloquium Lectures will be given at the Joint Mathematics Meetings by **Terence Tao**, University of California, Los Angeles.

#### "Machine Assisted Proof"

**Abstract**

For centuries, mathematicians have relied on computers to perform calculations, to suggest conjectures, and as components of mathematical proofs. In the light of more modern tools such as interactive theorem provers, machine learning algorithms, and generative AI, we are beginning to see machines used in more creative and substantive ways in our work. In this talk we survey some historical and recent developments, and speculate on the future roles of machine assistance in mathematics.

## Past lectures:

- January 2023, Boston, MA, Camillo De Lellis, Institute for Advanced Study.
*Flows of nonsmooth vector fields.* - April 2022, Virtual, Karen E. Smith, University of Michigan.
*Understanding and Measuring Singularities in Algebraic Geometry*. - January 2021, Virtual, There were no Colloquium Lectures.
- January 2020, Denver, CO, Ingrid Daubechies, Duke University.
*Mathematical frameworks for signal and image analysis.* - January 2019, Baltimore, MD, Benedict Gross, Harvard University.
*Complex Multiplication: Past, Present, Future.* - January 2018, San Diego, CA,
**Avi Wigderson**, Institute for Advanced Study. - January 2017, Atlanta, GA,
**Carlos E. Kenig**, University of Chicago,*The Focusing Energy Critical Wave Equation*(I),*The Focusing Energy Critical Wave Equation: The Radial Case in 3 Space Dimensions*(II), The*Focusing Energy Critical Wave Equation: The Non-Radial Case*(III). - January 2016, Seattle, WA,
**W. Timothy Gowers**, University of Cambridge, UK,*Quasirandom Sets, Quasirandom Graphs, and Applications*(I);*Arithmetic Progressions of Length 4*,*Quadratic Fourier Analysis, and 3-Uniform Hypergraphs*(II); and*Fourier Analysis on General Finite Groups*(III)*.* - January 2015, San Antonio, TX,
**Michael Hopkins**, Harvard University,*Algebraic Topology: New and Old Directions*(I),*The Kervaire Invariant Problem*(II), and*Chern-Weil Theory and Abstract Homotopy Theory*(III) - January 2014, Baltimore, MD,
**Dusa McDuff**, Barnard College, Columbia University,*Symplectic Topology Today: Recent results and open questions*(I),*Symplectic Topology Today: Embedding questions: obstructions and constructions*(II), and*Symplectic Topology Today: Embedding ellipsoids and Fibonacci numbers*(III). - January 2013, San Diego, CA,
**Alice Guionnet**, Ecole Normale Supérieure de Lyon,*Free Probability and Random Matrices* - January 2012, Boston, MA,
**Edward Frenkel**, University of California, Berkeley,*Langlands program, trace formulas, and their geometrization* - January 2011, New Orleans, LA,
**Alexander Lubotzky**, The Hebrew University of Jerusalem,*Expander graphs in pure and applied mathematics* - January 2010, San Francisco, CA,
**Richard P. Stanley**, M. I. T.,*Permutations: 1) Increasing and decreasing subsequences; 2) Alternating permutations; 3) Reduced decompositions.* - January 2009, Washington, DC,
**Gregory Margulis**, Yale University,*Homogenous dynamics and number theory* - January 2008, San Diego, CA,
**Wendelin Werner**, University of Paris-Sud,*Random conformally invariant pictures* - January 2007, New Orleans, LA,
**Andrei Okounkov**, Princeton University,*Limit shapes, real and imagined.* - January 2006, San Antonio, TX,
**Hendrik W. Lenstra, Jr.**, Universiteit Leiden,*Entangled radicals.* - January 2005, Atlanta, GA,
**Robert K. Lazarsfeld**, University of Michigan, Ann Arbor,*How polynomials vanish: Singularities, integrals, and ideals*. - January 2004, Phoenix, AZ,
**Sun-Yung Alice Chang**, Princeton University,*Conformal invariants and partial differential equations*. - January 2003, Baltimore, MD,
**Peter Sarnak**, Courant Institute and Princeton University,*Spectra of hyperbolic surfaces and applications*. - January 2002, San Diego, CA,
**Lawrence Craig Evans**, University of California, Berkeley,*Entropy methods for partial differential equations*. - January 2001, New Orleans, LA,
**János Kollár**, Princeton University,*Large rationally connected varieties*. - January 2000, Washington, DC,
**Curtis T. McMullen**, Harvard University,*Riemann surfaces in dynamics, topology, and arithmetic*. - January 1999, San Antonio, TX,
**Helmut H. Hofer**, Courant Institute, New York University,*Symplectic geometry from a dynamical systems point of view*. - January 1998, Baltimore, MD,
**Gian-Carlo Rota**, Massachusetts Institute of Technology,*Introduction to geometric probability*;*Invariant theory old and new;*and*Combinatorial snapshots.* - January 1997, San Diego, CA,
**Daniel W. Stroock**, Massachusetts Institute of Technology,*Analysis on spaces of paths*. - January 1996, Orlando, FL,
**Andrew J. Wiles**, Princeton University,*Modular forms, elliptic curves and Galois representations*. - January 1995, San Francisco, CA,
**Clifford H. Taubes**, Harvard University,*Mysteries in three and four dimensions*. - January 1994, Cincinnati, OH,
**Jean Bourgain**, IHES and the University of Illinois, Urbana-Champaign,*Harmonic analysis and nonlinear evolution equations*. - August 1993, Vancouver, British Columbia, Canada,
**Sergiu Klainerman**, Princeton University,*On the regularity properties of gauge theories in Minkowski space-time*. - January 1993, San Antonio, TX,
**Luis A. Caffarelli**, Institute for Advanced Study,*Nonlinear differential equations and Lagrangian coordinates*. - January 1992, Baltimore, MD,
**Robert P. Langlands**, Institute for Advanced Study,*Automorphic forms and Hasse-Wiel zeta-functions**and Finite models for percolation*. - January 1991, San Francisco, CA,
**Robert D. MacPherson**, Massachusetts Institute of Technology,*Intersection homology and perverse sheaves*. - January 1990, Louisville, KY,
**Shlomo Sternberg**, Harvard University,*Some thoughts on the interaction between group theory and physics*. - August 1989, Boulder, CO,
**William P. Thurston**, Princeton University,*Geometry, groups, and self-similar tilings*. - January 1989, Phoenix, AZ,
**Nicholas Katz**, Princeton University,*Exponential sums and differential equations*. - January 1988, Atlanta, GA,
**Victor W. Guillemin**, Massachusetts Institute of Technology,*Spectral properties of Riemannian manifolds*. - August 1987, Salt Lake City, UT,
**Edward Witten**, Princeton University,*Mathematical applications of quantum field theory*. - January 1987, San Antonio, TX,
**Peter D. Lax**, Courant Institute,*Uses of the non-Euclidean wave equation*. - January 1986, New Orleans, LA,
**Shing-Tung Yau**, University of California, San Diego,*Nonlinear analysis*. - August 1985, Laramie, WY,
**Karen K. Uhlenbeck**, University of Chicago,*Mathematical gauge field theory*. - January 1985, Anaheim, CA,
**Daniel Gorenstein**, Rutgers University,*The classification of the finite simple groups*. - August 1984, Eugene, OR,
**Paul H. Rabinowitz**, University of Wisconsin, Madison,*Minimax methods in critical point theory and applications to differential equations*. - January 1984, Louisville, KY,
**Barry Mazur**, Harvard University,*On the arithmetic of curves*. - August 1983, Albany, NY,
**Bertram Kostant,**Massachusetts Institute of Technology,*On the Coxeter element and the structure of the exceptional Lie groups*. - January 1983, Denver, CO,
**Charles L. Fefferman**, Princeton University,*The uncertainty principle*. - August 1982, Toronto, Ontario, Canada,
**Morris W. Hirsch**, University of California, Berkeley,*Convergence in ordinary and partial differential equations*. - January 1982, Cincinnati, OH,
**Dennis Sullivan**, CUNY, Graduate School and University Center,*Geometry, iteration, and group theory*. - August 1981, Pittsburgh, PA,
**Serge Lang**, Yale University,*Units and class numbers in algebraic geometry and number theory*. - January 1981, San Francisco, CA,
**Mark Kac**, Rockefeller University,*Some mathematical problems suggested by questions in physics*. - August 1980, Ann Arbor, MI,
**Julia Bowman Robinson**, University of California, Berkeley,*Between logic and arithmetic*. - January 1980, San Antonio, TX,
**Wolfgang M. Schmidt**, University of Colorado, Boulder,*Various methods in number theory*. - August 1979, Duluth, MN,
**George Daniel Mostow**, Yale University,*Discrete subgroups of Lie groups*. - January 1979, Biloxi, MS,
**Philip A. Griffiths**, Harvard University,*Complex analysis and algebraic geometry*. - January 1978, Atlanta, GA,
**Hyman Bass**, Columbia University,*Algebraic K-theory*. - August 1977, Seattle, WA,
**Herbert Federer**, Brown University,*Geometric measure theory*. - January 1977, St. Louis, MO,
**William Browder**, Princeton University,*Differential topology of higher dimensional manifolds.* - August 1976, Toronto, Ontario, Canada,
**Jürgen K. Moser**, Courant Institute,*Recent progress in dynamical systems*. - January 1976, San Antonio, TX,
**I. M. Singer**, Massachusetts Institute of Technology,*Connections between analysis, geometry and topology*. - August 1975, Kalamazoo, MI,
**Elias M. Stein**, Princeton University,*Singular integrals, old and new*. - August 1975, Kalamazoo, MI,
**Ellis R. Kolchin**, Columbia University,*Differential algebraic groups*. - January 1975, Washington, DC,
**H. Jerome Keisler**, University of Wisconsin, Madison,*New directions in model theory*. - January 1974, San Francisco, CA,
**John G. Thompson,**University of Cambridge,*Finite simple groups*. - January 1974, San Francisco, CA,
**Louis Nirenberg**, Courant Institute,*Selected topics in partial differential equations*. - August 1973, Missoula, MT,
**Errett A. Bishop**, University of California, San Diego,*Schizophrenia in contemporary mathematics.* - August 1973, Missoula, MT,
**Felix E. Browder**, University of Chicago,*Nonlinear functional analysis and its applications to nonlinear partial differential and integral equations.* - January, 1973, Dallas, TX,
**Michael F. Atiyah**, Institute for Advanced Study,*The index of elliptic operators*. - August 29-September 1, 1972, Hanover, NH,
**John T. Tate**, Harvard University,*The arithmetic of elliptic curves.* - August 29-September 1, 1972, Hanover, NH,
**Stephen Smale**, University of California, Berkeley,*Applications of global analysis to biology, economics, electrical circuits, and celestial mechanics*. - August 31-September 3, 1971, University Park, PA,
**Armand Borel**, Institute for Advanced Study,*Algebraic groups and arithmetic groups*. - August 31-September 3, 1971, University Park, PA,
**Lipman Bers**, Columbia University,*Uniformization, moduli, and Kleinian groups*. - August 1970, Laramie, WY,
**R. H. Bing**, University of Wisconsin, Madison,*Topology of 3-manifolds*. - August 1969, Eugene, OR,
**Harish-Chandra**, Institute for Advanced Study,*Harmonic analysis of semisimple Lie groups*. - August 1969, Eugene, OR,
**Raoul H. Bott**, Harvard University,*On the periodicity theorem of the classical groups**and its applications*. - August 1968, Madison, WI,
**John W. Milnor**, Princeton University and U.C.L.A,*Uses of the fundamental group*. - August 1968, Madison, WI,
**Donald C. Spencer**, Stanford University,*Overdetermined systems of partial differential equations*. - August 29-September 1, 1967, Toronto, Ontario, Canada,
**Samuel Eilenberg**, Columbia University,*Universal algebras and the theory of automata*. - August 31-September 3, 1965, Ithaca, NY,
**Alberto P. Calderón**, University of Chicago,*Singular integrals*. - August 1964, Amherst, MA,
**Charles Bradford Morrey, Jr**., University of California, Berkeley,*Multiple integrals in the calculus of variations*. - August 1963, Boulder, CO,
**Saunders Mac Lane**, University of Chicago,*Categorical algebra*. - August 29-September 1, 1961, Stillwater, OK,
**George W. Mackey**, Harvard University,*Infinite dimensional group representatives*. - August 30-September 2, 1960, East Lansing, MI,
**Shiing-Shen Chern**, University of California, Berkeley,*Geometrical structures on manifolds*. - September 1959, Salt Lake City, UT,
**J. L. Doob**, University of Illinois, Urbana-Champaign,*The first boundary value problem*. - August 1957, University Park, PA,
**N. E. Steenrod**, Princeton University,*Cohomology operations*. - August 1956, Seattle, WA,
**Salomon Bochner**, Princeton University,*Harmonic analysis and probability*. - August 31- September 2, 1955, Ann Arbor, MI,
**Nathan Jacobson**, Yale University,*Jordan algebras*. - August 31- September 5, 1953, Kingston, Ontario, Canada,
**Antoni Zygmund**, University of Chicago,*On the existence and properties of certain singular integrals*. - September 1952, East Lansing, MI,
**Alfred Tarski**, University of California, Berkeley,*Arithmetical classes and types of algebraic systems*. - September 1951, Minneapolis, MN,
**Deane Montgomery**, Institute for Advanced Study,*Topological transformation groups*. - August 30-September 2, 1949, Boulder, CO,
**G. A. Hedlund**, Yale University,*Topological dynamics*. - September 1948, Madison, WI,
**Richard Brauer**, University of Toronto,*Representation of groups and rings*. - September 1947, New Haven, CT,
**Oscar Zariski**, Harvard University,*Abstract algebraic geometry*. - August 1946, Ithaca, NY,
**Hassler Whitney,**Harvard University,*Topology of smooth manifolds*. - November 1945, Chicago, IL,
**Tibor Radó,**Ohio State University,*Length and area*. - August 1944, Wellesley, MA,
**Einar Hille**, Yale University,*Selected topics in the theory of semi-groups*. - September 1943, New Brunswick, NJ,
**Edward J. McShane**, University of Virginia,*Existence theorems in the calculus of variations*. - September 1942, Poughkeepsie, NY,
**Raymond L. Wilder,**University of Michigan, Ann Arbor,*Topology of manifolds*. - September 1941, Chicago, IL,
**Øystein Ore,**Yale University,*Mathematical relations and structures.* - September 1940, Hanover, NH,
**Gordon T. Whyburn**, University of Virginia,*Analytic topology.* - September 1939, Madison, WI,
**Marshall H. Stone**, Harvard University,*Convex bodies*. - September 1939, Madison, WI,
**A. Adrian Albert,**University of Chicago,*Structure of algebras*. - September 1937, State College, PA,
**John von Neumann**, Institute for Advanced Study,*Continuous geometry*. - September 1936, Cambridge, MA,
**Edward W. Chittenden,**University of Iowa,*Topics in general analysis*. - September 1935, Ann Arbor, MI,
**Harry S. Vandiver**, University of Texas,*Fermat's last theorem and related topics in number theory*. - September 1934, Williamstown, MA,
**Raymond E. A. C. Paley**, Trinity College, Cambridge University (deceased 1933) and**Norbert Wiener**, Massachusetts Institute of Technology,*Fourier transforms in the complex domain*. - August 30-September 2, 1932, Los Angeles, CA,
**Joseph F. Ritt**, Columbia University,*Differential equations from the algebraic standpoint.* - September 1931, Minneapolis, MN,
**Marston Morse**, Harvard University,*The calculus of variations in the large*. - September 1930, Providence, RI,
**Solomon Lefschetz,**Princeton University,*Topology*. - August 1929, Boulder, CO,
**R. L. (Robert Lee) Moore**, University of Texas,*Foundations of point set theory*. - September 1928, Amherst, MA,
**Arthur B. Coble,**University of Illinois, Urbana-Champaign,*The determination of the tritangent planes of the space sextic of genus four*. - September 1927, Madison, WI,
**Anna J. Pell Wheeler**, Bryn Mawr College,*The theory of quadratic forms in infinitely many variables and applications*. - September 1927, Madison, WI,
**E. T. (Eric Temple) Bell**, California Institute of Technology,*Algebraic arithmetic*. - September 1925, Ithaca, NY,
**Dunham Jackson**, University of Minnesota, Minneapolis, The*Theory of Approximations*. - September 1925, Ithaca, NY,
**Luther P. Eisenhart**, Princeton University,*Non-Riemannian geometry*. - September 1920, Chicago, IL,
**F. R. (Forest Ray) Moulton**, University of Chicago,*Topics from the theory of functions of infinitely many variables*. - September 1920, Chicago, IL,
**G. D. Birkhoff,**Harvard University,*Dynamical systems*. - September 1916, Cambridge, MA,
**Oswald Veblen,**Princeton University,*Analysis situs*. - September 1916, Cambridge, MA,
**Griffith C. Evans,**Rice University,*Functionals and their applications, selected topics including integral equations*. - September 1913, Madison, WI,
**William F. Osgood,**Harvard University,*Topics in the theory of functions of several complex variables*. - September 1913, Madison, WI,
**Leonard E. Dickson**, University of Chicago,*On invariants and the theory of numbers*. - September 1909, Princeton, NJ,
**Edward Kasner,**Columbia University,*Differential-geometric aspects of dynamics*. - September 1909, Princeton, NJ,
**Gilbert A. Bliss**, University of Chicago,*Fundamental existence theorems*. - September 1906, New Haven, CT,
**Max Mason**, Yale University,*Selected topics in the theory of boundary value problems of differential equations*. - September 1906, New Haven, CT,
**Ernest J. Wilczynski**, University of California, Berkeley,*Projective differential geometry*. - September 1906, New Haven, CT,
**Eliakim H. Moore**, University of Chicago,*On the theory of bilinear functional operations*. - September 1903, Boston, MA,
**Edward B. Van Vleck**, Wesleyan University,*Selected topics in the theory of divergent series and continued fractions.* - September 1903, Boston, MA,
**Frederick S. Woods,**Massachusetts Institute of Technology,*Forms of non-euclidean space*. - September 1903, Boston, MA,
**Henry S. White,**Northwestern University,*Linear systems of curves on algebraic surfaces*. - August 1901, Ithaca, NY,
**Ernest W. Brown**, Haverford College,*Modern methods of treating dynamical problems, and in particular the problem of three bodies.* - August 1901, Ithaca, NY,
**Oskar Bolza**, University of Chicago,*The simplest type of problems in the calculus of variations.* - August 1898, Cambridge, MA,
**Arthur G. Webster**, Clark University,*The partial differential equations of wave propagation.* - August 1898, Cambridge, MA,
**William F. Osgood,**Harvard University,*Selected topics in the theory of functions.* - September 1896, Buffalo, NY,
**Maxime Bôcher**, Harvard University,*Linear differential equations and their applications.* - September 1896, Buffalo, NY,
**James Pierpont**, Yale University,*Galois's theory of equations.*