Elected to
- National Academy of Sciences, 1996
- American Academy of Arts and Sciences, 1996
- Honorary Membership of London Mathematical Society (one or two such awarded worldwide/year) 2011
Fellowships and Honorary Degrees
- Fellow of the American Mathematical Society- 2016
- SIAM Fellow, 2009
- Massachusetts Academy of Sciences, Fellow, 2008
- Weldon Memorial Prize, Oxford University, 2006
- Honorary Doctorate, New Jersey Institute of Technology, May 2006
- John D. and Catherine T. MacArthur Fellow, 1990-1995
- J. S. Guggenheim Fellowship, 1984-1985
- Alfred P. Sloan Fellow, 1975-1977
- N.S.F. Graduate Fellow, 1963-1967
- Woodrow Wilson Fellow (honorary), 1963-1964
Special Invited Lectures and prizes
- Swartz Prize in Theoretical and Computational Neuroscience, Soc. for Neurosci, 2016.
- Mathematical Neuroscience Prize from Israel Brain Technologies (2 worldwide, every 2 years), 2015
- Moser Prize Lecture, SIAM Annual Meeting, Snowbird 2013
- Irene McCulloch Lecturer in Science and Engineering, Distinguished Lecturer, USC, 2011
- Weldon Memorial Prize lecture, Oxford, 2008
- Von Neumann Prize/Lecture, SIAM annual meeting, Zurich, 2007
- Shih-I Pai Lecture, University of Maryland, 2006
- Distinguished Lecturer, University of California, Irvine, 2006
- Roslyn Silver Science Lecture, Barnard, 2004
- Conference in honor of my 60th birthday, Boston University, 2003
- Rainich Lectures, University of Michigan, Ann Arbor, 2003
- Wasow Memorial Lectures, University of Wisconsin, Madison, 2003
- Plenary Speaker, International Congress of Industrial and Applied Math, Australia, 2003
- Invited Speaker, International Congress of Mathematics, China, 2002
- H. Dudley Wright Prize, Harvey Mudd College, 2001
- Plenary Speaker, Annual Meeting of SIAM, San Juan, 2000
- NSF Distinguished Lecturer, Washington D.C., 2000
- Josiah Willard Gibbs Lecturer, Annual Meeting of the AMS, San Antonio, 1999
- Invited Speaker, Annual Meeting of AMS, San Diego, 1997
- Issues in Modern Biology: Distinguished Lecture Series, Los Alamos National Lab., 1995
- Plenary Speaker, SIAM Meeting on Dynamical Systems, Snowbird, 1995
- Class of '27 Lecturer, Rensselaer Polytechnic Institute, 1995
- Matthew Vassar Lecturer, Vassar College, 1994
- Distinguished Lecturer, Fields Institute, 1994
- University Lecturer, Boston University, 1993
- KAC Memorial Lectures, CNLS, Los Alamos National Lab, 1992
- Emmy Noether Lecture, AMS Annual Meeting, Baltimore 1992
- Vollmer Fries Memorial Lecture, Rensselaer Polytechnic Institute, 1991
- Plenary Speaker, Canadian Math Society Annual Meeting, 1990
- Plenary Speaker, Annual Meeting of SIAM, Chicago, 1990
- Plenary Speaker, SIAM Meeting on Dynamical Systems, Orlando, 1990
- Lecturer, R. Bowen Memorial Lectures, Berkeley, 1986
- Invited Speaker, International Congress of Mathematicians, 1983
- University Lecturer, Northeastern University, 1980