Complexity and Computation
Professor Smale has made significant contributions in the fields of dynamical systems, geometry, econometrics, operational research, topology and the mathematical theory of computer science.
1965 M.S., Veblen Prize, American Mathematical Society
1966 Fields Medal, International Mathematical Union
1967 University of Michigan Sesquicentennial Award
1988 Chauvenet Prize, Mathematical Association of America
1989 Von Neumann Award, Society for Industrial and Applied Mathematics
1994 Class of the Grand Cross of the Brasilian National Order of Scientific Merit
1996 National Medal of Science, Washington, D. C.
Complexity and real computation (with L. Blum, F. Cucker, and M. Shub), Springer-Verlag 1998.
Finding a Horseshoe on the Beaches of Rio, Mathematical Intelligencer Vol 20, (1998) No. 1, 39-44.
Mathematical Problems for the Next Century, Mathematical Intelligencer Vol 20, (1998) No. 2, 7-15.
Some Lower Bounds for the Complexity of Continuation Methods (with J-P Dedieu) Jour of Complexity Vol 14 (1998) 454-465.
The Work of Curtis T. McMullen in Proceedings of the International Congress of Mathematicians Berlin 1998 Vol 1 Documenta Mathematica Bielefeld, Germany 1998 pp 127-132.
Finding a horseshoe on the beaches of rio, mathematical intelligencer, 1998, vol 1.
A Polynomial Time Algorithm for Diophantine Equations in One Variable, (with F. Cucker and P. Koiran) Jour. Symbolic Computation Vol 27 (1999) 21-29.
Complexity Estimates Depending on Condition and Round-off Error (with F. Cucker), Jour. of the Assoc. of Computing Machinery Vol 46 (1999) 113-184.