**Stephen Smale** received the Fields medal in 1966 for his work on differential geometry.

- For eight years Stephen attended elementary school about a mile from his farmhouse.
- Smale continued to work for his doctorate at the University of Michigan, Ann Arbor under R Bott's supervision and he was awarded his Ph D in 1957 for the thesis Regular Curves on Riemannian Manifolds.
- Smale was an instructor at the University of Chicago in 1956-58.
- In 1958 Smale learnt about Pontryagin's work on structurally stable vector fields and he began to apply topological methods to study the these problems.
- In 1960 Smale was appointed an associate professor of mathematics at the University of California at Berkeley, moving to a professorship at Columbia University the following year.
- Smale was awarded a Fields Medal at the International Congress at Moscow in 1966.
- One of Smale's impressive results was his work on the generalised Poincaré conjecture.
- Smale proved the higher dimensional Poincaré conjecture in 1961 for nnn at least 5.
- Smale attacked the generalised Poincaré conjecture using Morse theory.
- Another discovery of Smale's related to strange attractors.
- Smale discovered strange attractors which lead to chaotic dynamical systems.
- The nnn-body problem and electric circuit theory were among the applications that Smale framed in the language of dynamical systems.
- Having established the nature of equilibria, Smale began to think algorithms for their computation.
- While traditional approaches to the convergence theory of algorithms were local, Smale introduced a global perspective to the problems.
- Smale's recent work has been on theoetical computer science.
- Smale has received many honours for his work.
- After the fact, a Smale development seems so natural, yet no one else thought of it.
- Smale has been awarded honorary degrees by the University of Warwick (1974), Queens University, Kingston, Ontario (1987), the University of Michigan (1996), Université Pierre et Marie Curie, Paris (1997), the City University of Hong Kong (1997), Rostov State University (1999), and the University of Genoa (2004).
- In addition to the prizes mentioned above, Smale has been awarded the Chauvenet Prize by the Mathematical Association of America in 1988 for his paper On the Efficiency of Algorithms in Analysis.
- Finally we note that Smale continued as Distinguished University Professor at the City University of Hong Kong until 2001.

Born 15 July 1930, Flint, Michigan, USA.

View full biography at MacTutor

Prize Fields Medal, Origin Usa, Topology, Prize Wolf

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive