The Laureates

Copyright © Klaus Tschira Stiftung / Peter Badge

Stephen Smale

Born 15 July 1930 in Flint, Michigan (USA)

Fields Medal (1966) for his work in differential topology where he proved the generalized Poincaré conjecture in dimension n>=5.

Stephen Smale’s hometown Flint is renowned as the former production site of the U.S.’s largest car company General Motors. Smale’s father worked for GM and from the age of five Smale lived on a farm outside the city. The country elementary school where he spent eight years had just one teacher. Smale’s favourite subjects were chemistry and physics. As a student at the University of Michigan, it was after he first failed a Physics course that he turned to Mathematics (taking his Bachelor degree in 1952 and his Masters in 1953). Smale received his Ph.D. at the University of Michigan, Ann Arbor in 1957 and from 1956-58 worked as a lecturer at the University of Chicago. With the help of a postdoctoral fellowship from the National Science Foundation, he spent 1958-60 at the Institute for Advanced Study in Princeton and the Instituto de Mathematica Pura e Aplicada in Rio de Janeiro. In 1960, Smale was appointed assistant professor at the University of California, Berkeley. In 1961 he accepted an appointment at Columbia University in New York but returned to Berkeley in 1964. Since he retired from Berkeley in 1995, Smale has also been a professor at the City University of Hong Kong.

Smale was awarded the Veblen Prize for Geometry by the American Mathematical Society (1966). He has received the U.S. National Medal of Science (1996) and other awards including the Chauvenet Prize of the Mathematical Association of America ( 1988), the Von Neuman Award (1989), and the Jürgen Moser Prize (2005) from the Society for Industrial and Applied Mathematics. Smale holds seven honorary doctorates and is honorary member of the Instituto de Mathematica Pura e Aplicada Rio de Janeiro (since 1990), the Trinity Mathematical Society in Dublin (since 1991), the Moscow Mathematical Society (since 1997) and the London Mathematical Society (since 1998).

Stephen Smale is famous for his work in dynamical systems and the invention of  so-called horseshoe mapping. This method allowed him not only to solve problems from chaos theory, but also one of the great classic problems of topology, the generalized Poincaré conjecture for dimension 5 and higher. It says that every compact connected n-manifold, on which a circle can be contracted to a point, is homeomorphic to the surface of a sphere in dimension n+1 – that is, this manifold can be transformed without cutting or gluing into a spherical surface. Poincaré had formulated this conjecture for dimension 3; Smale was at able to show the generalized conjecture for dimension 5 and higher.

Later, Smale produced further significant results in the field of dynamical systems, topology, and in the calculus of variations, before turning to economics in the 1970s. There he formulated an economic equilibrium condition using methods from dynamical systems. This work led him later to the field of numerical analysis and complexity theory.

Stephen Smale is not only known for his mathematical achievements, but also for the world-class collection of minerals that he and his wife have over decades built up.