Stephen Smale, born in Flint in 1930, emerged as a prominent figure in topology and dynamical systems during the mid-twentieth century. An alumnus of the University of Michigan, his career evolved from early academic struggles into an extensive record of research across institutions including the University of Chicago, Columbia University, and the University of California, Berkeley.
Academic Trajectory
Smale completed his undergraduate education at the University of Michigan in 1952 after attending Grand Blanc Community High School. Despite uneven performance during his initial graduate studies, he obtained his doctorate in 1957 under the supervision of Raoul Bott. He subsequently held positions at the Institute for Advanced Study from 1958 to 1959 and served as an instructor at the University of Chicago starting in 1956. By 1960, he joined the faculty at the University of California, Berkeley, followed by a tenure at Columbia University between 1961 and 1964.
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His primary research interests encompass differential geometry, topology, and computational theory. Notable contributions include the Palais–Smale compactness condition, the Morse–Smale system, and the Smale conjecture. In 1998, he published Smale's problems, a curated list of mathematical challenges for the twenty-first century. Additionally, his work on the Blum–Shub–Smale machine and his involvement in immersion theory, specifically regarding sphere eversion, significantly influenced global analysis and dynamical systems research.
Professional Recognition
Smale received extensive international recognition for his work in mathematics. He was awarded the Oswald Veblen Prize in Geometry in 1965 and the Fields Medal in 1966. Later honors included the Chauvenet Prize in 1988, the Grand Cross of the National Order of Scientific Merit in 1994, the National Medal of Science in 1996, and the Wolf Prize in Mathematics in 2007. He is a member of the National Academy of Sciences, the American Academy of Arts and Sciences, the Econometric Society, and the Brazilian Academy of Sciences.
Later Career and Interests
In 1995, Smale became a professor emeritus at the University of California, Berkeley. That same year, he joined the City University of Hong Kong, where he later became a Distinguished University Professor in 2009. Outside of his mathematical research, he maintained a significant private collection of mineral specimens, which was documented in the book The Smale Collection: Beauty in Natural Crystals.
Fast facts
- Born: 1930, Flint
- Citizenship: United States
- Field: Mathematics, Topology, Differential Geometry
- Doctorate: University of Michigan
- Fields Medal recipient: 1966
- Wolf Prize recipient: 2007
- Notable work: Smale's problems
- Religion: Atheism
Questions readers ask
What is the Smale conjecture?
It concerns the homotopy type of the oriented diffeomorphism group of the two-dimensional sphere and its extensions to higher dimensions.
What are Smale's problems?
They are a collection of 18 mathematical problems proposed by Smale in 1998 to guide research in the 21st century.
Achievements
- Oswald Veblen Prize in Geometry — 1965
- Fields medal — 1966
- Chauvenet Prize — 1988
- Grand Cross of the National Order of Scientific Merit — 1994
- National Medal of Science — 1996
- Notable work: Smale conjecture
- Notable work: Smale's problems
- Notable work: Morse–Smale system
- Notable work: Palais–Smale compactness condition
- Held posts at University of California, Berkeley, University of Chicago and Columbia University
