Stephen Smale's (b 15 July 1930) youth in Flint, Michigan was fairly typical, and he really didn't stand out except possibly in chess until later in life. In college at the Univercity of Michigan he majored in mathematics, but was more interested in campus politics and travel. However, eventually Smale received his PhD from U-M in 1957, and until 1960 he taught at the University of Chicago.
In his first years an instructor, Smale proved the counter-intuitive theorem that one can turn a sphere in 3-dimensions inside out. Later Smale began to explore dynamic systems (and strange attractors) where he discovered his now famous "Smale Horseshoe." A few months later he proved the Poincaré Conjecture for dimensions greater than 4. For his work, Smale was awarded a Fields Medal at the International Congress at Moscow in 1966, and The Veblen Prize for Geometry by the American Mathematical Society also in 1966. Also, after quite some delay, he was awarded the National Medal of Science in 1996.
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. In 1964 he returned to a professorship at the Cal-Berkeley held the post for 30 years before taking early retirement and joining City University of Hong Kong as a Distinguished University Professor. He is currently working in the field of theoretical computer science and computational mathematics.
To learn more about Smale, read the excellent Stephen Smale: The Mathematician Who Broke the Dimension Barrier by Steve Batterson