Smale also identified the Smale horseshoe, inspiring much subsequent research. He also outlined a research program carried out by many others. Smale is also known for injecting Morse theory into mathematical economics, as well as recent explorations of various theories of computation. In 1998 he compiled a list of 18 problems in mathematics to be solved in the 21st century, known as Smale's problems. This list was compiled in the spirit of Hilbert's famous list of problems produced in 1900. In fact, Smale's list contains some of the original Hilbert problems, including the Riemann hypothesis and the second half of Hilbert's sixteenth problem, both of which are still unsolved. Other famous problems on his list include the Poincaré conjecture (now a theorem, proved by Grigori Perelman), the P = NP problem, and the Navier–Stokes equations, all of which have been designated Millennium Prize Problems by the Clay Mathematics Institute. Books Important publications * See also 5-manifold Axiom A Geometric mechanics Homotopy principle Mean value problem References External links Robion Kirby, Stephen Smale: The Mathematician Who Broke the Dimension Barrier, a book review of a biography in the Notices of the AMS. Personal websites at universities Steven Smale at the City University of Hong Kong Stephen Smale at the University of Chicago Steve Smale at the University of California, Berkeley 1930 births Living people 20th-century American mathematicians 21st-century American mathematicians American atheists American computer scientists Columbia University faculty Dynamical systems theorists Fields Medalists General equilibrium theorists Institute for Advanced Study visiting scholars Mathematical economists Members of the Brazilian Academy of Sciences Members of the United States National Academy of Sciences National Medal of Science laureates Numerical analysts People from Flint, Michigan Recipients of the Great Cross of the National Order of Scientific Merit (Brazil) Theoretical computer scientists Topologists University of California, Berkeley College of Letters and Science faculty University of Chicago faculty University of Michigan alumni Wolf Prize in Mathematics laureates Sloan Research Fellows Fellows of the Econometric Society Mathematicians from Michigan