Smale's problems is a list of eighteen unsolved problems in mathematics proposed by Steve Smale in 1998[1] and republished in 1999.
[2] Smale composed this list in reply to a request from Vladimir Arnold, then vice-president of the International Mathematical Union, who asked several mathematicians to propose a list of problems for the 21st century.
Arnold's inspiration came from the list of Hilbert's problems that had been published at the beginning of the 20th century.
In other words, is the subset of all diffeomorphisms whose centralizers are trivial dense in
In later versions, Smale also listed three additional problems, "that don't seem important enough to merit a place on our main list, but it would still be nice to solve them:"[25][26]