In mathematics, the Smith conjecture states that if f is a diffeomorphism of the 3-sphere of finite order, then the fixed point set of f cannot be a nontrivial knot. Paul A. Smith showed that a non-trivial orientation-preserving diffeomorphism of finite order with fixed points must have fixed point set equal to a circle, and asked in if the fixed point set can be knotted. Friedhelm Waldhausen proved the Smith conjecture for the special case of diffeomorphisms of order 2 (and hence any even order). The proof of the general case was described by John Morgan and Hyman Bass and depended on several major advances in 3-manifold theory, in particular the work of William Thurston on hyperbolic structures on 3-manifolds, and results by William Meeks a