John Norman Mather (b. June 9, 1942 Los Angeles, California) is a mathematician at Princeton University known for his work on singularity theory and Hamiltonian dynamics. He is descended from Atherton Mather, a cousin of Cotton Mather.
His early work dealt with the stability of smooth mappings between smooth manifolds of dimensions n (for the source manifold N) and p (for the target manifold P). He determined the precise dimensions (n,p) for which smooth mappings are stable with respect to smooth equivalence by diffeomorphisms of the source and target (i.e. infinitely differentiable coordinate changes). He also proved the conjecture of the French topologist René Thom that under topological equivalence smooth mappings are generically stable: the subset of the space of smooth mappings between two smooth manifolds consisting of the topologically stable mappings is a dense subset in the smooth Whitney topology. His notes on the topic of topological stability are still a standard reference on the topic of topologically stratified spaces.
He is a member of the National Academy of Sciences and received the John J. Carty Award of the National Academy of Sciences in 1978[1] and the George David Birkhoff Prize in Applied Mathematics in 2003. He also received the Brazilian Order of Scientific Merit in 2000.