John N. Mather
John N. Mather  

Mather at Oberwolfach in 2005


Born 
John Norman Mather June 9, 1942 Los Angeles, California 
Died  January 28, 2017 Princeton, New Jersey 
(aged 74)
Residence  United States 
Nationality  American 
Alma mater 
Harvard University Princeton University 
Known for 
Smooth functions Topologically stratified space AubryMather theory Mather theory 
Awards 
John J. Carty Award for the Advancement of Science (1978) National Order of Scientific Merit (Brazil) (2000) George David Birkhoff Prize (2003) Brouwer Medal (2014) 
Scientific career  
Fields  Mathematics 
Institutions 
Institut des Hautes Études Scientifiques Harvard University Princeton University 
Doctoral advisor  John Milnor 
Doctoral students 
Giovanni Forni Vadim Kaloshin 
John Norman Mather (June 9, 1942 – January 28, 2017) was a mathematician at Princeton University known for his work on singularity theory and Hamiltonian dynamics. He was descended from Atherton Mather (16631734), 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.^{[citation needed]}
In the 1970s, he switched to the field of dynamical systems. He made the following main contributions to dynamical systems that deeply influenced the field.
1. He introduced the concept of Mather spectrum and gave a characterization of Anosov diffeomorphisms.^{[1]}
2. Jointly with Richard McGehee, he gave an example of collinear fourbody problem which has initial conditions leading to solutions that blow up in finite time. This was the first result that made the Painleve conjecture plausible.^{[2]}
3. He developed a variational theory for the globally action minimizing orbits for twist maps (convex Hamiltonian systems of two degrees of freedom), along the line of the work of George David Birkhoff, Marston Morse, Gustav A. Hedlund, et al. This theory is now known as Aubry–Mather theory.^{[3]}^{[4]}
4. He developed the AubryMather theory in higher dimensions, a theory which is now called Mather theory.^{[5]}^{[6]} This theory turned out to be deeply related to the viscosity solution theory of Michael G. Crandall, PierreLouis Lions et al. for HamiltonJacobi equation. The link was revealed in the weak KAM theory of Albert Fathi.^{[7]}
Mather was one of the three editors of the Annals of Mathematics Studies series published by Princeton University Press.
He was a member of the National Academy of Sciences beginning in 1988. He received the John J. Carty Award of the National Academy of Sciences in 1978 (for pure mathematics)^{[8]} and the George David Birkhoff Prize in applied mathematics in 2003. He also received the Brazilian Order of Scientific Merit in 2000 and the Brouwer Medal from the Royal Dutch Mathematical Society in 2014.
See also
References
 ^ Mather, John N. "Characterization of Anosov diffeomorphisms." Indagationes Mathematicae (Proceedings). Vol. 71. NorthHolland, 1968.
 ^ Mather, John N., and Richard McGehee. "Solutions of the collinear four body problem which become unbounded in finite time." Dynamical systems, theory and applications. Springer Berlin Heidelberg, 1975. 573597.
 ^ Mather, John, and Giovanni Forni. "Action minimizing orbits in hamiltomian systems." Transition to chaos in classical and quantum mechanics (1994): 92186.
 ^ Bangert, Victor. "Mather sets for twist maps and geodesics on tori." Dynamics reported. Vieweg+ Teubner Verlag, 1988. 156.
 ^ Mather, John N. "Action minimizing invariant measures for positive definite Lagrangian systems", Mathematische Zeitschrift 207.1 (1991): 169207.
 ^ Mather, John N. "Variational construction of connecting orbits." Annales de l'Institut Fourier, Vol. 43. No. 5. 1993.
 ^ Fathi, Albert. "Weak KAM theorem in Lagrangian dynamics preliminary version number 10", Cambridge University Press (2008).
 ^ "John J. Carty Award for the Advancement of Science". Archived from the original on 20150228.
External links
 Mather notes on Topological Stability (on the Princeton University website, pdf file)
 John Mather bibliography on the Princeton University website (pdf file)
 John N. Mather at the Mathematics Genealogy Project
 Obituary on the Princeton University website
 1942 births
 2017 deaths
 Members of the United States National Academy of Sciences
 20thcentury American mathematicians
 21stcentury American mathematicians
 Princeton University faculty
 National Academy of Sciences laureates
 Recipients of the Great Cross of the National Order of Scientific Merit (Brazil)
 Guggenheim Fellows
 Brouwer Medalists
 Harvard University alumni
 Princeton University alumni
 Institute for Advanced Study visiting scholars
 Dynamical systems theorists
 People from Los Angeles
 Mathematicians from California