John Mather
Encyclopedia
John Norman Mather is a mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

 at Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....

 known for his work on singularity theory
Singularity theory
-The notion of singularity:In mathematics, singularity theory is the study of the failure of manifold structure. A loop of string can serve as an example of a one-dimensional manifold, if one neglects its width. What is meant by a singularity can be seen by dropping it on the floor...

 and Hamiltonian dynamics. He is descended from Atherton Mather, a cousin of Cotton Mather
Cotton Mather
Cotton Mather, FRS was a socially and politically influential New England Puritan minister, prolific author and pamphleteer; he is often remembered for his role in the Salem witch trials...

.

His early work dealt with the stability of smooth mappings
Smooth function
In mathematical analysis, a differentiability class is a classification of functions according to the properties of their derivatives. Higher order differentiability classes correspond to the existence of more derivatives. Functions that have derivatives of all orders are called smooth.Most of...

 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 diffeomorphism
Diffeomorphism
In mathematics, a diffeomorphism is an isomorphism in the category of smooth manifolds. It is an invertible function that maps one differentiable manifold to another, such that both the function and its inverse are smooth.- Definition :...

s of the source and target (i.e. infinitely differentiable coordinate changes). He also proved the conjecture of the French topologist René Thom
René Thom
René Frédéric Thom was a French mathematician. He made his reputation as a topologist, moving on to aspects of what would be called singularity theory; he became world-famous among the wider academic community and the educated general public for one aspect of this latter interest, his work as...

 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
Hassler Whitney
Hassler Whitney was an American mathematician. He was one of the founders of singularity theory, and did foundational work in manifolds, embeddings, immersions, and characteristic classes.-Work:...

 topology. His notes on the topic of topological stability are still a standard reference on the topic of topologically stratified space
Topologically stratified space
In topology, a branch of mathematics, a topologically stratified space is a space X that has been decomposed into pieces called strata; these strata are topological manifolds and are required to fit together in a certain way...

s.

He is a member of the National Academy of Sciences
United States National Academy of Sciences
The National Academy of Sciences is a corporation in the United States whose members serve pro bono as "advisers to the nation on science, engineering, and medicine." As a national academy, new members of the organization are elected annually by current members, based on their distinguished and...

 and received the John J. Carty Award of the National Academy of Sciences in 1978 and the George David Birkhoff Prize in Applied Mathematics in 2003. He also received the Brazilian Order of Scientific Merit
Brazilian Order of Scientific Merit
The National Order of Scientific Merit is an honor bestowed upon Brazilian and foreign personalities recognized for their scientific and technical contributions to the cause and development of science in Brazil.-Biology:* Marcelo Hermes-Lima* Jorge Curi...

in 2000.

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