Paul A. Smith
Encyclopedia
Paul Althaus Smith was an American
mathematician
. His name occurs in two significant conjectures in geometric topology
: the Smith conjecture
, which is now a theorem, and the Hilbert-Smith conjecture, still open . Smith theory is a theory about homeomorphism
s of finite order of manifold
s, particularly sphere
s.
Smith was a student of Solomon Lefschetz
at the University of Kansas
, moving to Princeton University
with Lefschetz in the mid-1920s. He finished his doctorate at Princeton, in 1926. His PhD thesis was published in the Annals of Mathematics
that same year.
He also worked with George David Birkhoff
, with whom he wrote a 1928 paper in ergodic theory
, entitled Structure analysis of surface transformations, which appeared in the Journal des Mathématiques.
He subsequently became a professor at Columbia University
and at the Barnard College
.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
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....
. His name occurs in two significant conjectures in geometric topology
Geometric topology
In mathematics, geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another.- Topics :...
: the Smith conjecture
Smith conjecture
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....
, which is now a theorem, and the Hilbert-Smith conjecture, still open . Smith theory is a theory about homeomorphism
Homeomorphism
In the mathematical field of topology, a homeomorphism or topological isomorphism or bicontinuous function is a continuous function between topological spaces that has a continuous inverse function. Homeomorphisms are the isomorphisms in the category of topological spaces—that is, they are...
s of finite order of manifold
Manifold
In mathematics , a manifold is a topological space that on a small enough scale resembles the Euclidean space of a specific dimension, called the dimension of the manifold....
s, particularly sphere
Sphere
A sphere is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle in two dimensions, a perfect sphere is completely symmetrical around its center, with all points on the surface lying the same distance r from the center point...
s.
Smith was a student of Solomon Lefschetz
Solomon Lefschetz
Solomon Lefschetz was an American mathematician who did fundamental work on algebraic topology, its applications to algebraic geometry, and the theory of non-linear ordinary differential equations.-Life:...
at the University of Kansas
University of Kansas
The University of Kansas is a public research university and the largest university in the state of Kansas. KU campuses are located in Lawrence, Wichita, Overland Park, and Kansas City, Kansas with the main campus being located in Lawrence on Mount Oread, the highest point in Lawrence. The...
, moving to 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....
with Lefschetz in the mid-1920s. He finished his doctorate at Princeton, in 1926. His PhD thesis was published in the Annals of Mathematics
Annals of Mathematics
The Annals of Mathematics is a bimonthly mathematical journal published by Princeton University and the Institute for Advanced Study. It ranks amongst the most prestigious mathematics journals in the world by criteria such as impact factor.-History:The journal began as The Analyst in 1874 and was...
that same year.
He also worked with George David Birkhoff
George David Birkhoff
-External links:* − from National Academies Press, by Oswald Veblen....
, with whom he wrote a 1928 paper in ergodic theory
Ergodic theory
Ergodic theory is a branch of mathematics that studies dynamical systems with an invariant measure and related problems. Its initial development was motivated by problems of statistical physics....
, entitled Structure analysis of surface transformations, which appeared in the Journal des Mathématiques.
He subsequently became a professor at Columbia University
Columbia University
Columbia University in the City of New York is a private, Ivy League university in Manhattan, New York City. Columbia is the oldest institution of higher learning in the state of New York, the fifth oldest in the United States, and one of the country's nine Colonial Colleges founded before the...
and at the Barnard College
Barnard College
Barnard College is a private women's liberal arts college and a member of the Seven Sisters. Founded in 1889, Barnard has been affiliated with Columbia University since 1900. The campus stretches along Broadway between 116th and 120th Streets in the Morningside Heights neighborhood in the borough...
.
External links
- Approximation of curves and surfaces by algebraic curves and surfaces, Annals of Mathematics, 2nd Ser., Vol. 27, No. 3 (Mar., 1926), pp. 224–244.
- Abstract of the New York Times description of his death