Paul Althaus Smith (May 18, 1900June 13, 1980) was an American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

. His name occurs in two significant conjectures in

geometric topology In mathematics, geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another. History Geometric topology as an area distinct from algebraic topology may be said to have originated i ...

: the

Smith conjecture In mathematics, the Smith conjecture states that if ''f'' is a diffeomorphism of the 3-sphere of Order (group theory), finite order, then the fixed point set of ''f'' cannot be a nontrivial knot (mathematics), knot. showed that a non-trivial or ...

, which is now a theorem, and the Hilbert–Smith conjecture, which was proved in dimension 3 in 2013. ''Smith theory'' is a theory about

homeomorphism In the mathematical field of topology, a homeomorphism, topological isomorphism, or bicontinuous function is a bijective and continuous function between topological spaces that has a continuous inverse function. Homeomorphisms are the isomorphi ...

s of finite order of

manifold In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n-dimensional manifold, or ''n-manifold'' for short, is a topological space with the property that each point has a n ...

s, particularly

sphere A sphere () is a Geometry, geometrical object that is a solid geometry, three-dimensional analogue to a two-dimensional circle. A sphere is the Locus (mathematics), set of points that are all at the same distance from a given point in three ...

s. Smith was a student of

Solomon Lefschetz Solomon Lefschetz (russian: Соломо́н Ле́фшец; 3 September 1884 – 5 October 1972) was an American mathematician who did fundamental work on algebraic topology, its applications to algebraic geometry, and the theory of non-linear o ...

at the

University of Kansas The University of Kansas (KU) is a public research university with its main campus in Lawrence, Kansas, United States, and several satellite campuses, research and educational centers, medical centers, and classes across the state of Kansas. Tw ...

, moving to

Princeton University Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...

with Lefschetz in the mid-1920s. He finished his doctorate at Princeton, in 1926. His

Ph.D. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...

thesis was published in the ''

Annals of Mathematics The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as the ...

'' that same year. He also worked with

George David Birkhoff George David Birkhoff (March 21, 1884 – November 12, 1944) was an American mathematician best known for what is now called the ergodic theorem. Birkhoff was one of the most important leaders in American mathematics in his generation, and durin ...

, with whom he wrote a 1928 paper in

ergodic theory Ergodic theory (Greek: ' "work", ' "way") is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this context, statistical properties means properties which are expres ...

, entitled ''Structure analysis of surface transformations'', which appeared in the ''

Journal des Mathématiques A journal, from the Old French ''journal'' (meaning "daily"), may refer to: *Bullet journal, a method of personal organization *Diary, a record of what happened over the course of a day or other period *Daybook, also known as a general journal, a ...

''. He subsequently became a professor at

Columbia University Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manhatt ...

and at

Barnard College Barnard College of Columbia University is a private women's liberal arts college in the borough of Manhattan in New York City. It was founded in 1889 by a group of women led by young student activist Annie Nathan Meyer, who petitioned Columbia ...

. His students at Columbia included

Sherman K. Stein Sherman Kopald Stein (born August 11, 1926) is an American mathematician and an author of mathematics textbooks. He is a professor emeritus at the University of California, Davis. His writings have won the Paul R. Halmos – Lester R. Ford Award, L ...

and

Moses Richardson Moses hbo, מֹשֶׁה, Mōše; also known as Moshe or Moshe Rabbeinu (Mishnaic Hebrew: מֹשֶׁה רַבֵּינוּ, ); syr, ܡܘܫܐ, Mūše; ar, موسى, Mūsā; grc, Mωϋσῆς, Mōÿsēs () is considered the most important pro ...

. He has many academic descendants through Richardson and his student

Louis Billera Louis Joseph Billera is a Professor of Mathematics at Cornell University. Career Billera completed his B.S. at the Rensselaer Polytechnic Institute in 1964. He earned his Ph.D. from the City University of New York in 1968, under the joint supervi ...

Family

Smith was married to a Swiss–American

early music Early music generally comprises Medieval music (500–1400) and Renaissance music (1400–1600), but can also include Baroque music (1600–1750). Originating in Europe, early music is a broad musical era for the beginning of Western classical m ...

pioneer, Suzanne Bloch.

External links

Approximation of curves and surfaces by algebraic curves and surfaces

, 2nd Ser., Vol. 27, No. 3 (Mar., 1926), pp. 224–244. * * {{DEFAULTSORT:Smith, Paul Althaus 1900 births 1980 deaths 20th-century American mathematicians Topologists Columbia University faculty Princeton University alumni