Arthur Norton Milgram (3 June 1912 – 30 January 1961) was an American mathematician. He made contributions in
functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (for example, Inner product space#Definition, inner product, Norm (mathematics ...
,
combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ...
,
differential geometry
Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, lin ...
,
topology
Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...
,
partial differential equations
In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives.
The function is often thought of as an "unknown" that solves the equation, similar to how ...
, and
Galois theory
In mathematics, Galois theory, originally introduced by Évariste Galois, provides a connection between field (mathematics), field theory and group theory. This connection, the fundamental theorem of Galois theory, allows reducing certain problems ...
. Perhaps one of his more famous contributions is the
Lax–Milgram theorem—a theorem in functional analysis that is particularly applicable in the study of partial differential equations. In the third chapter of
Emil Artin
Emil Artin (; March 3, 1898 – December 20, 1962) was an Austrians, Austrian mathematician of Armenians, Armenian descent.
Artin was one of the leading mathematicians of the twentieth century. He is best known for his work on algebraic number t ...
's book ''Galois Theory'', Milgram also discussed some applications of Galois theory. Milgram also contributed to
graph theory
In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph ...
, by co-authoring the article ''Verallgemeinerung eines graphentheoretischen Satzes von Rédei'' with
Tibor Gallai in 1960.
Milgram was born in
Philadelphia
Philadelphia ( ), colloquially referred to as Philly, is the List of municipalities in Pennsylvania, most populous city in the U.S. state of Pennsylvania and the List of United States cities by population, sixth-most populous city in the Unit ...
, and received his Ph.D. from the
University of Pennsylvania
The University of Pennsylvania (Penn or UPenn) is a Private university, private Ivy League research university in Philadelphia, Pennsylvania, United States. One of nine colonial colleges, it was chartered in 1755 through the efforts of f ...
in 1937. He worked under the supervision of
John Klinebr>
(a student of
Robert Lee Moore). His dissertation was titled "''Decompositions and Dimension of Closed Sets in'' ".
Milgram advised 2 students at
Syracuse University
Syracuse University (informally 'Cuse or SU) is a Private university, private research university in Syracuse, New York, United States. It was established in 1870 with roots in the Methodist Episcopal Church but has been nonsectarian since 1920 ...
in the 1940s and 1950s (
Robert M. Exnerbr>
and
Adnah Kostenbauderbr>
.
[See respectively and .] In the 1950s, Milgram moved to the
University of Minnesota at Minneapolis and helped found Minnesota's well-known
PDE group
. At Minnesota, Milgram was also the Ph.D. advisor for
Robert Duke Adamsbr>
Milgram's son
R. James Milgram, R. James (Richard) Milgrambr>
(Professor Emeritus at
Stanford
Leland Stanford Junior University, commonly referred to as Stanford University, is a private research university in Stanford, California, United States. It was founded in 1885 by railroad magnate Leland Stanford (the eighth governor of and th ...
br>
also studied mathematics and received his Ph.D. from Minnesota.
Selected publications
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See also
*
Babuška–Lax–Milgram theorem
*
Fichera's existence principle
*
Lions–Lax–Milgram theorem
*
List of Jewish American mathematicians
Notes
References
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External links
{{DEFAULTSORT:Milgram, Arthur
20th-century American mathematicians
Combinatorialists
Differential geometers
American mathematical analysts
American topologists
Mathematicians from New York (state)
Jewish American scientists
University of Minnesota faculty
Syracuse University faculty
Institute for Advanced Study visiting scholars
University of Notre Dame faculty
University of Pennsylvania alumni
1912 births
1960 deaths