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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