Arthur Norton Milgram (3 June 1912, in

Philadelphia Philadelphia, often called Philly, is the largest city in the Commonwealth of Pennsylvania, the sixth-largest city in the U.S., the second-largest city in both the Northeast megalopolis and Mid-Atlantic regions after New York City. Sinc ...

– 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 (e.g. Inner product space#Definition, inner product, Norm (mathematics)#Defini ...

combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many appl ...

differential geometry Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multili ...

topology In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such ...

partial differential equations In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to ...

, and

Galois theory In mathematics, Galois theory, originally introduced by Évariste Galois, provides a connection between field theory and group theory. This connection, the fundamental theorem of Galois theory, allows reducing certain problems in field theory to ...

. Perhaps one of his more famous contributions is the

Lax–Milgram theorem Weak formulations are important tools for the analysis of mathematical equations that permit the transfer of concepts of linear algebra to solve problems in other fields such as partial differential equations. In a weak formulation, equations or con ...

—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 Austrian mathematician of Armenian descent. Artin was one of the leading mathematicians of the twentieth century. He is best known for his work on algebraic number theory, contributing lar ...

's book ''Galois Theory'', Milgram also discussed some applications of Galois theory. Milgram also contributed to

graph theory In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conne ...

, by co-authoring the article ''Verallgemeinerung eines graphentheoretischen Satzes von Rédei'' with

Tibor Gallai Tibor Gallai (born Tibor Grünwald, 15 July 1912 – 2 January 1992) was a Hungarian mathematician. He worked in combinatorics, especially in graph theory, and was a lifelong friend and collaborator of Paul Erdős. He was a student of Dénes K� ...

in 1960. Milgram received his Ph.D. from the

University of Pennsylvania The University of Pennsylvania (also known as Penn or UPenn) is a private research university in Philadelphia. It is the fourth-oldest institution of higher education in the United States and is ranked among the highest-regarded universitie ...

in 1937. He worked under the supervision of John Klinebr>
(a student of

Robert Lee Moore Robert Lee Moore (November 14, 1882 – October 4, 1974) was an American mathematician who taught for many years at the University of Texas. He is known for his work in general topology, for the Moore method of teaching university mathematics, ...

). 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. Established in 1870 with roots in the Methodist Episcopal Church, the university has been nonsectarian since 1920. Locate ...

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 The University of Minnesota, formally the University of Minnesota, Twin Cities, (UMN Twin Cities, the U of M, or Minnesota) is a public land-grant research university in the Twin Cities of Minneapolis and Saint Paul, Minnesota, United States. ...

and helped found Minnesota's well-known PDE group

. At Minnesota, Milgram was also the Ph.D. advisor for Robert Duke Adamsbr>
It is also worth noting that Milgram's son R. James Milgram, R. James (Richard) Milgrambr>
(Professor Emeritus at

Stanford Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California. The campus occupies , among the largest in the United States, and enrolls over 17,000 students. Stanford is considere ...

br>
also studied mathematics and received his Ph.D. from Minnesota.

Selected publications

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Notes

References

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External links

{{DEFAULTSORT:Milgram, Arthur 20th-century American mathematicians Combinatorialists Differential geometers Mathematical analysts 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

Selected publications

See also

Notes

References

External links