Hans Heinrich Wilhelm Magnus known as Wilhelm Magnus (February 5, 1907 in
Berlin
Berlin ( , ) is the capital and largest city of Germany by both area and population. Its 3.7 million inhabitants make it the European Union's most populous city, according to population within city limits. One of Germany's sixteen constitue ...
,
Germany
Germany,, officially the Federal Republic of Germany, is a country in Central Europe. It is the second most populous country in Europe after Russia, and the most populous member state of the European Union. Germany is situated betwe ...
– October 15, 1990 in
New Rochelle, New York
New Rochelle (; older french: La Nouvelle-Rochelle) is a city in Westchester County, New York, United States, in the southeastern portion of the state. In 2020, the city had a population of 79,726, making it the seventh-largest in the state of ...
) was a German-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 ...
. He made important contributions in
combinatorial group theory In mathematics, combinatorial group theory is the theory of free groups, and the concept of a presentation of a group by generators and relations. It is much used in geometric topology, the fundamental group of a simplicial complex having in a nat ...
,
Lie algebra
In mathematics, a Lie algebra (pronounced ) is a vector space \mathfrak g together with an Binary operation, operation called the Lie bracket, an Alternating multilinear map, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow ...
s,
mathematical physics
Mathematical physics refers to the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and t ...
,
elliptic functions
In the mathematical field of complex analysis, elliptic functions are a special kind of meromorphic functions, that satisfy two periodicity conditions. They are named elliptic functions because they come from elliptic integrals. Originally those i ...
, and the study of
tessellation
A tessellation or tiling is the covering of a surface, often a plane (mathematics), plane, using one or more geometric shapes, called ''tiles'', with no overlaps and no gaps. In mathematics, tessellation can be generalized to high-dimensional ...
s.
Biography
In 1931, Magnus received his PhD from the
University of Frankfurt, in
Germany
Germany,, officially the Federal Republic of Germany, is a country in Central Europe. It is the second most populous country in Europe after Russia, and the most populous member state of the European Union. Germany is situated betwe ...
. His thesis, written under the direction of
Max Dehn
Max Wilhelm Dehn (November 13, 1878 – June 27, 1952) was a German mathematician most famous for his work in geometry, topology and geometric group theory. Born to a Jewish family in Germany, Dehn's early life and career took place in Germany. ...
, was entitled
''Über unendlich diskontinuierliche Gruppen von einer definierenden Relation (der Freiheitssatz)''.
Magnus was a faculty member in Frankfurt from 1933 until 1938. He refused to join the
Nazi Party
The Nazi Party, officially the National Socialist German Workers' Party (german: Nationalsozialistische Deutsche Arbeiterpartei or NSDAP), was a far-right politics, far-right political party in Germany active between 1920 and 1945 that crea ...
and, as a consequence, was not allowed to hold an academic post during
World War II
World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...
. In 1947 he became a professor at the
University of Göttingen
The University of Göttingen, officially the Georg August University of Göttingen, (german: Georg-August-Universität Göttingen, known informally as Georgia Augusta) is a public research university in the city of Göttingen, Germany. Founded ...
.
In 1948 he emigrated to the
United States
The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 states, a federal district, five major unincorporated territorie ...
to collaborate on the
Bateman Manuscript Project as a co-editor, while a visiting professor at the
California Institute of Technology
The California Institute of Technology (branded as Caltech or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasional ...
. In 1950 he was appointed professor at the
Courant Institute of Mathematical Sciences
The Courant Institute of Mathematical Sciences (commonly known as Courant or CIMS) is the mathematics research school of New York University (NYU), and is among the most prestigious mathematics schools and mathematical sciences research cente ...
, in
New York University
New York University (NYU) is a private research university in New York City. Chartered in 1831 by the New York State Legislature, NYU was founded by a group of New Yorkers led by then-Secretary of the Treasury Albert Gallatin.
In 1832, the ...
. He stayed there until 1973, when he moved to the
Polytechnic Institute of New York
The New York University Tandon School of Engineering (commonly referred to as Tandon) is the engineering and applied sciences school of New York University. Tandon is the second oldest private engineering and technology school in the United Sta ...
, before retiring in 1978. Among his doctoral students are
Joan Birman
Joan Sylvia Lyttle Birman (born May 30, 1927, in New York CityLarry Riddle., ''Biographies of Women Mathematicians'', at Agnes Scott College) is an American mathematician, specializing in low-dimensional topology. She has made contributions to th ...
, Martin Greendlinger,
Edna Grossman
Edna Grossman (born Edna Kalka) is an American mathematician. She was born in Germany, grew up in Brooklyn, New York, and graduated with a B.S. in mathematics from Brooklyn College. She earned her M.S. in mathematics from New York University's Co ...
,
Herbert Keller
Herbert Bishop Keller (19 June 1925 in Paterson, New Jersey – 26 January 2008 in Pasadena, California) was an American applied mathematician and numerical analyst. He was professor of applied mathematics, emeritus, at the California Institut ...
,
Seymour Lipschutz
Seymour Saul Lipschutz (born 1931 died March 2018) was an author of technical books on pure mathematics and probability, including a collection of Schaum's Outlines.
Lipschutz received his Ph.D. in 1960 from New York University's Courant Institute ...
, and
Kathryn F. Kuiken.
See also
*
Magnus expansion In mathematics and physics, the Magnus expansion, named after Wilhelm Magnus (1907–1990), provides an exponential representation of the solution of a first-order homogeneous linear differential equation for a linear operator. In particular, it f ...
*
Magnus–Moldavansky method
*
Commutator collecting process In group theory, a branch of mathematics, the commutator collecting process is a method for writing an element of a group as a product of generators and their higher commutators arranged in a certain order. The commutator collecting process was int ...
*
Free Lie algebra In mathematics, a free Lie algebra over a field ''K'' is a Lie algebra generated by a set ''X'', without any imposed relations other than the defining relations of alternating ''K''-bilinearity and the Jacobi identity.
Definition
The definition ...
*
Hall word
In mathematics, in the areas of group theory and combinatorics, Hall words provide a unique monoid factorisation of the free monoid. They are also totally ordered, and thus provide a total order on the monoid. This is analogous to the better-known ...
Selected works
*with
Gilbert Baumslag
Gilbert Baumslag (April 30, 1933 – October 20, 2014) was a Distinguished Professor at the City College of New York, with joint appointments in mathematics, computer science, and electrical engineering. He was director of thCenter for Algorithms ...
and Bruce Chandler, eds.: ''Wilhelm Magnus, Collected Papers.'' Springer-Verlag 1984.
*''Noneuclidean tessellations and their groups.'' Academic Press 1974.
*with Bruce Chandler: ''The History of Combinatorial Group Theory. A Case Study in the History of Ideas.'' Springer 1982.
* Wilhelm Magnus, Abraham Karrass, Donald Solitar, ''Combinatorial group theory. Presentations of groups in terms of generators and relations'', Reprint of the 1976 second edition, Dover Publications, Inc., Mineola, NY, 2004.
* Wilhelm Magnus, Stanley Winkler, ''Hill's equation'', Reprint of the 1979 second edition, Dover Publications, Inc., Mineola, NY, 2004. .
*with Israel Grossman: ''Groups and their Graphs.'' Random House (New Mathematical Library 14) 1965.
* ( The
Bateman Manuscript Project:
scan)
*Wilhelm Magnus, Fritz Oberhettinger, and Raz Pal Soni, ''Formulas and Theorems for the Special Functions of Mathematical Physics''. Springer-Verlag New York Inc., New York, 1966.
*with Fritz Oberhettinger: ''Formeln und Lehrsätze für die speziellen Funktionen der mathematischen Physik.'' Springer 1943; 2nd edition, 1948; 3rd edition in English, ''Formulas and theorems for the functions of mathematical physics'', Chelsea Pub. Co. 1966.
*with Fritz Oberhettinger: ''Anwendungen der elliptischen Funktionen in Physik und Technik.'' Springer 1949.
References
*
The Mathematical Legacy of Wilhelm Magnus Groups, Geometry, and Special Functions''. Conference on the Legacy of Wilhelm Magnus May 1–3, 1992 .
External links
*
*
1907 births
1990 deaths
20th-century American mathematicians
20th-century German mathematicians
Group theorists
Courant Institute of Mathematical Sciences faculty
Goethe University Frankfurt alumni
German emigrants to the United States
{{US-mathematician-stub