**Garrett Birkhoff** (January 19, 1911 – November 22, 1996) was an
American mathematician. He is best known for his work in lattice
theory.
The mathematician
**George Birkhoff**

George Birkhoff (1884–1944) was his father.

Contents

1 Life
2 Selected books
3 See also
4 References
5 External links

Life[edit]
The son of the mathematician George David Birkhoff, Garrett was born
in Princeton, New Jersey.[1] He began the
**Harvard University**

Harvard University BA course
in 1928 after less than seven years of prior formal education. Upon
completing his Harvard BA in 1932, he went to
**Cambridge University**

Cambridge University in
England to study mathematical physics but switched to studying
abstract algebra under Philip Hall. While visiting the University of
Munich, he met Carathéodory who pointed him towards two important
texts, Van der Waerden on abstract algebra and Speiser on group
theory.
Birkhoff held no Ph.D., a qualification British higher education did
not emphasize at that time, and did not even bother obtaining an M.A.
Nevertheless, after being a member of Harvard's Society of Fellows,
1933–36, he spent the rest of his career teaching at Harvard. From
these facts can be inferred the number and quality of Birkhoff's
papers published by his 25th year.
During the 1930s, Birkhoff, along with his Harvard colleagues Marshall
Stone and Saunders Mac Lane, substantially advanced American teaching
and research in abstract algebra. In 1941 he and Mac Lane published A
Survey of Modern Algebra, the second undergraduate textbook in English
on the subject (Cyrus Colton MacDuffee's An Introduction to Abstract
Algebra was published in 1940). Mac Lane and Birkhoff's Algebra (1967)
is a more advanced text on abstract algebra. A number of papers he
wrote in the 1930s, culminating in his monograph, Lattice Theory
(1940; the third edition remains in print), turned lattice theory into
a major branch of abstract algebra. His 1935 paper, "On the Structure
of Abstract Algebras" founded a new branch of mathematics, universal
algebra. Birkhoff's approach to this development of universal algebra
and lattice theory acknowledged prior ideas of Charles Sanders Peirce,
Ernst Schröder, and Alfred North Whitehead; in fact, Whitehead had
written an 1898 monograph entitled Universal Algebra.
During and after World War II, Birkhoff's interests gravitated towards
what he called "engineering" mathematics. During the war, he worked on
radar aiming and ballistics, including the bazooka. In the development
of weapons, mathematical questions arose, some of which had not yet
been addressed by the literature on fluid dynamics. Birkhoff's
research was presented in his texts on fluid dynamics, Hydrodynamics
(1950) and Jets, Wakes and Cavities (1957).
Birkhoff, a friend of John von Neumann, took a close interest in the
rise of the electronic computer. Birkhoff supervised the Ph.D. thesis
of David M. Young on the numerical solution of the partial
differential equation of Poisson, in which Young proposed the
successive over-relaxation (SOR) method. Birkhoff then worked with
Richard S. Varga, a former student, who was employed at Bettis Atomic
Power Laboratory of the Westinghouse Electronic Corporation in
Pittsburgh and was helping to design nuclear reactors. Extending the
results of Young, the Birkhoff-Varga collaboration led to many
publications on positive operators and iterative methods for p-cyclic
matrices.
Birkhoff's research and consulting work (notably for General Motors)
developed computational methods besides numerical linear algebra,
notably the representation of smooth curves via cubic splines.
Birkhoff published more than 200 papers and supervised more than 50
Ph.D.s. He was a member of the National Academy of Sciences and the
American Academy of Arts and Sciences. He was a
**Guggenheim Fellow** for
the academic year 1948–1949 and the president of the Society for
Industrial and Applied
**Mathematics**

Mathematics for 1966–1968. He won a Lester R.
Ford Award in 1974.[2]
Selected books[edit]

Birkhoff, Garrett (1979) [1940], Lattice theory, American Mathematical
Society Colloquium Publications, 25 (4th ed.), Providence, R.I.:
American Mathematical Society, ISBN 978-0-8218-1025-5,
MR 0598630 [3]
——; Mac Lane, Saunders (1997) [1941], A Survey of Modern Algebra,
A.K. Peters, ISBN 1-56881-068-7 [4]
—— (1978) [1950], Hydrodynamics: A study in logic, fact, and
similitude, Greenwood Press
——; Zarantonello, E.H. (1957), Jets, Wakes, and Cavities, Academic
Press
——; Rota, Gian-Carlo (1989) [1962], Ordinary Differential
Equations, John Wiley
——; Mac Lane, Saunders (1999) [1967], Algebra, Chelsea,
ISBN 0-8218-1646-2
——; Bartee, Thomas (1970), Modern Applied Algebra,
McGraw-Hill [5]
—— (1973), Source Book in Classical Analysis, Harvard University
Press

See also[edit]

Birkhoff polytope
Birkhoff's representation theorem
Birkhoff's HSP theorem
Birkhoff's theorem (other)
Pierce–Birkhoff conjecture
Poincaré–Birkhoff–Witt theorem

References[edit]

^ Staff. A COMMUNITY OF SCHOLARS: The Institute for Advanced Study
Faculty and Members 1930-1980, p. 90. Institute for Advanced Study,
1980. Accessed November 20, 2015. "Birkhoff, Garrett 40s M Born 1911
Princeton, NJ."
^ Birkhoff, Garrett (1973). "Current trends in algebra". Amer. Math.
Monthly. 80: 760–782. doi:10.2307/2318163.
^ Wilcox, L. R. (1941). "Review: Lattice Theory, by Garrett Birkhoff"
(PDF). Bull. Amer. Math. Soc. 47 (3): 194–196.
doi:10.1090/S0002-9904-1941-07409-4.
^ Thrall, R. M. (1942). "Review: A Survey of Modern Algebra, by
**Garrett Birkhoff** and Saunders Mac Lane" (PDF). Bull. Amer. Math. Soc.
48 (5): 342–345. doi:10.1090/S0002-9904-1942-07670-1.
^ Rheinboldt, Werner C. (1972). "Review: Modern Applied Algebra, by
**Garrett Birkhoff** and Thomas C. Bartee" (PDF). Bull. Amer. Math. Soc.
78 (3): 383–385. doi:10.1090/s0002-9904-1972-12908-2.

External links[edit]

**Garrett Birkhoff** at the
**Mathematics**

Mathematics Genealogy Project
O'Connor, John J.; Robertson, Edmund F., "Garrett Birkhoff", MacTutor
History of
**Mathematics**

Mathematics archive, University of St Andrews .

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t
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**John von Neumann**

John von Neumann Lecturers

**Lars Ahlfors**

Lars Ahlfors (1960)
**Mark Kac**

Mark Kac (1961)
**Jean Leray**

Jean Leray (1962)
**Stanislaw Ulam**

Stanislaw Ulam (1963)
**Solomon Lefschetz**

Solomon Lefschetz (1964)
**Freeman Dyson**

Freeman Dyson (1965)
**Eugene Wigner**

Eugene Wigner (1966)
**Chia-Chiao Lin** (1967)
**Peter Lax**

Peter Lax (1968)
**George F. Carrier**

George F. Carrier (1969)
**James H. Wilkinson** (1970)
**Paul Samuelson**

Paul Samuelson (1971)
Jule Charney (1974)
**James Lighthill**

James Lighthill (1975)
**René Thom**

René Thom (1976)
**Kenneth Arrow** (1977)
Peter Henrici (1978)
Kurt O. Friedrichs (1979)
**Keith Stewartson** (1980)
**Garrett Birkhoff** (1981)
**David Slepian**

David Slepian (1982)
Joseph B. Keller (1983)
**Jürgen Moser**

Jürgen Moser (1984)
John W. Tukey (1985)
**Jacques-Louis Lions**

Jacques-Louis Lions (1986)
**Richard M. Karp**

Richard M. Karp (1987)
**Germund Dahlquist** (1988)
**Stephen Smale**

Stephen Smale (1989)
**Andrew Majda**

Andrew Majda (1990)
**R. Tyrrell Rockafellar**

R. Tyrrell Rockafellar (1992)
Martin D. Kruskal (1994)
Carl de Boor (1996)
**William Kahan**

William Kahan (1997)
**Olga Ladyzhenskaya**

Olga Ladyzhenskaya (1998)
**Charles S. Peskin** (1999)
**Persi Diaconis**

Persi Diaconis (2000)
**David Donoho** (2001)
**Eric Lander**

Eric Lander (2002)
**Heinz-Otto Kreiss** (2003)
**Alan C. Newell** (2004)
**Jerrold E. Marsden**

Jerrold E. Marsden (2005)
**George C. Papanicolaou**

George C. Papanicolaou (2006)
**Nancy Kopell** (2007)
David Gottlieb (2008)
**Franco Brezzi**

Franco Brezzi (2009)
**Bernd Sturmfels**

Bernd Sturmfels (2010)
**Ingrid Daubechies**

Ingrid Daubechies (2011)
**John M. Ball**

John M. Ball (2012)
**Stanley J. Osher**

Stanley J. Osher (2013)
**Leslie Greengard** (2014)
**Jennifer Tour Chayes**

Jennifer Tour Chayes (2015)
**Donald Knuth**

Donald Knuth (2016)
Bernard J. Matkowsky (2017)

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WorldCat Identities
VIAF: 101828426
LCCN: n50015070
ISNI: 0000 0000 8170 7227
GND: 11882564X
SUDOC: 029789338
BNF: cb121339500 (data)
MGP: 16942
NKC: xx0011