Editing Garrett Birkhoff

{{Short description|American mathematician (1911–1996)}}
{{Infobox scientist
| name              = Garrett Birkhoff
| image             = Birkhoff Garrett 3.jpeg
| caption           = 
| birth_date        = {{birth date|1911|1|19}}
| birth_place       = [[Princeton, New Jersey|Princeton]], [[New Jersey]], US
| death_date        = {{death date and age|1996|11|22|1911|1|19}}
| death_place       = [[Water Mill, New York|Water Mill]], [[New York (state)|New York]], US
| fields            = [[Mathematics]]
| workplaces        = [[Harvard University]]
| alma_mater        = [[Cambridge University]]<br>[[Harvard University]]
| academic_advisors = {{plainlist|1=
* [[Ralph H. Fowler]]
* [[Philip Hall]]
}}
| doctoral_students = {{plainlist|1=
* [[Richard Friedrich Arens|Richard Arens]]
* [[Jerry L. Bona]]
* [[Thomas Caywood]]
* [[Chandler Davis]]
* [[George Fix]]
* [[Emmett Keeler]]
* [[Uta Merzbach]]
* [[George Mostow]]
* [[Peter J. Olver]]
* [[R. Tyrrell Rockafellar]]
* [[Henry C. Wente]]
* [[Philip M. Whitman]]
* [[David M. Young, Jr.]]
* [[Vern Poythress]]
}}
| notable_students  = [[Richard S. Varga]]
| known_for         = {{plainlist|1=
* [[Lattice theory]]
* [[Quantum logic]]
}}
| author_abbrev_bot = 
| author_abbrev_zoo = 
| awards            = {{plainlist|1=
* [[United States National Academy of Sciences|National Academy of Sciences]]
* [[American Academy of Arts and Sciences]]
* [[George David Birkhoff Prize]] <small>(1978)</small>
}}
| signature         = <!--(filename only)-->
}}

'''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]] (1884&ndash;1944) was his father.

== Life ==
The son of the mathematician [[George David Birkhoff]], Garrett was born in [[Princeton, New Jersey]].<ref>Staff. [https://library.ias.edu/files/pdfs/hs/cos.pdf#page=90 ''A COMMUNITY OF SCHOLARS: The Institute for Advanced Study Faculty and Members 1930-1980''] {{Webarchive|url=https://web.archive.org/web/20111124234612/http://library.ias.edu/files/pdfs/hs/cos.pdf#page=90 |date=2011-11-24 }}, p. 90. [[Institute for Advanced Study]], 1980. Accessed November 20, 2015. "Birkhoff, Garrett 40s M Born 1911 Princeton, NJ."</ref> He began the [[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]] to study [[mathematical physics]] but switched to studying [[abstract algebra]] under [[Philip Hall]]. While visiting the [[University of Munich]], he met [[Constantin Carathéodory]] who pointed him towards two important texts, [[Bartel Leendert van der Waerden|Van der Waerden]] on [[abstract algebra]] and [[Andreas Speiser|Speiser]] on [[group theory]].

Birkhoff held no Ph.D., a qualification British higher education did not emphasize at that time, and did not obtain an M.A. Nevertheless, after being a member of Harvard's [[Society of Fellows]], 1933&ndash;36, he spent the rest of his career teaching at Harvard.

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 (mathematician)|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, Jr.|David M. Young]] on the numerical solution of [[Poisson's equation|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 Electric (1886)|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 operator]]s and [[iterative method]]s for ''p''-cyclic matrices.

Birkhoff's research and consulting work (notably for [[General Motors Corporation|General Motors]]) developed computational methods besides [[numerical linear algebra]], notably the representation of smooth curves via [[cubic spline]]s.

Birkhoff published more than 200 papers and supervised more than 50 Ph.D.s. He was a member of the [[United States National Academy of Sciences|National Academy of Sciences]],<ref>{{Cite web |title=Garrett Birkhoff |url=http://www.nasonline.org/member-directory/deceased-members/57681.html |access-date=2022-11-30 |website=www.nasonline.org}}</ref> the [[American Philosophical Society]],<ref>{{Cite web |title=APS Member History |url=https://search.amphilsoc.org/memhist/search?creator=Garrett+Birkhoff&title=&subject=&subdiv=&mem=&year=&year-max=&dead=&keyword=&smode=advanced |access-date=2022-11-30 |website=search.amphilsoc.org}}</ref> and the [[American Academy of Arts and Sciences]].<ref>{{Cite web |title=Garrett Birkhoff |url=https://www.amacad.org/person/garrett-birkhoff |access-date=2022-11-30 |website=American Academy of Arts & Sciences |language=en}}</ref> He was a [[Guggenheim Fellow]] for the academic year 1948–1949 and the president of the [[Society for Industrial and Applied Mathematics]] for 1966–1968. He won a [[Lester R. Ford Award]] in 1974.<ref>{{cite journal|author=Birkhoff, Garrett|title=Current trends in algebra|journal=Amer. Math. Monthly|volume=80|year=1973|issue=7 |pages=760–782|url=http://www.maa.org/programs/maa-awards/writing-awards/current-trends-in-algebra|doi=10.2307/2318163|jstor=2318163 }}</ref>

== Selected books ==

* {{Citation | last1=Birkhoff | first1=Garrett | title=Lattice theory | orig-year=1940 | url=https://books.google.com/books?id=o4bu3ex9BdkC | publisher=[[American Mathematical Society]] | location=Providence, R.I. | edition=4th | series=American Mathematical Society Colloquium Publications | isbn=978-0-8218-1025-5 | mr=598630 | year=1979 | volume=25}}<ref>{{cite journal|author=Wilcox, L. R.|title=Review: ''Lattice Theory'', by Garrett Birkhoff|journal=Bull. Amer. Math. Soc.|year=1941|volume=47|issue=3|pages=194–196|url=https://www.ams.org/journals/bull/1941-47-03/S0002-9904-1941-07409-4/S0002-9904-1941-07409-4.pdf|doi=10.1090/S0002-9904-1941-07409-4|doi-access=free}}</ref>
* {{Citation | last1=Birkhoff | first1=Garrett |author-mask=2 |year=1997 | first2=Saunders |last2=Mac Lane |author2-link=Saunders Mac Lane |title=A Survey of Modern Algebra |publisher=A.K. Peters |isbn=1-56881-068-7 |orig-year=1941}}<ref>{{cite journal|author=Thrall, R. M.|author-link=Robert M. Thrall|title=Review: ''A Survey of Modern Algebra'', by Garrett Birkhoff and Saunders Mac Lane|journal=Bull. Amer. Math. Soc.|year=1942|volume=48|issue=5|pages=342–345|url=https://www.ams.org/journals/bull/1942-48-05/S0002-9904-1942-07670-1/S0002-9904-1942-07670-1.pdf|doi=10.1090/S0002-9904-1942-07670-1|doi-access=free}}</ref>
* {{Citation | last1=Birkhoff | first1=Garrett |author-mask=2 |year=1978 |orig-year=1950 |title=Hydrodynamics: A study in logic, fact, and similitude |publisher=Greenwood Press }}<ref name="Stoker1951">{{cite journal|last1=Stoker|first1=J. J.|author-link=James J. Stoker|title=Book Review: ''Hydrodynamics, a study in logic, fact, and similitude''|journal=Bulletin of the American Mathematical Society|volume=57|issue=6|year=1951|pages=497–500|issn=0002-9904|doi=10.1090/S0002-9904-1951-09552-X|doi-access=free}}</ref> [https://books.google.com/books?id=Vj7WCgAAQBAJ 2015 pbk reprint of 1960 2nd edition] 
* {{Citation | last1=Birkhoff | first1=Garrett |author-mask=2 | year=1957 | first2=E.H. |last2=Zarantonello |author2-link=Eduardo Héctor Zarantonello|title=Jets, Wakes, and Cavities| publisher=Academic Press}}<ref>{{cite journal|author=Lighthill, M. J.|author-link=James Lighthill|title=Review of ''Jets, Wakes and Cavities'' by Garrett Birkhoff and E. H. Zarantonello|journal=Journal of Fluid Mechanics|volume=3|issue=4|year=1958|pages=437–440|doi=10.1017/S0022112058210100 |s2cid=123461272 |url=https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/abs/jets-wakes-and-cavities-by-garrett-birkhoff-and-e-h-zarantonello-new-york-academic-press-1957-353-pp-1000-or-80s/95F0DFF393775181EF43EDF4959F81C2}}</ref>
* {{Citation | last1=Birkhoff | first1=Garrett |author-mask=2 | year=1989 |orig-year=1962 | first2=Gian-Carlo |last2=Rota |author2-link=Gian-Carlo Rota |title=Ordinary Differential Equations |publisher=John Wiley}}<ref>{{cite journal|title=Review of ''Ordinary Differential Equations'' by G. Blrkhoff and G. Rota|author=Burkill, J. C.|author-link=John Charles Burkill|journal=The Mathematical Gazette|volume=48|issue=364|date=May 1964|pages=240–241|doi=10.1017/S0025557200051068|s2cid=195544336 |url=https://www.cambridge.org/core/journals/mathematical-gazette/article/abs/ordinary-differential-equations-by-g-blrkhoff-and-g-rota-pp-vi-318-850-1962-ginn-and-company/B7A4F33B7EF76E7E48C1C001AE699F8A}}</ref>
* {{Citation | last1=Birkhoff | first1=Garrett |author-mask=2 | year=1999 |orig-year=1967 |first2=Saunders |last2=Mac Lane |author2-link=Saunders Mac Lane |title=Algebra |publisher=Chelsea |isbn=0-8218-1646-2 |url=https://books.google.com/books?id=L6FENd8GHIUC}}
* {{Citation | last1=Birkhoff | first1=Garrett |author-mask=2 | year=1970 |first2=Thomas |last2=Bartee |title=Modern Applied Algebra |publisher=McGraw-Hill}}<ref>{{cite journal|author=Rheinboldt, Werner C.|title=Review: ''Modern Applied Algebra'', by Garrett Birkhoff and Thomas C. Bartee|journal=Bull. Amer. Math. Soc.|year=1972|volume=78|issue=3|pages=383–385|url=https://www.ams.org/journals/bull/1972-78-03/S0002-9904-1972-12908-2/S0002-9904-1972-12908-2.pdf|doi=10.1090/s0002-9904-1972-12908-2|doi-access=free}}</ref>
* {{cite book|title=Numerical solution of elliptic problems|author=Birkhoff, Garrett Birkhoff|author-mask=2|author2=Lynch, Robert Edward|year=1984|publisher=Society of Industrial and Applied Mathematics (SIAM)|location=Philadelphia|series=SIAM Studies in Applied Mathematics, vol. 6|doi=10.1137/1.9781611970869.fm |url=https://epubs.siam.org/doi/pdf/10.1137/1.9781611970869.fm}}
* {{Citation | last1=Birkhoff | first1=Garrett |author-mask=2 | year=1973 |title=Source Book in Classical Analysis |publisher=Harvard University Press}}
* {{cite book|editor1=Oliveira, J. S.|editor2=Rota, G.-C.|title=Selected Papers on Algebra and Topology by Garrett Birkhoff|url=https://books.google.com/books?id=BBykgLvJ3yAC|date=1 January 1987|publisher=Springer Science & Business Media|isbn=978-0-8176-3114-7}}

== See also ==
* [[Birkhoff algorithm]]
* [[Semimodular lattice#Birkhoff's condition|Birkhoff's condition]]
* [[Birkhoff polytope]]
* [[Birkhoff's representation theorem]]
* [[Birkhoff's HSP theorem]]
* [[Birkhoff's theorem (disambiguation)|Birkhoff's theorem]]
* [[Topological group#Properties|Birkhoff–Kakutani theorem]]
* [[Pierce–Birkhoff conjecture]]
* [[Partially ordered ring#f-rings|Pierce–Birkhoff ring]]
* [[Poincaré–Birkhoff–Witt theorem]]
* [[Algebraic statistics]]
* [[Median algebra]]
* [[Universal algebra]]

== References ==
{{reflist}}

== External links ==
* {{MathGenealogy |id=16942}}
* {{MacTutor Biography|id=Birkhoff_Garrett}}

{{John von Neumann Lecturers}}
{{Authority control}}

{{DEFAULTSORT:Birkhoff, Garrett}}
[[Category:1911 births]]
[[Category:Members of the United States National Academy of Sciences]]
[[Category:1996 deaths]]
[[Category:20th-century American mathematicians]]
[[Category:Harvard University Department of Mathematics faculty]]
[[Category:Institute for Advanced Study visiting scholars]]
[[Category:American algebraists]]
[[Category:Lattice theorists]]
[[Category:American fluid dynamicists]]
[[Category:Harvard University alumni]]
[[Category:Scientists from Princeton, New Jersey]]
[[Category:Presidents of the Society for Industrial and Applied Mathematics]]
[[Category:American expatriates in England]]
[[Category:Mathematicians from New Jersey]]
[[Category:Members of the American Philosophical Society]]