Editing Garrett Birkhoff (section)

== 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>