Garrett Birkhoff (January 19, 1911, Princeton, New Jersey, USA - November 22, 1996, Water Mill, New York, USA) was an American mathematician. He taught mainly at Harvard University. January 19 is the 19th day of the year in the Gregorian calendar. ... 1911 (MCMXI) was a common year starting on Sunday (click on link for calendar). ... Princeton, New Jersey is the name of a section of Mercer County, New Jersey, United States. ... November 22 is the 326th day (327th on leap years) of the year in the Gregorian calendar. ... 1996 (MCMXCVI) is a leap year starting on Monday of the Gregorian calendar, and was designated the International Year for the Eradication of Poverty. ... A watermill is a machine constructed by connecting a water wheel to a pair of millstones. ... Official language(s) None, English de facto Capital Albany Largest city New York City Area  - Total  - Width  - Length  - % water  - Latitude  - Longitude Ranked 27th 141,205 km² 455 km 530 km 13. ... This article is in need of attention from an expert on the subject. ... Harvard University is a private university in Cambridge, Massachusetts, USA and a member of the Ivy League. ...

The son of the mathematician George David Birkhoff, Garrett 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 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. George David Birkhoff (21 March 1884 - 12 November 1944) was an American mathematician, and one of the most important leaders in mathematics in the USA in his generation. ... Harvard University is a private university in Cambridge, Massachusetts, USA and a member of the Ivy League. ... The University of Cambridge is the second-oldest university in the English-speaking world, with one of the most selective sets of entry requirements in the United Kingdom. ... Royal motto (French): Dieu et mon droit (Translated: God and my right) Englands location within the British Isles Official language English de facto Capital London de facto Largest city London Area – Total Ranked 1st UK 130,395 km² Population – Total (mid-2004) – Total (2001 Census) – Density Ranked 1st UK... Mathematical physics is the scientific discipline concerned with the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories1. ... Abstract algebra is the field of mathematics concerned with the study of algebraic structures such as groups, rings and fields. ... Philip Hall (11 April 1904 - 30 December 1982) was an English mathematician. ... With approximately 48,000 students, the Ludwig-Maximilians-University Munich (German: Ludwig-Maximilians-Universität München or LMU) is one of the largest universities in Germany. ... Constantin Carathéodory (Greek: Κωνσταντίνος Καραθεοδωρής) (September 13, 1873 – February 2, 1950) was a Greek mathematician of the Modern Era. ... Bartel Leendert van der Waerden (February 2, 1903-January 12, 1996) was a Dutch mathematician who born in Amsterdam, Netherlands and died in Zürich, Switzerland. ... Abstract algebra is the field of mathematics concerned with the study of algebraic structures such as groups, rings and fields. ... Group theory is that branch of mathematics concerned with the study of groups. ...

Birkhoff held no Ph.D., a qualification British higher education did not emphasize at that time, and did not even bother obtaining an MA. Nevertheless, after being a member 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. The Harvard Society of Fellows is a collection of luminaries selected by Harvard University to be held close to its bosom, given special honors, thrown elegant dinners, and upon whom various privileges are bestowed. ...

During the 1930s, Birkhoff, along with his Harvard colleagues Marshall Stone and Saunders MacLane, substantially advanced American teaching and research in abstract algebra. In 1941 he and MacLane published A Survey of Modern Algebra, the first undergraduate textbook in English on the subject. Birkhoff and MacLane (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 subject owed little to Alfred North Whitehead's 1898 monograph bearing the same name. Marshall Harvey Stone (April 8, 1903–January 9, 1989) was a American mathematician who made several important contributions in various areas of mathematical analysis, including in particular functional analysis. ... Saunders Mac Lane (born 4 August 1909) is a US mathematician. ... Abstract algebra is the field of mathematics concerned with the study of algebraic structures such as groups, rings and fields. ... For the movie, see 1941 (film) 1941 (MCMXLI) was a common year starting on Wednesday. ... Abstract algebra is the field of mathematics concerned with the study of algebraic structures such as groups, rings and fields. ... The ordinary meaning of lattice is the basis for several technical usages A cherry lattice pastry A mathematical lattice that is a type of partially ordered set. ... Abstract algebra is the field of mathematics concerned with the study of algebraic structures such as groups, rings and fields. ... 1935 (MCMXXXV) was a common year starting on Tuesday (link will take you to calendar). ... Universal algebra is the field of mathematics that studies the ideas common to all algebraic structures. ... Alfred North Whitehead, OM (February 15, 1861 – December 30, 1947) was a British mathematician who evolved into a philosopher. ...

During and after WWII, Birkhoff's interests gravitated towards what he called "engineering" mathematics. During the war, he worked on radar aiming and ballistics. This weapons-related work culminated 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. His research and consulting work (notably for General Motors) began to employ computational methods, such as numerical linear algebra and the representation of smooth curves via cubic splines. German soldiers at the Battle of Stalingrad World War II was the most extensive and costly armed conflict in the history of the world, involving the great majority of the worlds nations, being fought simultaneously in several major theatres, and costing tens of millions of lives. ... John von Neumann in the 1940s. ... General Motors Corporation (NYSE: GM), also known as GM, is a United States-based automobile maker with worldwide operations and brands including Buick, Cadillac, Chevrolet, GMC, Holden, Hummer, Opel, Pontiac, Saturn, Saab and Vauxhall. ... In the mathematical subfield of numerical analysis a spline is a special curve defined piecewise by polynomials. ...

Birkhoff published more than 200 papers and supervised more than 50 Ph.Ds. He was a member of the National Academy of Sciences and the American Academy of Arts and Sciences. President Harding and the National Academy of Sciences at the White House, Washington, DC, April 1921 The National Academy of Sciences (NAS) is a corporation in the United States whose members serve pro bono as advisers to the nation on science, engineering, and medicine. ... The House of the Academy, Cambridge, Massachusetts. ...

Books by

• 1967 (1940). Lattice Theory, 3rd ed. American Mathematical Society.
• 1977 (1941) (with MacLane). A Survey of Modern Algebra.
• 1960 (1950). Hydrodynamics.
• 1957 (with E. Zarantello). Jets, Wakes, and Cavities.
• 1978 (1962) (with Gian Carlo Rota). Ordinary Differential Equations.
• 1979 (1967) (with MacLane). Algebra.
• 1970 (with Thomas Bartee). Modern Applied Algebra.
• 1973. Source Book in Classical Analysis.

External link

• John J. O'Connor and Edmund F. Robertson. Garrett Birkhoff at the MacTutor archive.