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, the American Philosophical Society, 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 for 1966–1968. He won a Lester R. Ford Award in 1974. Selected books 2015 pbk reprint of 1960 2nd edition See also Birkhoff algorithm Birkhoff's condition Birkhoff polytope Birkhoff's representation theorem Birkhoff's HSP theorem Birkhoff's theorem Birkhoff-Kakutani theorem Pierce–Birkhoff conjecture Pierce-Birkhoff ring Poincaré–Birkhoff–Witt theorem Algebraic statistics Median algebra Universal algebra References External links 1911 births Members of the United States National Academy of Sciences 1996 deaths 20th-century American mathematicians Harvard University faculty Institute for Advanced Study visiting scholars Algebraists Lattice theorists Fluid dynamicists Harvard University alumni People from Princeton, New Jersey Presidents of the Society for Industrial and Applied Mathematics American expatriates in the United Kingdom Mathematicians from New Jersey Members of the American Philosophical Society