BIRKHOFF, GEORGE DAVID

born March 21, 1884, Overisel, Mich., U.S. died Nov. 12, 1944, Cambridge, Mass. foremost American mathematician of the early 20th century, who formulated the ergodic theorem, which transformed the Maxwell-Boltzmann ergodic hypothesis of the kinetic theory of gases (to which exceptions are known) into a rigorous principle through use of the Lebesgue measure theory. Birkhoff taught at the University of Wisconsin, Madison (190709); Princeton University (190912); and Harvard University (191244). He was an extraordinarily stimulating lecturer and director of research. In the mid-20th century, many of the leading American mathematicians had either written their doctoral dissertations under his direction or had done postdoctoral research with him. He conducted research mainly in mathematical analysis and analysis applied to dynamics. His dissertation and much of his later work dealt with the solutions of ordinary differential equations and the associated expansions of arbitrary functions. Using matrix methods, he also contributed fundamentally to the theory of difference equations. His proof in 1913 of a geometric theorem of Henri Poincar in topology (the study of surfaces and spaces) was a striking achievement. Birkhoff's formulation of the ergodic theorem (the so-called strong form), which was published shortly before the weak formulation of John von Neumann appeared, has important applications to modern analysis and is applicable in more cases than is the weak form. Birkhoff developed his own theory of gravitation after Albert Einstein had developed his, and he constructed a mathematical theory of aesthetics, which he applied to art, music, and poetry. All this internationally renowned creative work stimulated further scientific discoveries. Birkhoff served as president of the American Mathematical Society (192426), as dean of the Harvard faculty of arts and sciences (193539), and as president of the American Association for the Advancement of Science (193637). His works include Relativity and Modern Physics (1923), Dynamical Systems (1928), Aesthetic Measure (1933), and Basic Geometry (1941; with Ralph Beatley).