## David Birkhoff [1884-1944] Academic/Scholar

George David Birkhoff was a mathematician whose main field of study during his academic career was focused on the modern theory of dynamical systems. His main accomplishment during his life career was proving the ergodic and geometrical theorems. According to his biographers, he was one of the most important leaders in American mathematics during his generation. During his prime, he was considered by many to be the preeminent American mathematician.

Birkhoff received his Ph. D. degree in mathematics from the University of Chicago in 1907. Prior to his doctoral work he graduated from Harvard University with B.A. and M.A. degrees in mathematics. After having taught at the University of Wisconsin at Madison, and Princeton University for several years, he was appointed to a professorial appointment at Harvard University in 1919. He would remain at Harvard University until his early death from a heart attack in 1944, at the age of 60.

Some of Birkhoff's mathematical contributions are listed below. In 1913, he proved Poincarre's "Last Geometric Theorem", a special case of the three body problem, a result that made him world famous. In 1923, he proved that the Schwarzschild geometry is the unique spherically symmetric solution of the Einstein field equations. A consequence of that theory is that black holes are not merely a mathematical curiosity, but could result from any spherical star having sufficient mass.

As was stated above, in 1931, he made the discovery of what is now the ergodic theorem. The theorem solved a fundamental problem of statistical mechanics, and also had repercussions for probability theory, group theory, and functional analysis. Other theorems for which Birkhoff is well known are the Birkhoff-Grothendieck theorem, the Birkhoff's axioms, the Poincarre-Birkhoff-Witt theorem, Birkhoff interpolation and the equi-distribution theorem.

Birkhoff is the author of a number of books consisting of, "Relativity and Modern Physics", in 1923, "Dynamical Systems", in 1927, "Asthetic Measure", in 1933, "Electricity as a Fluid", in 1938, and "Basic Geometry", in 1941.

Birkhoff served as Dean of Arts and Sciences at Harvard University from 1935 to 1939. During that time period there was quite an influx of German, and mostly Jewish, mathematicians to the United States, because of the rise of the Nazi era in Germany. Apparently, Birkhoff was very protective of maintaining Americans in academic positions at American universities. Since it was also the period of the depression, jobs were scarce, a scarcity that even affected academic positions.

As a result of the above situation, many highly qualified German academics had difficulty finding academic positions at American universities, unless they were of extremely high stature. As a result of the above condition, Einstein accused Birkhoff of being anti-semitic, because of his stance favoring Americans over immigrants for the few academic openings that appeared. Whether the accusation was fair, or unfair, is difficult to determine at this time.

During his academic life, Birkhoff was affiliated with many academic and professional associations. He was a member of the American Association for the Advancement of Science, the American Academy of Arts and Sciences, and the American Mathematical Society, for which he served as president in 1919, and again from 1925 to1926. He was also a member of the American Philosophical Society, the National Academy of Sciences, the Pontificial Academy of Sciences, and he received the French Legion of Honor in 1936. From 1921 to 1924, he was the editor of the Transactions of the Mathematical Society.

Professor George Birkhoff was born in Overisel, Michigan, on March 21, 1884. He married Margaret Elizabeth Grafius on September 2, 1908. The couple had three children, Barbara Birkhoff Paine [1909-1995], Rodney Birkhoff, and Garrett Birkhoff [1911-1996], who also became a mathematician. Birkhoff's parents were David Birkhoff, a physician, and Jane Gertrude Droppers Birkhoff. As was stated above, Birkhoff passed away on November 12, 1944, in Cambridge, Massachusetts.

**REFERENCES**

George David Birkhoff, NNDB, http://www.nndb.com/people/926/000166428/

George David Birkhoff, Wikipedia, http://en.wikipedia.org/wiki/George_David_Birkhoff

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