# George David Birkhoff

George David Birkhoff | |
---|---|

George David Birkhoff | |

Born |
Overisel Township, Michigan | March 21, 1884

Died |
November 12, 1944 60) Cambridge, Massachusetts | (aged

Nationality | American |

Alma mater | University of Chicago |

Known for |
Ergodic theorem Birkhoff's axioms |

Awards |
Bôcher Memorial Prize (1923) Newcomb Cleveland Prize (1926) |

Scientific career | |

Fields | Mathematics |

Institutions |
Harvard University Yale University Princeton University Radcliffe College |

Doctoral advisor | E. H. Moore |

Doctoral students |
Clarence Adams Raymond Brink Robert D. Carmichael Bernard Koopman Rudolph Langer Charles Morrey Marston Morse G. Baley Price I. M. Sheffer Marshall H. Stone Joseph L. Walsh Hassler Whitney David Widder Kenneth Williams |

**George David Birkhoff** (March 21, 1884 – November 12, 1944) was an American mathematician best known for what is now called the ergodic theorem. Birkhoff was one of the most important leaders in American mathematics in his generation, and during his time he was considered by many to be the preeminent American mathematician.^{[1]}

The George D. Birkhoff House, his residence in Cambridge, Massachusetts, has been designated a National Historic Landmark.

## Personal life

He was born in Overisel Township, Michigan,^{[2]} the son of David Birkhoff and Jane Gertrude Droppers.^{[3]} The mathematician Garrett Birkhoff (1911–1996) was his son.

## Career

Birkhoff obtained his A.B. and A.M. from Harvard University. He completed his Ph.D. in 1907, on differential equations, at the University of Chicago. While E. H. Moore was his supervisor, he was most influenced by the writings of Henri Poincaré. After teaching at the University of Wisconsin–Madison and Princeton University, he taught at Harvard from 1912 until his death.

### Awards and honors

In 1923, he was awarded the inaugural Bôcher Memorial Prize by the American Mathematical Society for his paper in 1917 containing, among other things, what is now called the Birkhoff curve shortening process.^{[4]}

He was elected to the National Academy of Sciences, the American Philosophical Society, the American Academy of Arts and Sciences, the Académie des Sciences in Paris, the Pontifical Academy of Sciences,^{[5]} and the London and Edinburgh Mathematical Societies.

The George David Birkhoff Prize in applied mathematics is awarded jointly by the American Mathematical Society and the Society for Industrial and Applied Mathematics in his honor.

### Service

- Vice-president of the American Mathematical Society, 1919.
- President of the American Mathematical Society, 1925–1926.
- Editor of Transactions of the American Mathematical Society, 1920–1924.

## Work

In 1912, attempting to solve the four color problem, Birkhoff introduced the chromatic polynomial. Even though this line of attack did not prove fruitful, the polynomial itself became an important object of study in algebraic graph theory.

In 1913, he proved Poincaré's "Last Geometric Theorem," a special case of the three-body problem, a result that made him world-famous. In 1927, he published his *Dynamical Systems*. He wrote on the foundations of relativity and quantum mechanics, publishing (with R. E. Langer) the monograph *Relativity and Modern Physics* in 1923. In 1923, Birkhoff also proved that the Schwarzschild geometry is the unique spherically symmetric solution of the Einstein field equations. A consequence is that black holes are not merely a mathematical curiosity, but could result from any spherical star having sufficient mass.

Birkhoff's most durable result has been his 1931 discovery of what is now called the ergodic theorem. Combining insights from physics on the ergodic hypothesis with measure theory, this theorem solved, at least in principle, a fundamental problem of statistical mechanics. The ergodic theorem has also had repercussions for dynamics, probability theory, group theory, and functional analysis. He also worked on number theory, the Riemann–Hilbert problem, and the four colour problem. He proposed an axiomatization of Euclidean geometry different from Hilbert's (see Birkhoff's axioms); this work culminated in his text *Basic Geometry* (1941).

In his later years, Birkhoff published two curious works. His 1933 *Aesthetic Measure* proposed a mathematical theory of aesthetics.^{[6]} While writing this book, he spent a year studying the art, music and poetry of various cultures around the world. His 1938 *Electricity as a Fluid* combined his ideas on philosophy and science. His 1943 theory of gravitation is also puzzling since Birkhoff knew (but didn't seem to mind) that his theory allows as sources only matter which is a perfect fluid in which the speed of sound must equal the speed of light.

## Influence on hiring practices

Albert Einstein and Norbert Wiener, among others, accused^{[7]}^{[8]} Birkhoff of advocating anti-Semitic hiring practices. During the 1930s, when many Jewish mathematicians fled Europe and tried to obtain jobs in the USA, Birkhoff is alleged to have influenced the hiring process at American institutions to exclude Jews. Birkhoff's anti-Semitic views and remarks are well-documented,^{[9]} but Saunders Mac Lane has argued that Birkhoff's efforts were motivated less by animus towards Jews than by a desire to find jobs for home-grown American mathematicians.^{[10]}

However, Birkhoff took a particular liking to certain Jewish mathematicians, including Stanislaw Ulam. Gian-Carlo Rota writes: "Like other persons rumored to be anti-Semitic, he would occasionally feel the urge to shower his protective instincts on some good-looking young Jew. Ulam's sparkling manners were diametrically opposite to Birkhoff's hard-working, aggressive, touchy personality. Birkhoff tried to keep Ulam at Harvard, but his colleagues balked at the idea."^{[11]}

## Selected publications

- Birkhoff, George David (1912). "A determinant formula for the number of ways of coloring a map".
*Ann. Math*.**14**: 42–46. doi:10.2307/1967597. - Birkhoff, George David (1913). "Proof of Poincaré's geometric theorem".
*Trans. Amer. Math. Soc*.**14**: 14–22. doi:10.1090/s0002-9947-1913-1500933-9. - Birkhoff, George David (1917). "Dynamical Systems with Two Degrees of Freedom".
*Trans. Amer. Math. Soc*.**18**: 199–300. doi:10.1090/s0002-9947-1917-1501070-3. PMC 1091243. - Birkhoff, George David and Ralph Beatley. 1959.
*Basic Geometry,*3rd ed. Chelsea Publishing Co. [Reprint: American Mathematical Society, 2000. ISBN 978-0-8218-2101-5]

## See also

## Notes

- ↑ Morse, Marston (1946). "George David Birkhoff and his mathematical work".
*Bulletin of the American Mathematical Society*.**52**(5, Part 1): 357–391. doi:10.1090/s0002-9904-1946-08553-5. MR 0016341. - ↑ "Former Fellows of The Royal Society of Edinburgh" (PDF).
- ↑ Hockey, Thomas (2009).
*The Biographical Encyclopedia of Astronomers*. Springer Publishing. ISBN 978-0-387-31022-0. Retrieved August 22, 2012. - ↑ Birkhoff, George D. (1917). "Dynamical systems with two degrees of freedom".
*Transactions of the American Mathematical Society*. American Mathematical Society.**18**(2): 199–300. doi:10.2307/1988861. JSTOR 1988861. PMC 1091243. - ↑ "George David Birkhoff". Casinapioiv.va. Retrieved 2012-08-17.
- ↑ Cucker, Felix (2013).
*Manifold Mirrors: The Crossing Paths of the Arts and Mathematics*. Cambridge University Press. pp. 116–120. ISBN 978-0-521-72876-8. - ↑ Nadis, Steve; Yau, Shing-Tung (2014).
*A History in Sum*. Harvard University Press. - ↑ "Math and Anti-Semitism Went Hand-in-Hand at Harvard for Decades -- (Note: While this may be a tertiary source, it clearly mentions, in detail, by way of reference [see the quote] a book that is a reliable secondary source ["A History in Sum," a new account of mathematics teaching at Harvard -- published by Harvard University Press].)". Archived from the original on January 12, 2014. Retrieved January 12, 2014.
[QUOTE:] For over three decades, the math department at Harvard was ruled by a man whom Albert Einstein called “one of the world’s great anti-Semites.” This is one of the key revelations in “A History in Sum,” a new account of mathematics teaching at Harvard published by Harvard University Press. Co-authored by science journalist Steve Nadis and current Harvard math professor Shing-Tung Yau, “A History in Sum” describes how George Birkhoff reigned over the Harvard department from 1912 to 1944. Birkhoff, an American of Dutch origin, was instrumental in preventing Jewish mathematicians from being hired. It may seem counterintuitive that a Harvard professor would shed light on this shameful legacy in a book published by the university’s own press, but Yau is a veteran whistle-blower who has frequently criticized academic corruption and educational abuses in his native China.

- ↑ Siegmund-Schultze, Reinhard (2001),
*Rockefeller and the Internationalization of Mathematics Between the Two Worlds Wars: Documents and Studies for the Social History of Mathematics in the 20th Century*, Progress in Mathematics,**25**, Springer, p. 200, ISBN 9783764364687,The most blatant utterances of anti-semitism among mathematicians came from George David Birkhoff

. - ↑ Eisenberg, Ted (2008), "Reaction to the reactors",
*The Montana Mathematics Enthusiast*,**5**(1): 37–44. - ↑
*From cardinals to chaos: reflections on the life and legacy of Stanislaw Ulam*, Necia Grant Cooper, Roger Eckhardt, Nancy Shera, CUP Archive, 1989, Chapter:*The Lost Cafe*by Gian-Carlo Rota, page 26

## References

- Aubin, David, 2005, "Dynamical systems" in Grattan-Guinness, I., ed.,
*Landmark Writings in Western Mathematics*. Elsevier: 871–81. - Mac Lane, Saunders (1994). "Jobs in the 1930s and the views of George D. Birkhoff".
*Math. Intelligencer*.**16**: 9–10. doi:10.1007/bf03024350. - Kip Thorne, 19nn.
*Black Holes and Time Warps*. W. W. Norton. ISBN 0-393-31276-3. - Vandiver, H. S. (1963). "Some of my recollections of George David Birkhoff".
*J. Math. Anal. Appl*.**7**: 271–83. doi:10.1016/0022-247x(63)90052-0. - Norbert Wiener, 1956.
*I am a Mathematician*. MIT Press. Especially pp. 27–28. - George D. Birkhoff, Proc Natl Acad Sci U S A. 1943 August; 29(8): 231–239, "Matter, Electricity and Gravitation in Flat Space-Time".

## Further reading

- Morse, Marston (1970–80). "Birkhoff, George David".
*Dictionary of Scientific Biography*.**2**. New York: Charles Scribner's Sons. pp. 143–146. ISBN 978-0-684-10114-9.

## External links

- O'Connor, John J.; Robertson, Edmund F., "George David Birkhoff",
*MacTutor History of Mathematics archive*, University of St Andrews. - George David Birkhoff at the Mathematics Genealogy Project
- Birkhoff's biography − from National Academies Press, by Oswald Veblen.
- National Academy of Sciences Biographical Memoir