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. 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 .
Read more about this topic: George David Birkhoff
Famous quotes containing the word work:
“No man can call himself liberal, or radical, or even a conservative advocate of fair play, if his work depends in any way on the unpaid or underpaid labor of women at home, or in the office.”
—Gloria Steinem (b. 1934)
“Some are “industrious,” and appear to love labor for its own sake, or perhaps because it keeps them out of worse mischief; to such I have at present nothing to say. Those who would not know what to do with more leisure than they now enjoy, I might advise to work twice as hard as they do,—work till they pay for themselves, and get their free papers.”
—Henry David Thoreau (1817–1862)
““Which is more important to you, your field or your children?” the department head asked. She replied, “That’s like asking me if I could walk better if you amputated my right leg or my left leg.””
—Anonymous Parent. As quoted in Women and the Work Family Dilemma, by Deborah J. Swiss and Judith P. Walker, ch. 2 (1993)