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:
“Having an identity at work separate from an identity at home means that the work role can help absorb some of the emotional shock of domestic distress. Even a mediocre performance at the office can help a person repair self-esteem damaged in domestic battles.”
—Faye J. Crosby (20th century)
“The work of vegetation begins first in the irritability of the bark and leaf-buds.”
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“There is no mystery in a looking glass until someone looks into it. Then, though it remains the same glass, it presents a different face to each man who holds it in front of him. The same is true of a work of art. It has no proper existence as art until someone is reflected in it—and no two will ever be reflected in the same way. However much we all see in common in such a work, at the center we behold a fragment of our own soul, and the greater the art the greater the fragment.”
—Harold C. Goddard (1878–1950)