# George David Birkhoff

# George David Birkhoff

**1884-1944**

**American Mathematician**

Founder of the modern theory of dynamical systems, which investigates the interrelation of separate motions in individual bodies and their impact on one another, George David Birkhoff is considered one of the most significant mathematicians of the twentieth century. Continuing the work of the distinguished French mathematician Jules Henri Poincaré (1854-1912) on celestial mechanics, he first attracted international attention when in 1913 he proved a geometrical theorem that Poincaré had proposed but not proved. He also made contributions in the study or relativity, quantum mechanics, and the four-color theorem, and developed a mathematical theory of aesthetics.

Birkhoff was born in Oversiel, Michigan, on March 21, 1884, the eldest of six children born to David Birkhoff, a physician, and his wife Jane Droppers Birkhoff. When he was two years old, his family moved to Chicago, where they lived during most of his childhood.

He studied at the Lewis Institute in Chicago, now the Illinois Institute of Technology, from 1896 to 1902, and went on to the University of Chicago. Birkhoff did not remain there long, however: in 1903 he transferred to Harvard University, where he earned his B.A. in 1905. In the following year, he received his M.A.

Birkhoff returned to the University of Chicago to begin work on his doctorate with a thesis on differential equations, which he wrote under the direction of Eliakim Hastings Moore. In 1907, he was awarded his Ph.D. degree with summa cum laude honors.

From 1907 to 1909, Birkhoff taught mathematics at the University of Wisconsin. During this time, he married Margaret Grafius of Chicago, with whom he had three children. In 1909 he took a job as assistant professor at Princeton University, and in 1912, he moved to Harvard, where he continued to teach for the remainder of his career. Among his students were some of the most notable American mathematicians of the later period, including Marston Morse and Marshall Stone.

The year 1912 also marked the death of Poincaré, whose work Birkhoff continued, first by proving Poincaré's geometrical theorem in 1913. The latter concerned the problem of three bodies in celestial mechanics, involving the trajectories and orbits of entities and the effect of their movement on one another. These investigations led him to his contributions in dynamical systems, a field of study for which he laid the foundations by defining and classifying possible types of dynamic motions.

Birkhoff wrote extensively during the 1920s and in following years, producing *Relativity and Modern Physics* (1923), in which he contributed to the growing study of relativity theory; *Dynamical Systems* (1928); *Aesthetic Measure* (1933), in which he applied Pythagorean notions in an attempt to reach a mathematical understanding of beauty; and the textbook *Basic Geometry* (1941). In 1931, he proved the ergodic theorem, concerning the behavior of large dynamical systems, an issue that had confounded physicists for half a century.

Birkhoff received the first Bôcher Memorial Prize from the American Mathematical Society in 1923. An active member of the Society, he served as its vice president in 1919, and its president from 1925 to 1926. He also edited its journal, *Transactions of the American Mathematical Society,* from 1921 to 1924. Birkhoff earned a number of other international awards. On November 12, 1944, Birkhoff died of a heart attack in Cambridge, Massachusetts.

**JUDSON KNIGHT**

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**George David Birkhoff**