## Quick Reference

(1884–1944)

US mathematician, who made great contributions to dynamics and other aspects of mathematics.

The son of a physician, Birkhoff was born in Overisl, Michigan, and educated at the University of Chicago, where he obtained his PhD in 1907. After an initial teaching appointment at Princeton, Birkhoff moved to Harvard in 1912, becoming professor of mathematics there in 1919, a post he continued to occupy for the rest of his life.

A powerful mathematician with wide interests, Birkhoff contributed at some time or other to most major areas of his subject. He established his reputation with some drama. The dying Henri Poincaré (1854–1912), the leading mathematician of his generation, had published without proof an important conjecture on the three-body problem. Known variously as Poincaré's unfinished symphony and Poincaré's last theorem, it was proved by Birkhoff shortly after its publication in 1912 and is known as the Poincaré–Birkhoff fixed-point theorem. Birkhoff continued to work in dynamics. He also made significant contributions to the study of differential equations and probability theory.

To nonmathematicians Birkhoff is probably best known as the author of a curious work, Aesthetic Measure (1933). He identified two elements in a work of art, complexity (*C*) and order or symmetry (*O*), and went on to define the aesthetic measure (*M*) of such works. If *M*, *O*, and *C* are treated as measurable variables, he concluded that *M* = *O*/ *C* – ‘the conjecture that the aesthetic measure is determined by the density of order relations in the aesthetic object’. This proposition did not find many supporters, perhaps because it seems that the square turns out to have the highest *M* value.

*Subjects:*
Contemporary History (Post 1945) — Science and Mathematics.