He was born in Overisel Township, Michigan,[2] the son of two Dutch immigrants, David Birkhoff, who arrived in the United States in 1870, and Jane Gertrude Droppers.

[4] Birkhoff was part of a generation of American mathematicians who were the first to study entirely within the United States and not participate in academics within Europe.

[4] Being the only American familiar with the three main mathematical institutions within the United States—Chicago, Harvard and Princeton—he was held in high regard by his colleagues.

During his tenure as president of the society, Birkhoff sought to create a lectureship program to travel the United States to promote mathematics.

[5] During his time in Europe, Birkhoff attempted to create links between American and French institutions, especially due to his affection for Paris.

[8] In 1937, he served as president of the American Association for the Advancement of Science, a rare occurrence for mathematicians and was proof of his respect amongst the scientific community.

In 1913, he proved Poincaré's "Last Geometric Theorem,"[10] a special case of the three-body problem, a result that made him world-famous and improved the international recognition of American mathematics.

Combining insights from physics on the ergodic hypothesis with measure theory, this theorem solved, at least in principle, a fundamental problem of statistical mechanics.

During the 1930s, when many Jewish mathematicians fled Europe and tried to obtain positions in the United States, Birkhoff is alleged to have influenced the selection process at American institutions to exclude Jews.

[18] Mac Lane also stated that Birkhoff's efforts were motivated less by animus towards Jews than by a desire to find jobs for home-grown American mathematicians.

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.