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We are one of the largest mathematical sciences schools in Australia, and the University of Sydney is the only Australian university to have received the highest rating of 5 out of 5 for research in the mathematical sciences in every Australian Research Council Excellence in Research for Australia assessment to date.
The University's flexible courses allow you to combine mathematics with other areas of interest. Many courses are also offered at an advanced level, so you can choose a program that suits your level of ability and interest.
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.[3][4] Birkhoff's father worked as a physician in Chicago while he was a child.[4] From 1896 to 1902, he would attend the Lewis Institute as a teenager.[4]
During his membership in the American Mathematical Society, Birkhoff served multiple positions in the organization. In 1919, he served as vice president of the society. He was editor of Transactions of the American Mathematical Society from 1920 to 1924.
From 1925 to 1926, he was President of the American Mathematical Society. During his tenure as president of the society, Birkhoff sought to create a lectureship program to travel the United States to promote mathematics.[7] In 1926, he travelled Europe to serve as an unofficial representative if the Rockefeller Foundation's International Education Board.[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 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 Poincar'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.[5]
His 1933 Aesthetic Measure proposed a mathematical theory of aesthetics.[11] 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.
Birkhoff believed that fellowships from foreign nations would improve the mathematic standards in the United States,[12] though he wanted to raise the standards for fellowships, believing that the qualifications in less-developed countries were different and that access should be limited.[13] He also was adamant that foreign fellows be able to meet language requirements.[14]
Albert Einstein and Norbert Wiener, among others, accused[15][16][17] Birkhoff of advocating anti-Semitic selection processes. 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.[16] Saunders Mac Lane, who was at Harvard at the time, would call Einstein's allegations "worthless" as he was not familiar with American processes and that the two had competing ideas regarding general relativity while also rebutting the reports of anti-Semitism against Wiener, writing "Birkhoff clearly listened to Norbert's ideas. There could be many reasons why Birkhoff did not take steps to appoint him".[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.[19]
Birkhoff was also close to Jewish mathematician Stanislaw Ulam. 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. Ulam's sparkling manners were diametrically opposite to Birkhoff's hard-working, aggressive, touchy personality. Birkhoff tried to keep Ulam at Harvard, but his colleagues balked at the idea."[20]
While Birkhoff was subject to as many prejudices as most of us, he kept always what most of us lose as we grow older, the power to see people and events simply and naively rather than with reference to current opinion.
In 1923, he was awarded the inaugural Bcher Memorial Prize by the American Mathematical Society for his paper in 1917 containing, among other things, what is now called the Birkhoff curve shortening process.[21]
He was elected to the National Academy of Sciences, the American Philosophical Society, the American Academy of Arts and Sciences, the Acadmie des Sciences in Paris, the Pontifical Academy of Sciences,[22] and the London and Edinburgh Mathematical Societies.
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