**William Osgood** was important in bringing the latest ideas of mathematical research to the United States.

- He studied at the Boston Latin School where Benjamin Osgood Peirce taught mathematics for the year 1880-81 but at this stage Osgood was interested in studying the classics.
- However F N Cole and B O Peirce, who had begun teaching at Harvard the year before Osgood entered, persuaded him to study mathematics.
- Osgood graduated with a A.B. in 1886, coming second out of 286 students, then undertook graduate work at Harvard for a year, graduating with a Master's Degree in 1887.
- Cole had attended Klein's lectures at Harvard in 1885-87 on function theory and he persuaded Osgood to go to Göttingen in 1887 and study with Klein.
- Osgood was awarded a Parker Fellowship and set off for Germany in the autumn of 1887 having already an excellent command of the German language and a deep respect for German learning.
- After working with Klein for two years, Osgood wondered if he might not benefit by spending some time at another German University before the end of his three year fellowship.
- Osgood took Tyler's advice and undertook graduate work with Max Noether at Erlangen in 1889.
- There was no spirit of research at Harvard then, except what Osgood himself brought, but a year later Maxime Bôcher joined him there, also a student greatly influenced by Felix Klein, and a man of mathematical background and ideals similar to those of Osgood.
- At Harvard Osgood was an instructor in mathematics from 1890 to 1893 when he was promoted to assistant professor.
- He held this post until 1903 when he was promoted to full professor, being named Perkin Professor of Mathematics in 1913 on the death of the holder of the chair William Elwood Byerly who had taught Osgood as an undergraduate and had then been his colleague for 23 years.
- Osgood's main work was on the convergence of sequences of continuous functions, solutions of differential equations, the calculus of variations and space filling curves.
- Osgood showed that if f(x,y)f (x, y)f(x,y) is merely continuous there exists at least one solution ...
- In 1900 Osgood established, by methods due to H Poincaré, the Riemann mapping theorem, namely that an arbitrary simply connected region of the plane with at least two boundary points, can be mapped uniformly and conformally onto the interior of a circle.
- This theorem remains as Osgood's outstanding single result.
- After he retired from Harvard in 1933, Osgood taught for two years at the National University of Peking.
- Osgood is important in bringing the latest ideas of mathematical research to the United States.

Born 10 March 1864, Boston, Massachusetts, USA. Died 22 July 1943, Belmont, Massachusetts, USA.

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**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive