William Fogg Osgood

William Fogg Osgood (March 10, 1864 – July 22, 1943) was an American mathematician.

William Fogg Osgood
Born	(1864-03-10)March 10, 1864 Boston, Massachusetts
Died	July 22, 1943(1943-07-22) (aged 79) Belmont, Massachusetts
Resting place	Forest Hills Cemetery, Boston
Nationality	American
Alma mater	Harvard University, University of Göttingen, Friedrich-Alexander-University, Erlangen-Nuremberg
Known for	Complex analysis, conformal mapping, calculus of variations
Spouse(s)	Teresa Osgood, Celeste Phelpes Morse
Children	3
Scientific career
Fields	Mathematics
Institutions	Harvard University, Friedrich-Alexander-University, Erlangen-Nuremberg
Doctoral advisor	Max Noether
Doctoral students	David Raymond Curtiss
Signature

Education and career

Osgood at Harvard, c. 1886

William Fogg Osgood was born in Boston on March 10, 1864.^[1] In 1886, he graduated from Harvard, where, after studying at the universities of Göttingen (1887–1889) and Erlangen (Ph.D., 1890), he was instructor (1890–1893), assistant professor (1893–1903), and thenceforth professor of mathematics. From 1918 to 1922, he was chairman of the department of mathematics at Harvard. He became professor emeritus in 1933. From 1934 to 1936, he was visiting professor of mathematics at Peking University.^[2]

From 1899 to 1902, he served as editor of the Annals of Mathematics, and in 1905–1906 was president of the American Mathematical Society, whose Transactions he edited in 1909–1910.

Contributions

The works of Osgood dealt with complex analysis, in particular conformal mapping and uniformization of analytic functions, and calculus of variations. He was invited by Felix Klein to write an article on complex analysis in the Enzyklopädie der mathematischen Wissenschaften, which was later expanded in the book Lehrbuch der Funktionentheorie.

Osgood curves – Jordan curves with positive area – are named after Osgood, who published a paper proving their existence in 1903.^[3]

Besides his research on analysis, Osgood was also interested in mathematical physics and wrote on the theory of the gyroscope.

Awards and honors

Osgood was elected to the American Academy of Arts and Sciences in 1899.^[4] In 1904, he was elected to the National Academy of Sciences.^[5] He was elected to the American Philosophical Society in 1915.^[6]

Personal life

Osgood's cousin, Louise Osgood, was the mother of Bernard Koopman.^[7]

William Fogg Osgood died at his home in Belmont, Massachusetts on July 22, 1943.^[8]

Selected publications

Osgood's books include:

• Introduction to Infinite Series (Harvard University Press 1897; third edition, 1906)
• Lehrbuch der Funktionentheorie (Teubner, Berlin, 1907; second edition, 1912)
• First Course in Differential and Integral Calculus (1907; revised edition, 1909)
• (with W. C. Graustein) Plane and Solid Analytic Geometry (Macmillan, NY, 1921)
• Elementary Calculus (MacMillan, NY, 1921)
• Advanced Calculus (MacMillan, NY, 1925)
• Mechanics (MacMillan, NY, 1937)

See also

• Riemann mapping theorem
• Osgood's lemma
• Osgood–Brown theorem
• Moore–Osgood theorem
• Stieltjes–Osgood theorem