William Fogg Osgood (March 10, 1864,

Boston Boston (), officially the City of Boston, is the state capital and most populous city of the Commonwealth of Massachusetts, as well as the cultural and financial center of the New England region of the United States. It is the 24th- mo ...

– July 22, 1943,

Belmont, Massachusetts Belmont is a town in Middlesex County, Massachusetts. It is a western suburb of Boston, Massachusetts, United States; and is part of the Greater Boston metropolitan area. At the time of the 2020 U.S. Census, the town's population stood at 27,29 ...

) was an American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

Education and career

In 1886, he graduated from

Harvard Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...

, where, after studying at the universities of

Göttingen Göttingen (, , ; nds, Chöttingen) is a university city in Lower Saxony, central Germany, the capital of the eponymous district. The River Leine runs through it. At the end of 2019, the population was 118,911. General information The ori ...

(1887–1889) and

Erlangen Erlangen (; East Franconian: ''Erlang'', Bavarian: ''Erlanga'') is a Middle Franconian city in Bavaria, Germany. It is the seat of the administrative district Erlangen-Höchstadt (former administrative district Erlangen), and with 116,062 inha ...

( Ph.D., 1890), he was instructor (1890–1893), assistant professor (1893–1903), and thenceforth

professor Professor (commonly abbreviated as Prof.) is an academic rank at universities and other post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin as a "person who professes". Professo ...

of mathematics. From 1918 to 1922, he was chairman of the department of mathematics at Harvard. He became

professor emeritus ''Emeritus'' (; female: ''emerita'') is an adjective used to designate a retired chair, professor, pastor, bishop, pope, director, president, prime minister, rabbi, emperor, or other person who has been "permitted to retain as an honorary title ...

in 1933. From 1934 to 1936, he was visiting professor of mathematics at

Peking University Peking University (PKU; ) is a public research university in Beijing, China. The university is funded by the Ministry of Education. Peking University was established as the Imperial University of Peking in 1898 when it received its royal charte ...

. From 1899 to 1902, he served as editor of the ''

Annals of Mathematics The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as th ...

'', and in 1905–1906 was president of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meeting ...

, whose ''Transactions'' he edited in 1909–1910.

Contributions

The works of Osgood dealt with

complex analysis Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates Function (mathematics), functions of complex numbers. It is helpful in many branches of mathemati ...

, in particular

conformal mapping In mathematics, a conformal map is a function that locally preserves angles, but not necessarily lengths. More formally, let U and V be open subsets of \mathbb^n. A function f:U\to V is called conformal (or angle-preserving) at a point u_0\in ...

and uniformization of analytic functions, and

calculus of variations The calculus of variations (or Variational Calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions t ...

. He was invited by

Felix Klein Christian Felix Klein (; 25 April 1849 – 22 June 1925) was a German mathematician and mathematics educator, known for his work with group theory, complex analysis, non-Euclidean geometry, and on the associations between geometry and grou ...

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 curve In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight. Intuitively, a curve may be thought of as the trace left by a moving point. This is the definition that a ...

s with positive area, are named after Osgood, who published a paper proving their existence in 1903. Besides his research on analysis, Osgood was also interested in mathematical physics and wrote on the theory of the

gyroscope A gyroscope (from Ancient Greek γῦρος ''gŷros'', "round" and σκοπέω ''skopéō'', "to look") is a device used for measuring or maintaining orientation and angular velocity. It is a spinning wheel or disc in which the axis of rot ...

Awards and honors

In 1904, he was elected to the

National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the Nat ...

Personal

Osgood's cousin, Louise Osgood, was the mother of

Bernard Koopman Bernard Osgood Koopman (January 19, 1900 – August 18, 1981) was a French-born American mathematician, known for his work in ergodic theory, the foundations of probability, statistical theory and operations research. Education and work Af ...

.See his obituary by .

Selected publications

Osgood's books include: *
Introduction to Infinite Series
' (Harvard University Press 1897; third edition, 1906) * (with W. C. Graustein)
Plane and solid analytic geometry
' (Macmillan, NY, 1921) *
Lehrbuch der Funktionentheorie
' (Teubner, Berlin, 1907; second edition, 1912) * ''First Course in Differential and Integral

Calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizati ...

'' (1907; revised edition, 1909) *
Elementary calculus
' (MacMillan, NY, 1921) *
Mechanics
' (MacMillan, NY, 1937)

Notes

References

*. *. * J. L. Coolidge, G. D. Birkhoff & E. C. Kemble (1943) ''William Fogg Osgood'',

Science Science is a systematic endeavor that builds and organizes knowledge in the form of testable explanations and predictions about the universe. Science may be as old as the human species, and some of the earliest archeological evidence ...

98:399–400 (issue #2549). * . *. *. *.

External links

* * {{DEFAULTSORT:Osgood, William Fogg 1864 births 1943 deaths 19th-century American mathematicians 20th-century American mathematicians American science writers Harvard University faculty Harvard University alumni Complex analysts Mathematical analysts Members of the United States National Academy of Sciences Writers from Boston Presidents of the American Mathematical Society Mathematicians from Massachusetts