William Fogg Osgood (March 10, 1864 – July 22, 1943) 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, mathematical structure, structure, space, Mathematica ...

Education and career

William Fogg Osgood was born in

Boston Boston is the capital and most populous city in the Commonwealth (U.S. state), Commonwealth of Massachusetts in the United States. The city serves as the cultural and Financial centre, financial center of New England, a region of the Northeas ...

on March 10, 1864. In 1886, he graduated from

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

, where, after studying at the universities of

Göttingen Göttingen (, ; ; ) is a college town, university city in Lower Saxony, central Germany, the Capital (political), capital of Göttingen (district), the eponymous district. The River Leine runs through it. According to the 2022 German census, t ...

(1887–1889) and

Erlangen Erlangen (; , ) is a Middle Franconian city in Bavaria, Germany. It is the seat of the administrative district Erlangen-Höchstadt (former administrative district Erlangen), and with 119,810 inhabitants (as of 30 September 2024), it is the smalle ...

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

professor Professor (commonly abbreviated as Prof.) is an Academy, academic rank at university, universities and other tertiary education, post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin ...

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

professor emeritus ''Emeritus/Emerita'' () is an honorary title granted to someone who retirement, retires from a position of distinction, most commonly an academic faculty position, but is allowed to continue using the previous title, as in "professor emeritus". ...

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

Peking University Peking University (PKU) is a Public university, public Types of universities and colleges in China#By designated academic emphasis, university in Haidian, Beijing, China. It is affiliated with and funded by the Ministry of Education of the Peop ...

. 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 t ...

'', 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, meetings, ...

, 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 functions of complex numbers. It is helpful in many branches of mathematics, including algebraic ...

, 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\i ...

and uniformization of

analytic function In mathematics, an analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions. Functions of each type are infinitely differentiable, but complex ...

s, 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 Function (mathematics), functions and functional (mathematics), functionals, to find maxima and minima of f ...

. He was invited by

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

to write an article on complex analysis in the '' Enzyklopädie der mathematischen Wissenschaften'', which was later expanded in the book ''Lehrbuch der Funktionentheorie''.

Osgood curve In mathematical analysis, an Osgood curve is a non-self-intersecting curve that has positive area. Despite its area, it is not possible for such a curve to cover any Domain (mathematical analysis), two-dimensional region, distinguishing them from ...

s –

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 ...

s with positive area – are named after Osgood, who published a paper proving their existence in 1903. Besides his research on

analysis Analysis (: analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (38 ...

, Osgood was also interested in

mathematical physics Mathematical physics is the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the de ...

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 (geometry), orientation and angular velocity. It is a spinning wheel or disc in ...

Awards and honors

Osgood was elected to the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (The Academy) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and other ...

in 1899. In 1904, he was elected to the

National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, NGO, 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 ...

. He was elected to the

American Philosophical Society The American Philosophical Society (APS) is an American scholarly organization and learned society founded in 1743 in Philadelphia that promotes knowledge in the humanities and natural sciences through research, professional meetings, publicat ...

in 1915.

Personal life

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 ...

. William Fogg Osgood died at his home in

Belmont, Massachusetts Belmont is a town in Middlesex County, Massachusetts, United States. It is a western suburb of Boston and is part of the Greater Boston metropolitan area. As of the 2020 U.S. census, its population was 27,295, an increase of 10.4% from 2010. H ...

on July 22, 1943.

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 Calculus 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 generalizations of arithmetic operations. Originally called infinitesimal calculus or "the ...

'' (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)

Notes

References

*. *. *

J. L. Coolidge Julian Lowell Coolidge (September 28, 1873 – March 5, 1954) was an American mathematician, historian, a professor and chairman of the Harvard University Mathematics Department. Biography Born in Brookline, Massachusetts, he graduated from Harv ...

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

Science Science is a systematic discipline that builds and organises knowledge in the form of testable hypotheses and predictions about the universe. Modern science is typically divided into twoor threemajor branches: the natural sciences, which stu ...

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 Department of Mathematics faculty Harvard University alumni Complex analysts American mathematical analysts Members of the United States National Academy of Sciences Writers from Boston Presidents of the American Mathematical Society Mathematicians from Massachusetts Members of the American Philosophical Society