mathematics

William Fogg Osgood

William Fogg Osgood is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand William Fogg Osgood rather than just read about it. In short: William Fogg Osgood (March 10, 1864 – July 22, 1943) was an American mathematician. Education and career William Fogg Osgood was born in Boston on March 10, 1864.

Key takeaways

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Reference excerpt

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

Education and career

William Fogg Osgood was born in Boston on March 10, 1864. 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. 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. 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. In 1904, he was elected to the National Academy of Sciences. He was elected to the American Philosophical Society in 1915.

Personal life Osgood's cousin, Louise Osgood, was the mother of Bernard Koopman. William Fogg Osgood died at his home in Belmont, Massachusetts 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 (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

Notes

References American Mathematical Society (2011), "8. William Fogg Osgood (1905–1908)", AMS Presidents: A Timeline, Providence, RI: University of California, Berkeley, retrieved October 31, 2011. Archibald, Raymond Clare (1938), A Semicentennial History of the American Mathematical Society, 1888--1938. Volume I, Providence, RI: American Mathematical Society, p. 262, ISBN 0-8218-0118-X, JFM 64.0004.01, MR 0959537, Zbl 0019.24305 {{citation}}: ISBN / Date incompatibility (help). J. L. Coolidge, G. D. Birkhoff & E. C. Kemble (1943) William Fogg Osgood, Science 98:399–400 (issue #2549). Koopman, Bernard Osgood (March 1944), "William Fogg Osgood—In memoriam", Bulletin of the American Mathematical Society, 50 (3): 139–142, doi:10.1090/s0002-9904-1944-08080-4, MR 0010143, Zbl 0060.01703. Morse, Philip M. (1982), "In Memoriam: Bernard Osgood Koopman, 1900–1981", Operations Research, 30 (3): viii+417–427, doi:10.1287/opre.30.3.417, JSTOR 170181. Osgood, William F. (1903), "A Jordan Curve of Positive Area" (PDF), Transactions of the American Mathematical Society, 4 (1): 107–112, doi:10.1090/S0002-9947-1903-1500628-5, ISSN 0002-9947, JFM 34.0533.02, JSTOR 1986455, MR 1500628. Walsh, J. L. (1973), "History of the Riemann mapping theorem", The American Mathematical Monthly, 80 (3): 270–276, doi:10.1080/00029890.1973.11993266, ISSN 0002-9890, JSTOR 2318448, MR 0323996, Zbl 0273.30003. Walsh, Joseph L. (2002), "William Fogg Osgood", in National Academy of Sciences of the United States of America (ed.), Biographical Memoirs, vol. 81, Washington, D.C.: National Academy Press, pp. 246–257, doi:10.17226/577, ISBN 978-0-309-03391-6. Twenty-Fifth Anniversary Report (Report VII) of the Secretary of the Class of 1886 of Harvard College. The University Press. 1911. pp. 166–167. Retrieved April 17, 2023 – via Internet Archive.. "William F. Osgood". Hartford Courant. Belmont, Massachusetts (published July 24, 1943). AP. July 23, 1943. p. 4. Retrieved April 17, 2023 – via Newspapers.com..

External links O'Connor, John J.; Robertson, Edmund F. (August 2005), "William Fogg Osgood", MacTutor History of Mathematics Archive, University of St Andrews William Fogg Osgood at the Mathematics Genealogy Project This article incorporates text from a publication now in the public domain: Gilman, D. C.; Peck, H. T.; Colby, F. M., eds. (1905). "Osgood, William Fogg". New International Encyclopedia (1st ed.). New York: Dodd, Mead.

Illustrations

William Fogg Osgood: Osgood at Harvard, c. 1886 — Osgood at Harvard, c. 1886

Worked examples

Example 1 — a first encounter with William Fogg Osgood

Start with the simplest possible case. Write down what William Fogg Osgood claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to William Fogg Osgood before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about William Fogg Osgood ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of William Fogg Osgood

In research: William Fogg Osgood appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses William Fogg Osgood in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: William Fogg Osgood is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1864 births, 1943 deaths, 19th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for William Fogg Osgood outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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Frequently asked questions

What is William Fogg Osgood in simple terms?

William Fogg Osgood (March 10, 1864 – July 22, 1943) was an American mathematician. Education and career William Fogg Osgood was born in Boston on March 10, 1864.

Why does William Fogg Osgood matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study William Fogg Osgood?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

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