Stone, Marshall

Born in New York in the family of US Supreme Court President Harlan F. Stone (1872-1946). He graduated from Harvard University (1922), taught at it for a year, then moved to Columbia University (1925-1927). The dissertation (on differential equations ) was defended at Harvard under the direction of George Birkhoff in 1926. In 1927-1931 he again taught at Harvard University, in 1931-1933 he was a professor at Yale University , in 1933-1946 again at Harvard University (since 1937 - full professor).

During the war years, he performed tasks of the Ministry of War. In 1946-1968 he taught at the Faculty of Mathematics of the University of Chicago (until 1952 he directed it). To improve the quality of teaching, Stone invited outstanding mathematicians to the faculty - Paul Halmos , Andre Weil , Saunders MacLane, Chen Xinsheng .

From 1968 to 1980, Stone taught at the . He died in 1989.

Research in the field of functional analysis (spectral theory of operators), topology, Boolean algebras. He investigated linear transformations in Hilbert space and their application to analysis. Among his most important results are the representation theorem of unitary groups with one parameter , the representation theorem for Boolean algebras, and the approximation theorem (Stone - Weierstrass theorem). He built an abstract theory of Boolean rings ^[7] .

One of the authors of the famous Stone – von Neumann theorem on the uniqueness of the canonical commutation relation between coordinates and momentum (1930). He participated in the reform of the teaching of higher mathematics in the United States.

• 1936 - Guggenheim Scholarship ^[8]
• 1956 - Gibbs Lecture
• 1982 - US National Science Medal in the category "Mathematics, Statistics and Computer Science", "For his original synthesis of analysis, algebra, and topology, the new vital area of ​​functional analysis in modern mathematics" ^[9]

• A comparison of the series of Fourier and Birkhoff (English) // Trans. Amer. Math. Soc. . - 1926. - Vol. 28 , no. 4 . - P. 695-761 . - DOI : 10.1090 / s0002-9947-1926-1501372-6 .
• Linear transformations in Hilbert space and their applications to analysis. - New York: American Mathematical Society, 1932. ^[10]
• Boolean algebras and their applications to topology (English) // Proceedings of the National Academy of Sciences of the United States of America : journal. - 1934. - Vol. 20 , no. 3 . - P. 197-202 . - DOI : 10.1073 / pnas.20.3.197 . - PMID 16587875 .
• The theory of real functions. - Ann Arbor: Edwards Brothers, 1940.
• Mathematics and the future of science (Eng.) // Bull. Amer. Math. Soc. : journal. - 1957. - Vol. 63 , no. 2 . - P. 61—76 . - DOI : 10.1090 / s0002-9904-1957-10098-6 .
• Lectures on preliminaries to functional analysis. - Madras: Institute of Mathematical Sciences, 1963. (50 pages)

Russian translations

• Mathematics and the future of science. (Translated from English by L. A. Markushevich edited by A. I. Markushevich). Mathematical Education, Series 2, 4 (1959), pp. 111–127.

• Weierstrass – Stone Theorem
• Compactification of Stone - Cech

• Bogolyubov A.N. Stone Marshall Harvey // Mathematics. The mechanics. Biographical reference . - Kiev: Naukova Dumka, 1983 .-- 639 p.
• Kurber G. Mathematical Club. International congresses .. - M .: De Agostini, 2014. - 160 p. - (World of Mathematics: in 45 volumes, volume 39). - ISBN 978-5-9774-0734-2 .
• Stone Marshall Harvey // Mathematical Encyclopedic Dictionary. M., Sov. Encyclopedia, 1988.
• Lehto, Olli. Mathematics Without Borders. A History of the International Mathematical Union . - Springer, 1998 .-- xvi + 399 p. - ISBN 0-387-98358-9 .
• Johnstone, Peter. Stone Spaces. - Cambridge: Cambridge University Press , 1982. - ISBN 0-521-23893-5 .

• John J. O'Connor and Edmund F. Robertson . Stone, Marshall (Eng.) - Biography archived by MacTutor .
• Everett Pitcher. History of the Second Fifty Years: American Mathematical Society, 1939-1988 (AMS, 1988).