Marshall H. Stone
Marshall Harvey Stone | |
---|---|
Born | April 8, 1903 New York City,U.S. |
Died | January 9, 1989 | (aged 85)
Education | Harvard University(BA,PhD) |
Known for | Stone duality Stone functor Stone space Stone's theorem on one-parameter unitary groups Stone's representation theorem for Boolean algebras Stone–von Neumann theorem Stone–Čech compactification Stone–Weierstrass theorem Banach–Stone theorem Glivenko–Stone theorem |
Awards | National Medal of Science(1982) Gibbs Lecture(1956) ICM Speaker(1936) |
Scientific career | |
Fields | Real analysis,Functional analysis,Boolean algebra,Topology |
Institutions | Harvard University University of Chicago University of Massachusetts Amherst |
Thesis | Ordinary Linear Homogeneous Differential Equations of Order n and the Related Expansion Problems(1926) |
Doctoral advisor | G. D. Birkhoff |
Doctoral students |
![](https://upload.wikimedia.org/wikipedia/commons/thumb/2/21/Marshall_Stone_ICM_1950_letter.jpg/220px-Marshall_Stone_ICM_1950_letter.jpg)
Marshall Harvey Stone(April 8, 1903 – January 9, 1989) was an American mathematician who contributed toreal analysis,functional analysis,topologyand the study ofBoolean algebras.
Biography[edit]
Stone was the son ofHarlan Fiske Stone,who was theChief Justice of the United Statesin 1941–1946. Marshall Stone's family expected him to become a lawyer like his father, but he became enamored of mathematics while he was an undergraduate atHarvard University,where he was a classmate of future judgeHenry Friendly.He completed aPhDthere in 1926, with a thesis ondifferential equationsthat was supervised byGeorge David Birkhoff.[1]Between 1925 and 1937, he taught at Harvard,Yale University,andColumbia University.Stone was promoted to a full professor at Harvard in 1937.
DuringWorld War II,Stone did classified research as part of the "Office of Naval Operations" and the "Office of the Chief of Staff" of theUnited States Department of War.In 1946, he became the chairman of the Mathematics Department at theUniversity of Chicago,a position that he held until 1952. While chairman, Stone hired several notable mathematicians includingPaul Halmos,André Weil,Saunders Mac Lane,Antoni Zygmund,andShiing-Shen Chern.He remained on the faculty at this university until 1968, after which he taught at theUniversity of Massachusetts Amherstuntil 1980.
In 1989, Stone died inMadras, India(now referred to as Chennai), due to a stroke. Following his death, many mathematicians praised Stone for his contributions to various mathematical fields. For instance, University of Massachusetts Amherst mathematician Larry Mann claimed that "Professor Stone was one of the greatest American mathematicians of this century," while Mac Lane described how Stone made the University of Chicago mathematics department the "best department in mathematics in the country in that period."[2]
Accomplishments[edit]
Stone made several advances in the 1930s:
- In 1930, he proved theStone–von Neumannuniqueness theorem.
- In 1932, he published a 662 page long monograph titledLinear transformations inHilbert spaceand their applications to analysis,which was a presentation aboutself-adjoint operators.Much of its content is now deemed to be part offunctional analysis.
- In 1932, he proved conjectures byHermann Weylonspectral theory,arising from the application ofgroup theorytoquantum mechanics.
- In 1934, he published two papers setting out what is now calledStone–Čech compactificationtheory. This theory grew out of his attempts to understand more deeply his results on spectral theory.
- In 1936, he published a long paper that includedStone's representation theorem for Boolean algebras,an important result inmathematical logic,topology,universal algebraandcategory theory.The theorem has been the starting point for what is now calledStone duality.
- In 1937, he published theStone–Weierstrass theoremwhich generalizedWeierstrass's theorem on the uniform approximation of continuous functions by polynomials.
Stone was elected to theAmerican Academy of Arts and Sciencesin 1933 and theNational Academy of Sciences(United States) in 1938.[3][4]He was elected to theAmerican Philosophical Societyin 1943.[5]He presided over theAmerican Mathematical Society,1943–44, and theInternational Mathematical Union,1952–54. In 1982, he was awarded theNational Medal of Science.[6]
Selected publications[edit]
- Stone, M. H. (1926)."A comparison of the series of Fourier and Birkhoff".Trans. Amer. Math. Soc.28(4): 695–761.doi:10.1090/s0002-9947-1926-1501372-6.MR1501372.
- Linear transformations in Hilbert space and their applications to analysis.New York: American Mathematical Society. 1932.[7]
- Stone, M. H. (1934)."Boolean algebras and their applications to topology".Proc Natl Acad Sci U S A.20(3): 197–202.Bibcode:1934PNAS...20..197S.doi:10.1073/pnas.20.3.197.PMC1076376.PMID16587875.
- The theory of real functions.Ann Arbor: Edwards Brothers. 1940.
- Stone, Marshall H. (1957)."Mathematics and the future of science".Bull. Amer. Math. Soc.63(2): 61–76.doi:10.1090/s0002-9904-1957-10098-6.MR0086013.
- Lectures on preliminaries to functional analysis.Madras: Institute of Mathematical Sciences. 1963. Notes by B. Ramachandran
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:CS1 maint: postscript (link)(50 pages)
See also[edit]
References[edit]
- ^"Marshall Stone - The Mathematics Genealogy Project".genealogy.math.ndsu.nodak.edu.Retrieved2024-01-09.
- ^Kolata, Gina."M.H. Stone, Acclaimed Mathematician, Dies at 85".New York Times.
- ^"Marshall Harvey Stone".American Academy of Arts & Sciences.Retrieved2023-04-14.
- ^"Marshall H. Stone".nasonline.org.Retrieved2023-04-14.
- ^"APS Member History".search.amphilsoc.org.Retrieved2023-04-14.
- ^National Science Foundation - The President's National Medal of Science
- ^Hille, Einar(1934)."Review:Linear transformations in Hilbert space and their applications to analysis,by M. H. Stone ".Bull. Amer. Math. Soc.40(11): 777–780.doi:10.1090/s0002-9904-1934-05973-1.
External links[edit]
- O'Connor, John J.;Robertson, Edmund F.,"Marshall H. Stone",MacTutor History of Mathematics Archive,University of St Andrews
- Johnstone, Peter (1982).Stone Spaces.Cambridge:Cambridge University Press.ISBN0-521-23893-5.
- 1903 births
- 1989 deaths
- 20th-century American mathematicians
- Harvard University alumni
- Yale University faculty
- Columbia University faculty
- Harvard University Department of Mathematics faculty
- Harvard University faculty
- Members of the United States National Academy of Sciences
- National Medal of Science laureates
- University of Chicago faculty
- University of Massachusetts Amherst faculty
- Presidents of the American Mathematical Society
- Presidents of the International Mathematical Union
- Members of the American Philosophical Society