Information about Marshall Stone

Marshall Harvey Stone (April 8, 1903, New York City – January 9, 1989, Madras India) was an American mathematician who contributed to real analysis, functional analysis, and the study of Boolean algebras.

Life

Stone was the son of Harlan Fiske Stone, Chief Justice of the United States, 1941-46. Marshall’s family expected him to become a lawyer like his father, but he became enamored of mathematics while a Harvard undergraduate. He completed a Harvard Ph.D. in 1926, with a thesis on differential equations supervised by George Birkhoff. Between 1925 and 1937, he taught at Harvard, Yale, and Columbia. He was promoted to full professor at Harvard in 1937.

During World War II Stone did classified research as part of the Office of Naval Operations and the Office of the Chief of Staff of the War Department. In 1946, he became chairman of the mathematics department at the University of Chicago, a post he held until 1952. He remained on the faculty at Chicago until 1968, after which he taught at the University of Massachusetts until 1980.

The department he joined in 1946 was in the doldrums, after having been at the turn of the 20th century arguably the best American mathematics department, thanks to the leadership of Eliakim Hastings Moore. Stone did an outstanding job of making the Chicago department eminent again, mainly by hiring Paul Halmos, André Weil, Saunders Mac Lane, Antoni Zygmund, and Shiing-Shen Chern.

Accomplishments

During the 1930s, Stone did much important work:

• In 1930, he proved the celebrated Stone-von Neumann uniqueness theorem.
• In 1932, he published a classic monograph of 662pp titled Linear transformations in Hilbert space and their applications to analysis, treating of self-adjoint operators. Much of its content is now deemed part of functional analysis.
• In 1932, he proved conjectures by Hermann Weyl on spectral theory, arising from the application of group theory to quantum mechanics.
• In 1934, he published two papers setting out what is now called Stone-Čech compactification theory. This theory grew out of his attempts to understand more deeply his results on spectral theory.
• In 1936, he published a long paper that included Stone's representation theorem for Boolean algebras, an important result in mathematical logic and universal algebra.
• The Stone-Weierstrass theorem substantially generalized Weierstrass's theorem on the uniform approximation of continuous functions by polynomials.

Stone was elected to the National Academy of Sciences (United States) in 1938. He presided over the American Mathematical Society, 1943-44, and the International Mathematical Union, 1952-54.

Students

• Holbrook Mann MacNeille, Harvard University, 1935
• John Williams Calkin, Harvard University, 1937
• William Frederick Eberlein, Harvard University, 1942
• Edwin Hewitt, Harvard University, 1942
• George Whitelaw Mackey, Harvard University, 1942
• Michael Joseph Norris, Harvard University, 1944
• Richard V. Kadison, The University of Chicago, 1950
• John Vernor Finch, The University of Chicago, 1951
• Matthew P. Gaffney, Jr., The University of Chicago, 1951
• Bernard A. Galler, The University of Chicago, 1955
• John J. McKibben, The University of Chicago, 1957
• Royal Bruce Kellogg, The University of Chicago, 1958
• Adam Koranyi, The University of Chicago, 1959
• Christopher Ian Byrnes, University of Massachusetts, Amherst, 1975

See also

• Stone-Weierstrass theorem
• Stone's representation theorem for Boolean algebras
• Stone's theorem on one-parameter unitary groups
• Stone-Čech compactification
• Stone-von Neumann theorem
• Stone-Tukey theorem.

External links

• O'Connor, John J; Edmund F. Robertson "Marshall Harvey Stone". MacTutor History of Mathematics archive.  
• Marshall Harvey Stone at the Mathematics Genealogy Project