# Marshall Harvey Stone

**Marshall Harvey Stone** (born April 8, 1903 in New York City , † January 9, 1989 in Madras , India ) was an American mathematician who mainly dealt with functional analysis .

## life and work

Stone attended school in Englewood ( New Jersey ) and studied at Harvard from 1919 . After completing his bachelor's degree in law, he switched to mathematics, which was made palatable to him through a probationary period as an instructor in 1922/23. In 1926 he received his doctorate under George David Birkhoff with a thesis on ordinary differential equations and development according to orthogonal function systems. In 1925 he became an instructor at Columbia University and in 1927 again at Harvard, where he became an associate professor in 1928. After a period from 1931 to 1933 as an associate professor at Yale , he became an associate professor in 1933 and a professor at Harvard in 1937. From 1928 he worked on self adjoint operators in Hilbert spaces , about which his book *Linear Transformations in Hilbert Space and their Applications to Analysis* appeared in 1932 . He himself coined the term self-adjoint operator. In 1930 he published the famous *Stone von Neumann theorem* in the *Proceedings of the National Academy of Sciences* (which, however, was not included in his 1932 monograph due to lack of space).

Then Stone dealt with spectral theory and the problems arising there from the group-theoretical treatment of quantum mechanics by Hermann Weyl . In 1933 he was elected to the American Academy of Arts and Sciences . In 1934 he published work on Boolean algebras that included the Stone-Čech compactification . He also extended the approximation of continuous functions by polynomials by Karl Weierstrass to the Stone-Weierstrass theorem. In 1942/43 he worked for the *Office of Naval Operations* and then for the General Staff during World War II . In 1946 he moved to the University of Chicago , where he became faculty chair. There he wanted above all to raise the level of research and made sure that André Weil , Saunders Mac Lane , Antoni Zygmund and Shiing-Shen Chern came to Chicago. In 1952 he gave up the chairmanship of the faculty in favor of Mac Lane, but stayed in Chicago until his retirement in 1968. He was then a professor at the University of Massachusetts until 1980 (from 1973 only part-time).

In the 1950s, Marshall Stone was an energetic advocate of the Bourbaki movement (which was one of the reasons why he brought Weil to the university) and associated it with New Mathematics .

In 1938 he was elected to the National Academy of Sciences and in 1943 to the American Philosophical Society . In 1943/44 he was President of the American Mathematical Society . In 1956 he was a Gibbs lecturer . From 1952 to 1954 he was President of the International Mathematical Union . From 1961 to 1967 he was President of the International Committee of Mathematical Instruction.

Stone loved to travel and was on a trip to India at the time of his death.

## Namesake

Among the results that bear Stone's name are

- the set of Stone-von Neumann
- the Stone-Weierstrass theorem
- the Stone-Čech compacting
- Stones notation set for Boolean algebras
- the set of Stone-Tukey (along with John Tukey )
- the set of Daniell-Stone (supplemented the set of Percy John Daniell in 1948 to an important prerequisite)
- the set of Stone
- the Banach-Stone theorem

## family

Stone's father was the lawyer Harlan Fiske Stone , who was a judge on the US Supreme Court for 21 years , including between 1941 and 1946 as Chief Justice ; his mother was Agnes Harvey Stone (1873-1958).

Stone was married twice. The first marriage between 1927 and 1962 had three children.

## Fonts

- Linear transformations in Hilbert space and their applications to analysis, American Mathematical Society 1932
- Theory of real functions, Ann Arbor 1940
- Linear Transformations in Hilbert Space. III. Operational Methods and Group Theory, Proceedings of the National Academy of Sciences (USA), Volume 16, 1930, pp. 172-175
- On one-parameter unitary groups in Hilbert Space, Annals of Mathematics, Volume 33, 1932, pp. 643-648

## Web links

- John J. O'Connor, Edmund F. Robertson :
*Marshall Harvey Stone.*In:*MacTutor History of Mathematics archive .*

personal data | |
---|---|

SURNAME | Stone, Marshall Harvey |

BRIEF DESCRIPTION | American mathematician and university professor |

DATE OF BIRTH | April 8, 1903 |

PLACE OF BIRTH | New York City |

DATE OF DEATH | January 9, 1989 |

Place of death | Madras , India |