Marshall Harvey Stone
Encyclopedia
Marshall Harvey Stone was an American
mathematician
who contributed to real analysis
, functional analysis
, and the study of Boolean algebras.
, who was the Chief Justice of the United States
in 1941–1946. Marshall Stone’s family expected him to become a lawyer like his father, but he became enamored of mathematics while he was a Harvard University
undergraduate. He completed a Harvard Ph.D.
in 1926, with a thesis on differential equations that was supervised by George David Birkhoff
. Between 1925 and 1937, he taught at Harvard, Yale University
, and Columbia University
. Stone was promoted to a 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 United States Department of War
. In 1946, he became the chairman of the Mathematics Department at the University of Chicago
, a position that he held until 1952. He remained on the faculty at this university 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
.
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. In 1982, he was awarded the National Medal of Science
.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
who contributed to real analysis
Real analysis
Real analysis, is a branch of mathematical analysis dealing with the set of real numbers and functions of a real variable. In particular, it deals with the analytic properties of real functions and sequences, including convergence and limits of sequences of real numbers, the calculus of the real...
, functional analysis
Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
, and the study of Boolean algebras.
Biography
Stone was the son of Harlan Fiske StoneHarlan Fiske Stone
Harlan Fiske Stone was an American lawyer and jurist. A native of New Hampshire, he served as the dean of Columbia Law School, his alma mater, in the early 20th century. As a member of the Republican Party, he was appointed as the 52nd Attorney General of the United States before becoming an...
, who was the Chief Justice of the United States
Chief Justice of the United States
The Chief Justice of the United States is the head of the United States federal court system and the chief judge of the Supreme Court of the United States. The Chief Justice is one of nine Supreme Court justices; the other eight are the Associate Justices of the Supreme Court of the United States...
in 1941–1946. Marshall Stone’s family expected him to become a lawyer like his father, but he became enamored of mathematics while he was a Harvard University
Harvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
undergraduate. He completed a Harvard Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
in 1926, with a thesis on differential equations that was supervised by George David Birkhoff
George David Birkhoff
-External links:* − from National Academies Press, by Oswald Veblen....
. Between 1925 and 1937, he taught at Harvard, Yale University
Yale University
Yale University is a private, Ivy League university located in New Haven, Connecticut, United States. Founded in 1701 in the Colony of Connecticut, the university is the third-oldest institution of higher education in the United States...
, and Columbia University
Columbia University
Columbia University in the City of New York is a private, Ivy League university in Manhattan, New York City. Columbia is the oldest institution of higher learning in the state of New York, the fifth oldest in the United States, and one of the country's nine Colonial Colleges founded before the...
. Stone was promoted to a full Professor at Harvard in 1937.
During World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
, Stone did classified research as part of the "Office of Naval Operations" and the "Office of the Chief of Staff" of the United States Department of War
United States Department of War
The United States Department of War, also called the War Department , was the United States Cabinet department originally responsible for the operation and maintenance of the United States Army...
. In 1946, he became the chairman of the Mathematics Department at the University of Chicago
University of Chicago
The University of Chicago is a private research university in Chicago, Illinois, USA. It was founded by the American Baptist Education Society with a donation from oil magnate and philanthropist John D. Rockefeller and incorporated in 1890...
, a position that he held until 1952. He remained on the faculty at this university until 1968, after which he taught at the University of Massachusetts
University of Massachusetts
This article relates to the statewide university system. For the flagship campus often referred to as "UMass", see University of Massachusetts Amherst...
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
E. H. Moore
Eliakim Hastings Moore was an American mathematician.-Life:Moore, the son of a Methodist minister and grandson of US Congressman Eliakim H. Moore, discovered mathematics through a summer job at the Cincinnati Observatory while in high school. He learned mathematics at Yale University, where he was...
. Stone did an outstanding job of making the Chicago department eminent again, mainly by hiring Paul Halmos
Paul Halmos
Paul Richard Halmos was a Hungarian-born American mathematician who made fundamental advances in the areas of probability theory, statistics, operator theory, ergodic theory, and functional analysis . He was also recognized as a great mathematical expositor.-Career:Halmos obtained his B.A...
, André Weil
André Weil
André Weil was an influential mathematician of the 20th century, renowned for the breadth and quality of his research output, its influence on future work, and the elegance of his exposition. He is especially known for his foundational work in number theory and algebraic geometry...
, Saunders Mac Lane
Saunders Mac Lane
Saunders Mac Lane was an American mathematician who cofounded category theory with Samuel Eilenberg.-Career:...
, Antoni Zygmund
Antoni Zygmund
Antoni Zygmund was a Polish-born American mathematician.-Life:Born in Warsaw, Zygmund obtained his PhD from Warsaw University and became a professor at Stefan Batory University at Wilno...
, and Shiing-Shen Chern
Shiing-Shen Chern
Shiing-Shen Chern was a Chinese American mathematician, one of the leaders in differential geometry of the twentieth century.-Early years in China:...
.
Accomplishments
During the 1930s, Stone did much important work:- In 1930, he proved the celebrated Stone–von NeumannStone–von Neumann theoremIn mathematics and in theoretical physics, the Stone–von Neumann theorem is any one of a number of different formulations of the uniqueness of the canonical commutation relations between position and momentum operators...
uniqueness theorem. - In 1932, he published a classic monograph 662 pages long titled Linear transformations in Hilbert spaceHilbert spaceThe mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It extends the methods of vector algebra and calculus from the two-dimensional Euclidean plane and three-dimensional space to spaces with any finite or infinite number of dimensions...
and their applications to analysis, a presentation about self-adjoint operatorSelf-adjoint operatorIn mathematics, on a finite-dimensional inner product space, a self-adjoint operator is an operator that is its own adjoint, or, equivalently, one whose matrix is Hermitian, where a Hermitian matrix is one which is equal to its own conjugate transpose...
s. Much of its content is now deemed to be part of functional analysisFunctional analysisFunctional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
. - In 1932, he proved conjectures by Hermann WeylHermann WeylHermann Klaus Hugo Weyl was a German mathematician and theoretical physicist. Although much of his working life was spent in Zürich, Switzerland and then Princeton, he is associated with the University of Göttingen tradition of mathematics, represented by David Hilbert and Hermann Minkowski.His...
on spectral theorySpectral theoryIn mathematics, spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue theory of a single square matrix to a much broader theory of the structure of operators in a variety of mathematical spaces. It is a result of studies of linear algebra and the solutions of...
, arising from the application of group theoryGroup theoryIn mathematics and abstract algebra, group theory studies the algebraic structures known as groups.The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces can all be seen as groups endowed with additional operations and...
to quantum mechanicsQuantum mechanicsQuantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
. - In 1934, he published two papers setting out what is now called Stone–Čech compactificationStone–Cech compactificationIn the mathematical discipline of general topology, Stone–Čech compactification is a technique for constructing a universal map from a topological space X to a compact Hausdorff space βX...
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 algebrasStone's representation theorem for Boolean algebrasIn mathematics, Stone's representation theorem for Boolean algebras states that every Boolean algebra is isomorphic to a field of sets. The theorem is fundamental to the deeper understanding of Boolean algebra that emerged in the first half of the 20th century. The theorem was first proved by Stone...
, an important result in mathematical logicMathematical logicMathematical logic is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic. The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics...
and universal algebraUniversal algebraUniversal algebra is the field of mathematics that studies algebraic structures themselves, not examples of algebraic structures....
. - 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 National Academy of Sciences
The National Academy of Sciences is a corporation in the United States whose members serve pro bono as "advisers to the nation on science, engineering, and medicine." As a national academy, new members of the organization are elected annually by current members, based on their distinguished and...
(United States) in 1938. He presided over the American Mathematical Society
American Mathematical Society
The American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
, 1943–44, and the International Mathematical Union
International Mathematical Union
The International Mathematical Union is an international non-governmental organisation devoted to international cooperation in the field of mathematics across the world. It is a member of the International Council for Science and supports the International Congress of Mathematicians...
, 1952–54. In 1982, he was awarded the National Medal of Science
National Medal of Science
The National Medal of Science is an honor bestowed by the President of the United States to individuals in science and engineering who have made important contributions to the advancement of knowledge in the fields of behavioral and social sciences, biology, chemistry, engineering, mathematics and...
.
See also
- Glivenko–Stone theorem
- Stone–Weierstrass theorem
- Stone's representation theorem for Boolean algebrasStone's representation theorem for Boolean algebrasIn mathematics, Stone's representation theorem for Boolean algebras states that every Boolean algebra is isomorphic to a field of sets. The theorem is fundamental to the deeper understanding of Boolean algebra that emerged in the first half of the 20th century. The theorem was first proved by Stone...
- Stone's theorem on one-parameter unitary groupsStone's theorem on one-parameter unitary groupsIn mathematics, Stone's theorem on one-parameter unitary groups is a basic theorem of functional analysis which establishes a one-to-one correspondence between self-adjoint operators on a Hilbert space H and one-parameter families of unitary operators...
- Stone–Čech compactificationStone–Cech compactificationIn the mathematical discipline of general topology, Stone–Čech compactification is a technique for constructing a universal map from a topological space X to a compact Hausdorff space βX...
- Stone–von Neumann theoremStone–von Neumann theoremIn mathematics and in theoretical physics, the Stone–von Neumann theorem is any one of a number of different formulations of the uniqueness of the canonical commutation relations between position and momentum operators...