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Marshall Harvey Stone (April 8, 1903, New York City
New York City

The City of New York is the List of United States cities by population in the United States, while the New York metropolitan area ranks among the List of urban areas by population....
 – January 9, 1989, Madras India
India

India, officially the Republic of India , is a country in South Asia. It is the List of countries and outlying territories by total area country by geographical area, the List of countries by population country, and the most populous liberal democracy in the world....
) was an American
United States

The United States of America is a Federal government constitutional republic comprising U.S. state and a federal district. The country is situated mostly in central North America, where its Contiguous United States and Washington, D.C., the Capital districts and territories, lie between the Pacific Ocean and Atlantic Oceans, Borders of the U...
 mathematician
Mathematician

A mathematician is a person whose primary area of study and/or research is the field of mathematics....
 who contributed to real analysis
Real analysis

Real analysis, or theory of functions of a real variable is a branch of mathematical analysis dealing with the Set of real numbers. In particular, it deals with the analytic function properties of real function and sequences, including convergence and limit s of sequences of real numbers, the calculus of the real numbers, and continu...
, functional analysis
Functional analysis

Functional analysis is the branch of mathematics, and specifically of mathematical analysis, concerned with the study of vector spaces and operators acting upon them....
, and the study of Boolean algebras.

e was the son of Harlan Fiske Stone
Harlan Fiske Stone

Harlan Fiske Stone was an United States lawyer and judge. A native of New Hampshire he served as the dean of Columbia Law School, his alma mater in the early 20th century....
, 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 courts and the chief judge of the Supreme Court of the United States....
 in 1941-1946. Marshall Stone’s family expected him to become a lawyer
Lawyer

A lawyer, according to Black's Law Dictionary, is "a person learned in the law; as an Attorney at law, counsel or solicitor; a person licensed to practice fraud." Law is the system of rules of conduct established by the sovereign government of a society to correct wrongs, maintain stability, and deliver justice....
 like his father, but he became enamored of mathematics while he was a Harvard University
Harvard University

Harvard University is a private university in Cambridge, Massachusetts, Massachusetts, United States, and a member of the Ivy League. Founded in 1636 by the colonial Massachusetts legislature, Harvard is the Colonial Colleges institution of higher learning in the United States....
 undergraduate. He completed a Harvard Ph.D.
Ph.D.

Ph.D. or PHD may stand for:* Doctor of Philosophy, an academic degree* Ph.D. , a 1980s British group* Piled Higher and Deeper, a web comic strip...
 in 1926, with a thesis on differential equations that was supervised by George David Birkhoff
George David Birkhoff

George David Birkhoff was an United States mathematics, best known for what is now called the ergodic theorem. Birkhoff was one of the most important leaders in United States mathematics in his generation, and during his prime he was considered by many to be the preeminent American mathematician....
.






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Marshall Harvey Stone (April 8, 1903, New York City
New York City

The City of New York is the List of United States cities by population in the United States, while the New York metropolitan area ranks among the List of urban areas by population....
 – January 9, 1989, Madras India
India

India, officially the Republic of India , is a country in South Asia. It is the List of countries and outlying territories by total area country by geographical area, the List of countries by population country, and the most populous liberal democracy in the world....
) was an American
United States

The United States of America is a Federal government constitutional republic comprising U.S. state and a federal district. The country is situated mostly in central North America, where its Contiguous United States and Washington, D.C., the Capital districts and territories, lie between the Pacific Ocean and Atlantic Oceans, Borders of the U...
 mathematician
Mathematician

A mathematician is a person whose primary area of study and/or research is the field of mathematics....
 who contributed to real analysis
Real analysis

Real analysis, or theory of functions of a real variable is a branch of mathematical analysis dealing with the Set of real numbers. In particular, it deals with the analytic function properties of real function and sequences, including convergence and limit s of sequences of real numbers, the calculus of the real numbers, and continu...
, functional analysis
Functional analysis

Functional analysis is the branch of mathematics, and specifically of mathematical analysis, concerned with the study of vector spaces and operators acting upon them....
, and the study of Boolean algebras.

Biography

Stone was the son of Harlan Fiske Stone
Harlan Fiske Stone

Harlan Fiske Stone was an United States lawyer and judge. A native of New Hampshire he served as the dean of Columbia Law School, his alma mater in the early 20th century....
, 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 courts and the chief judge of the Supreme Court of the United States....
 in 1941-1946. Marshall Stone’s family expected him to become a lawyer
Lawyer

A lawyer, according to Black's Law Dictionary, is "a person learned in the law; as an Attorney at law, counsel or solicitor; a person licensed to practice fraud." Law is the system of rules of conduct established by the sovereign government of a society to correct wrongs, maintain stability, and deliver justice....
 like his father, but he became enamored of mathematics while he was a Harvard University
Harvard University

Harvard University is a private university in Cambridge, Massachusetts, Massachusetts, United States, and a member of the Ivy League. Founded in 1636 by the colonial Massachusetts legislature, Harvard is the Colonial Colleges institution of higher learning in the United States....
 undergraduate. He completed a Harvard Ph.D.
Ph.D.

Ph.D. or PHD may stand for:* Doctor of Philosophy, an academic degree* Ph.D. , a 1980s British group* Piled Higher and Deeper, a web comic strip...
 in 1926, with a thesis on differential equations that was supervised by George David Birkhoff
George David Birkhoff

George David Birkhoff was an United States mathematics, best known for what is now called the ergodic theorem. Birkhoff was one of the most important leaders in United States mathematics in his generation, and during his prime he was considered by many to be the preeminent American mathematician....
. Between 1925 and 1937, he taught at Harvard, Yale University
Yale University

Yale University is a private university in New Haven, Connecticut. Founded in 1701 as the Collegiate School, Yale is the Colonial Colleges institution of higher education in the United States and is a member of the Ivy League....
, and Columbia University
Columbia University

Columbia University in the City of New York , is a private university in the United States and a member of the Ivy League. Columbia's main campus lies in the Morningside Heights, Manhattan neighborhood in the borough of Manhattan, in New York City....
. 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 military conflict which involved a Participants in World War II, including all of the great powers, organised into two opposing military alliances: the Allies of World War II and the Axis powers....
, 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
University of Chicago

The University of Chicago is a private university located principally in the Hyde Park, Chicago neighborhood of Chicago. Although an older university by the same name existed prior to its founding, the modern University of Chicago credits its founding to the oil magnate John D....
, 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

The University of Massachusetts is the five-campus public university system of the Massachusetts.The system includes University of Massachusetts Amherst, University of Massachusetts Boston, University of Massachusetts Dartmouth , University of Massachusetts Lowell, and the University of Massachusetts Medical School....
 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
Eliakim Hastings Moore

* Eliakim H. Moore - U.S. Congressman from Ohio* E. H. Moore - American mathematician...
. Stone did an outstanding job of making the Chicago department eminent again, mainly by hiring Paul Halmos
Paul Halmos

Paul Richard Halmos was a Hungary-born Jewish United States mathematician who made fundamental advances in the areas of probability theory, statistics, operator theory, ergodic theory, functional analysis , and mathematical logic....
, André Weil
André Weil

Andr? 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....
, Saunders Mac Lane
Saunders Mac Lane

Saunders Mac Lane was an United States mathematician who cofounded category theory with Samuel Eilenberg....
, Antoni Zygmund
Antoni Zygmund

Antoni Zygmund was a Poland born United States mathematician who exerted a major influence on 20th-century mathematics.Born in Warsaw, Zygmund obtained his PhD from Uniwersytet Warszawski , and became a professor at the Vilnius University from 1930 until 1939....
, and Shiing-Shen Chern
Shiing-Shen Chern

Shiing-Shen Chern was a Chinese American mathematician, one of the leaders in differential geometry and topology of the twentieth century....
.

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 662 pages long titled Linear transformations in Hilbert space
    Hilbert space

    The mathematics concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It extends the methods of vector algebra from the two-dimensional plane and three-dimensional space to infinite-dimensional spaces....
     and their applications to analysis    , a presentation about self-adjoint operator
    Self-adjoint operator

    In mathematics, on a finite-dimensional inner product space, a self-adjoint operator is one that is its own Adjoint of an operator, or, equivalently, one whose matrix is Hermitian matrix, 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 analysis
    Functional analysis

    Functional analysis is the branch of mathematics, and specifically of mathematical analysis, concerned with the study of vector spaces and operators acting upon them....
    .
  • In 1932, he proved conjectures by Hermann Weyl
    Hermann Weyl

    Hermann Klaus Hugo Weyl was a Germany mathematician. Although much of his working life was spent in Z?rich, Switzerland and then Princeton, New Jersey, he is associated with the University of G?ttingen tradition of mathematics, represented by David Hilbert and Hermann Minkowski....
     on spectral theory
    Spectral theory

    In mathematics, spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue theory of a single square matrix. The name was introduced by David Hilbert in his original formulation of Hilbert space theory, which was cast in terms of quadratic forms in infinitely many variables....
    , arising from the application of group theory
    Group theory

    In mathematics and abstract algebra, group theory studies the algebraic structures known as group .The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring , field , and vector spaces can all be seen as groups endowed with additional operations and axioms....
     to quantum mechanics
    Quantum mechanics

    Quantum mechanics is a set of principles underlying the most fundamental known description of all physical systems at the microscopic scale . Notable amongst these principles are both a dual wave-like and particle-like behavior of matter and radiation, and prediction of probabilities in situations where classical physics predicts certaintie...
    .
  • In 1934, he published two papers setting out what is now called Stone–Cech compactification
    Stone–Cech compactification

    In the mathematical discipline of general topology, Stone?Cech 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 algebras
    Stone's representation theorem for Boolean algebras

    In 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....
    , an important result in mathematical logic
    Mathematical logic

    Mathematical logic is a subfield of mathematics and logic with close connections to computer science and philosophical logic. The field includes the mathematical study of logic and the applications of formal logic to other areas of mathematics....
     and universal algebra
    Universal algebra

    Universal algebra is the field of mathematics that studies algebraic structures themselves, not examples of algebraic structures.For instance, rather than take particular groups as the object of study, in universal algebra one takes "the theory of groups" as an object of study....
    .
  • The Stone-Weierstrass theorem
    Stone-Weierstrass theorem

    In mathematical analysis, the Weierstrass approximation theorem states that every continuous function defined on an interval [a,b] can be uniform convergence as closely as desired by a polynomial function....
     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."...
 (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 mathematics research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians....
, 1943-44, and the International Mathematical Union
International Mathematical Union

The International Mathematical Union is an international non-governmental organization devoted to international cooperation in the field of mathematics....
, 1952-54.

Major Students on the Doctoral Level

  • Holbrook Mann MacNeille
    Holbrook Mann MacNeille

    Holbrook Mann MacNeille was an United States mathematician who worked for the United States Atomic Energy Commission before becoming the first Executive Director of the American Mathematical Society....
    , Harvard University
    Harvard University

    Harvard University is a private university in Cambridge, Massachusetts, Massachusetts, United States, and a member of the Ivy League. Founded in 1636 by the colonial Massachusetts legislature, Harvard is the Colonial Colleges institution of higher learning in the United States....
    , 1935
  • John Williams Calkin, Harvard University
    Harvard University

    Harvard University is a private university in Cambridge, Massachusetts, Massachusetts, United States, and a member of the Ivy League. Founded in 1636 by the colonial Massachusetts legislature, Harvard is the Colonial Colleges institution of higher learning in the United States....
    , 1937
  • William Frederick Eberlein, Harvard University
    Harvard University

    Harvard University is a private university in Cambridge, Massachusetts, Massachusetts, United States, and a member of the Ivy League. Founded in 1636 by the colonial Massachusetts legislature, Harvard is the Colonial Colleges institution of higher learning in the United States....
    , 1942
  • Edwin Hewitt
    Edwin Hewitt

    Edwin Hewitt was an United States mathematician known for his work in abstract harmonic analysis and for his discovery, in collaboration with Leonard Jimmie Savage, of the Hewitt?Savage zero-one law....
    , Harvard University
    Harvard University

    Harvard University is a private university in Cambridge, Massachusetts, Massachusetts, United States, and a member of the Ivy League. Founded in 1636 by the colonial Massachusetts legislature, Harvard is the Colonial Colleges institution of higher learning in the United States....
    , 1942
  • George Whitelaw Mackey, Harvard University
    Harvard University

    Harvard University is a private university in Cambridge, Massachusetts, Massachusetts, United States, and a member of the Ivy League. Founded in 1636 by the colonial Massachusetts legislature, Harvard is the Colonial Colleges institution of higher learning in the United States....
    , 1942
  • Michael Joseph Norris, Harvard University
    Harvard University

    Harvard University is a private university in Cambridge, Massachusetts, Massachusetts, United States, and a member of the Ivy League. Founded in 1636 by the colonial Massachusetts legislature, Harvard is the Colonial Colleges institution of higher learning in the United States....
    , 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
    Bernard Galler

    Bernard A. Galler was an American mathematician and computer scientist at the University of Michigan who was involved in the development of large-scale operating systems and computer languages including the MAD programming language and the Michigan Terminal System operating system....
    , 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-Weierstrass theorem

    In mathematical analysis, the Weierstrass approximation theorem states that every continuous function defined on an interval [a,b] can be uniform convergence as closely as desired by a polynomial function....
  • Stone's representation theorem for Boolean algebras
    Stone's representation theorem for Boolean algebras

    In 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....
  • Stone's theorem on one-parameter unitary groups
    Stone's theorem on one-parameter unitary groups

    In mathematics, Stone's theorem on one-parameter group 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–Cech compactification
    Stone–Cech compactification

    In the mathematical discipline of general topology, Stone?Cech compactification is a technique for constructing a universal map from a topological space X to a compact Hausdorff space βX....
  • Stone-von Neumann theorem


External links