M. H. Stone
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Marshall Harvey Stone (April 8, 1903 – January 9, 1989) was an American
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...
who contributed to
real analysis In mathematics, the branch of real analysis studies the behavior of real numbers, sequences and series of real numbers, and real functions. Some particular properties of real-valued sequences and functions that real analysis studies include conv ...
,
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 (e.g. inner product, norm, topology, etc.) and the linear functions defined o ...
,
topology In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...
and the study of
Boolean algebra In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values ''true'' and ''false'', usually denoted 1 and 0, whereas i ...
s.


Biography

Stone was the son of
Harlan Fiske Stone Harlan is a given name and a surname which may refer to: Surname * Bob Harlan (born 1936 Robert E. Harlan), American football executive *Bruce Harlan (1926–1959), American Olympic diver *Byron B. Harlan (1886–1949), American politician * Byron ...
, 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 Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of high ...
undergraduate. He completed a Harvard PhD 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 Yale University is a Private university, private research university in New Haven, Connecticut. Established in 1701 as the Collegiate School, it is the List of Colonial Colleges, third-oldest institution of higher education in the United Sta ...
, and
Columbia University Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manhatt ...
. Stone was promoted to a full professor at Harvard in 1937. During
World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposing ...
, 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 The United States Department of War, also called the War Department (and occasionally War Office in the early years), 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 The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private university, private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park, Chicago, Hyde Park neighborhood. The University of Chic ...
, a position that he held until 1952. While chairman, Stone hired several notable mathematicians including
Paul Halmos Paul Richard Halmos ( hu, Halmos Pál; March 3, 1916 – October 2, 2006) was a Hungarian-born American mathematician and statistician who made fundamental advances in the areas of mathematical logic, probability theory, statistics, operator ...
, André Weil,
Saunders Mac Lane Saunders Mac Lane (4 August 1909 – 14 April 2005) was an American mathematician who co-founded category theory with Samuel Eilenberg. Early life and education Mac Lane was born in Norwich, Connecticut, near where his family lived in Taftville ...
,
Antoni Zygmund Antoni Zygmund (December 25, 1900 – May 30, 1992) was a Polish mathematician. He worked mostly in the area of mathematical analysis, including especially harmonic analysis, and he is considered one of the greatest analysts of the 20th century. ...
, and
Shiing-Shen Chern Shiing-Shen Chern (; , ; October 28, 1911 – December 3, 2004) was a Chinese-American mathematician and poet. He made fundamental contributions to differential geometry and topology. He has been called the "father of modern differential geome ...
. He remained on the faculty at this university until 1968, after which he taught at the
University of Massachusetts Amherst The University of Massachusetts Amherst (UMass Amherst, UMass) is a public research university in Amherst, Massachusetts and the sole public land-grant university in Commonwealth of Massachusetts. Founded in 1863 as an agricultural college, ...
until 1980.


Accomplishments

Stone made several advances in the 1930s: *In 1930, he proved the Stone–von Neumann uniqueness theorem. *In 1932, he published a 662 page long monograph titled ''Linear transformations in Hilbert space and their applications to analysis'', which was a presentation about
self-adjoint operator In mathematics, a self-adjoint operator on an infinite-dimensional complex vector space ''V'' with inner product \langle\cdot,\cdot\rangle (equivalently, a Hermitian operator in the finite-dimensional case) is a linear map ''A'' (from ''V'' to its ...
s. Much of its content is now deemed to be part of
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 (e.g. inner product, norm, topology, etc.) and the linear functions defined o ...
. *In 1932, he proved conjectures by Hermann Weyl on
spectral theory In 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 ...
, arising from the application of
group theory In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ...
to
quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistr ...
. *In 1934, he published two papers setting out what is now called
Stone–Čech compactification In the mathematical discipline of general topology, Stone–Čech compactification (or Čech–Stone compactification) is a technique for constructing a universal map from a topological space ''X'' to a compact Hausdorff space ''βX''. The Ston ...
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 Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal ...
,
topology In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...
,
universal algebra Universal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures themselves, not examples ("models") of algebraic structures. For instance, rather than take particular groups as the object of stu ...
and category theory. The theorem has been the starting point for what is now called Stone duality. *In 1937, he published the Stone–Weierstrass theorem which generalized
Weierstrass Karl Theodor Wilhelm Weierstrass (german: link=no, Weierstraß ; 31 October 1815 – 19 February 1897) was a German mathematician often cited as the "father of modern analysis". Despite leaving university without a degree, he studied mathematics ...
'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 The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
, 1943–44, and the
International Mathematical Union The International Mathematical Union (IMU) is an international non-governmental organization devoted to international cooperation in the field of mathematics across the world. It is a member of the International Science Council (ISC) and supports ...
, 1952–54. In 1982, he was awarded the
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 scienc ...
.


Selected publications

* * * * * * (50 pages)


See also

*
Banach–Stone theorem In mathematics, the Banach–Stone theorem is a classical result in the theory of continuous functions on topological spaces, named after the mathematicians Stefan Banach and Marshall Stone. In brief, the Banach–Stone theorem allows one to recove ...
* Glivenko–Stone theorem * Stone duality * Stone–Weierstrass theorem * Stone's representation theorem for Boolean algebras *
Stone's theorem on one-parameter unitary groups In mathematics, Stone's theorem on one-parameter unitary groups is a basic theorem of functional analysis that establishes a one-to-one correspondence between self-adjoint operators on a Hilbert space \mathcal and one-parameter families :(U_)_ o ...
*
Stone–Čech compactification In the mathematical discipline of general topology, Stone–Čech compactification (or Čech–Stone compactification) is a technique for constructing a universal map from a topological space ''X'' to a compact Hausdorff space ''βX''. The Ston ...
* Stone–von Neumann theorem


References


External links

* * {{DEFAULTSORT:Stone, Marshall Harvey 1903 births 1989 deaths 20th-century American mathematicians Harvard University alumni Yale University faculty Columbia University 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