Marshall Stone (director)
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Marshall Harvey Stone (April 8, 1903 – January 9, 1989) was an American mathematician 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 co ...
,
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 (for example, Inner product space#Definition, inner product, Norm (mathematics ...
,
topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...
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 variable (mathematics), variables are the truth values ''true'' and ''false'', usually denot ...
s.


Biography

Stone was the son of
Harlan Fiske Stone Harlan is a given name and a surname which may refer to: Surname * Abram D. Harlan (1833–1908), American politician from Pennsylvania * Bob Harlan (born 1936 Robert E. Harlan), American football executive * Bruce Harlan (1926–1959), America ...
, who was the
Chief Justice of the United States The chief justice of the United States is the chief judge of the Supreme Court of the United States and is the highest-ranking officer of the U.S. federal judiciary. Appointments Clause, Article II, Section 2, Clause 2 of the U.S. Constitution g ...
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 an undergraduate at
Harvard University Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...
, where he was a classmate of future judge
Henry Friendly Henry Jacob Friendly (July 3, 1903 – March 11, 1986) was an American jurist who served as a United States federal judge, federal circuit judge on the United States Court of Appeals for the Second Circuit from 1959 to 1986, and as the court's Ch ...
. He completed a
PhD A Doctor of Philosophy (PhD, DPhil; or ) is a terminal degree that usually denotes the highest level of academic achievement in a given discipline and is awarded following a course of graduate study and original research. The name of the deg ...
there in 1926, with a thesis on differential equations that was supervised by
George David Birkhoff George David Birkhoff (March21, 1884November12, 1944) was one of the top American mathematicians of his generation. He made valuable contributions to the theory of differential equations, dynamical systems, the four-color problem, the three-body ...
. Between 1925 and 1937, he taught at Harvard,
Yale University Yale University is a Private university, private Ivy League research university in New Haven, Connecticut, United States. Founded in 1701, Yale is the List of Colonial Colleges, third-oldest institution of higher education in the United Stat ...
, and
Columbia University Columbia University in the City of New York, commonly referred to as Columbia University, is a Private university, private Ivy League research university in New York City. Established in 1754 as King's College on the grounds of Trinity Churc ...
. Stone was promoted to a full professor at Harvard in 1937. During
World War II World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...
, 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, als ...
. In 1946, he became the chairman of the Mathematics Department at the
University of Chicago The University of Chicago (UChicago, Chicago, or UChi) is a Private university, private research university in Chicago, Illinois, United States. Its main campus is in the Hyde Park, Chicago, Hyde Park neighborhood on Chicago's South Side, Chic ...
, a position that he held until 1952. While chairman, Stone hired several notable mathematicians including
Paul Halmos Paul Richard Halmos (; 3 March 1916 – 2 October 2006) was a Kingdom of Hungary, Hungarian-born United States, American mathematician and probabilist who made fundamental advances in the areas of mathematical logic, probability theory, operat ...
,
André Weil André Weil (; ; 6 May 1906 – 6 August 1998) was a French mathematician, known for his foundational work in number theory and algebraic geometry. He was one of the most influential mathematicians of the twentieth century. His influence is du ...
,
Saunders Mac Lane Saunders Mac Lane (August 4, 1909 – April 14, 2005), born Leslie Saunders MacLane, was an American mathematician who co-founded category theory with Samuel Eilenberg. Early life and education Mac Lane was born in Norwich, Connecticut, near w ...
,
Antoni Zygmund Antoni Zygmund (December 26, 1900 – May 30, 1992) was a Polish-American mathematician. He worked mostly in the area of mathematical analysis, including harmonic analysis, and he is considered one of the greatest analysts of the 20th century. ...
, and
Shiing-Shen Chern Shiing-Shen Chern (; , ; October 26, 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) is a public land-grant research university in Amherst, Massachusetts, United States. It is the flagship campus of the University of Massachusetts system and was founded in 1863 as the ...
until 1980. In 1989, Stone died in
Madras, India Chennai, also known as Madras ( its official name until 1996), is the capital and largest city of Tamil Nadu, the southernmost state of India. It is located on the Coromandel Coast of the Bay of Bengal. According to the 2011 Indian censu ...
(now referred to as Chennai), due to a stroke. Following his death, many mathematicians praised Stone for his contributions to various mathematical fields. For instance, University of Massachusetts Amherst mathematician Larry Mann claimed that "Professor Stone was one of the greatest American mathematicians of this century," while Mac Lane described how Stone made the University of Chicago mathematics department the "best department in mathematics in the country in that period."


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 In mathematics, a Hilbert space is a real number, real or complex number, complex inner product space that is also a complete metric space with respect to the metric induced by the inner product. It generalizes the notion of Euclidean space. The ...
and their applications to analysis'', which was a presentation about
self-adjoint operator In mathematics, a self-adjoint operator on a complex vector space ''V'' with inner product \langle\cdot,\cdot\rangle is a linear map ''A'' (from ''V'' to itself) that is its own adjoint. That is, \langle Ax,y \rangle = \langle x,Ay \rangle for al ...
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 (for example, Inner product space#Definition, inner product, Norm (mathematics ...
. *In 1932, he proved conjectures by
Hermann Weyl Hermann Klaus Hugo Weyl (; ; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist, logician and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, ...
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 operator (mathematics), operators in a variety of mathematical ...
, 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 the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...
. *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 property, universal map from a topological space ''X'' to a Compact space, compact Ha ...
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 In mathematics, Stone's representation theorem for Boolean algebras states that every Boolean algebra is isomorphic to a certain field of sets. The theorem is fundamental to the deeper understanding of Boolean algebra that emerged in the first ha ...
, an important result in
mathematical logic Mathematical logic is the study of Logic#Formal logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic com ...
,
topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...
,
universal algebra Universal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures in general, not specific types of algebraic structures. For instance, rather than considering groups or rings as the object of stud ...
and
category theory Category theory is a general theory of mathematical structures and their relations. It was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Category theory ...
. The theorem has been the starting point for what is now called
Stone duality In mathematics, there is an ample supply of categorical dualities between certain categories of topological spaces and categories of partially ordered sets. Today, these dualities are usually collected under the label Stone duality, since they ...
. *In 1937, he published the
Stone–Weierstrass theorem In mathematical analysis, the Weierstrass approximation theorem states that every continuous function defined on a closed interval (mathematics), interval can be uniform convergence, uniformly approximated as closely as desired by a polynomial fun ...
which generalized
Weierstrass Karl Theodor Wilhelm 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 and trained as a school t ...
's theorem on the uniform approximation of continuous functions by polynomials. Stone was elected to the
American Academy of Arts and Sciences The American Academy of Arts and Sciences (The Academy) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and other ...
in 1933 and the
National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, NGO, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the ...
(United States) in 1938. He was elected to the
American Philosophical Society The American Philosophical Society (APS) is an American scholarly organization and learned society founded in 1743 in Philadelphia that promotes knowledge in the humanities and natural sciences through research, professional meetings, publicat ...
in 1943. 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 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 the International ...
, 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 science, behavior ...
.


Selected publications

* * * * * * (50 pages)


See also

*
Convex space In mathematics, a convex space (or barycentric algebra) is a space in which it is possible to take convex combinations of any sets of points. Formal Definition A convex space can be defined as a set X equipped with a binary convex combination op ...
* Ideals *
Unbounded operator In mathematics, more specifically functional analysis and operator theory, the notion of unbounded operator provides an abstract framework for dealing with differential operators, unbounded observables in quantum mechanics, and other cases. The t ...
*
Stone algebra In mathematics, a Stone algebra or Stone lattice is a pseudocomplemented distributive lattice ''L'' in which any of the following equivalent statements hold for all x, y \in L: * (x\wedge y)^* = x^*\vee y^*; * (x\vee y)^ = x^\vee y^; * x^* \vee x^ ...


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 Department of Mathematics 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 Members of the American Philosophical Society