E. H. Moore
Encyclopedia
Eliakim Hastings Moore (January 26, 1862 – December 30, 1932) was an American mathematician
.
, discovered mathematics through a summer job at the Cincinnati Observatory while in high school. He learned mathematics at Yale University
, where he was a member of Skull and Bones
and obtained a B.A. in 1883 and the Ph.D. in 1885 with a thesis, supervised by Hubert Anson Newton
, on some work of William Kingdon Clifford
and Arthur Cayley
. Newton encouraged Moore to study in Germany, and thus he spent an academic year at the University of Berlin, attending lectures by Kronecker and Weierstrass.
On his return to the United States, Moore taught at Yale and at Northwestern University
. When the University of Chicago
opened its doors in 1892, Moore was the first head of its mathematics department, a position he retained until his death in 1931. His first two colleagues were Bolza and Maschke. The resulting department was the second research-oriented mathematics department in American history, after Johns Hopkins University
.
, proving in 1893 the classification of the structure of finite fields (also called Galois fields). Around 1900, he began working on the foundations of geometry
. He reformulated Hilbert's axioms
for geometry so that point
s were the only primitive notion
, thus turning Hilbert
's primitive lines and planes into defined notions. In 1902, he further showed that one of Hilbert's axioms for geometry was redundant. Independently, the twenty year old R.L. Moore (no relation) also proved this, but in a more elegant fashion than E. H. Moore used. When E. H. Moore heard of the feat, he arranged for a scholarship that would allow R.L. Moore to study for a doctorate at Chicago. E.H. Moore's work on axiom systems is considered one of the starting points for metamathematics
and model theory
. After 1906, he turned to the foundations of analysis
. The concept of closure operator
first appeared in his 1910 Introduction to a form of general analysis. He also wrote on algebraic geometry
, number theory
, and integral equations.
At Chicago, Moore supervised 31 doctoral dissertations, including those of George Birkhoff, Leonard Dickson, Robert Lee Moore
(no relation), and Oswald Veblen
. Birkhoff and Veblen went on to forge and lead the first-rate departments at Harvard and Princeton, respectively. Dickson became the first great American algebraist and number theorist. Robert Moore founded American topology. According to the Mathematics Genealogy Project
, as of January 2011, E. H. Moore had over 14,900 known "descendants."
Moore convinced the New York Mathematical Society to change its name to the American Mathematical Society
, whose Chicago branch he led. He presided over the AMS, 1901–02, and edited the Transactions of the American Mathematical Society, 1899–1907. He was elected to the National Academy of Sciences
, the American Academy of Arts and Sciences
, and the American Philosophical Society
.
The American Mathematical Society
established a prize in his honor in 2002.
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....
.
Life
Moore, the son of a Methodist minister and grandson of US Congressman Eliakim H. MooreEliakim H. Moore
Eliakim Hastings Moore was a U.S. Representative from Ohio.Born to David & Dolly Moore in Boylston, Massachusetts, and moved with his parents to Marietta and thence to Athens County, Ohio, in 1817....
, discovered mathematics through a summer job at the Cincinnati Observatory while in high school. He learned mathematics at 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...
, where he was a member of Skull and Bones
Skull and Bones
Skull and Bones is an undergraduate senior or secret society at Yale University, New Haven, Connecticut. It is a traditional peer society to Scroll and Key and Wolf's Head, as the three senior class 'landed societies' at Yale....
and obtained a B.A. in 1883 and the Ph.D. in 1885 with a thesis, supervised by Hubert Anson Newton
Hubert Anson Newton
Hubert Anson Newton was an American astronomer and mathematician, noted for his research on meteors.He was born at Sherburne, New York, and graduated from Yale in 1850. The Mathematics Genealogy Project lists his advisor as Michel Chasles. In 1855, he was appointed professor of mathematics at Yale...
, on some work of William Kingdon Clifford
William Kingdon Clifford
William Kingdon Clifford FRS was an English mathematician and philosopher. Building on the work of Hermann Grassmann, he introduced what is now termed geometric algebra, a special case of the Clifford algebra named in his honour, with interesting applications in contemporary mathematical physics...
and Arthur Cayley
Arthur Cayley
Arthur Cayley F.R.S. was a British mathematician. He helped found the modern British school of pure mathematics....
. Newton encouraged Moore to study in Germany, and thus he spent an academic year at the University of Berlin, attending lectures by Kronecker and Weierstrass.
On his return to the United States, Moore taught at Yale and at Northwestern University
Northwestern University
Northwestern University is a private research university in Evanston and Chicago, Illinois, USA. Northwestern has eleven undergraduate, graduate, and professional schools offering 124 undergraduate degrees and 145 graduate and professional degrees....
. When 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...
opened its doors in 1892, Moore was the first head of its mathematics department, a position he retained until his death in 1931. His first two colleagues were Bolza and Maschke. The resulting department was the second research-oriented mathematics department in American history, after Johns Hopkins University
Johns Hopkins University
The Johns Hopkins University, commonly referred to as Johns Hopkins, JHU, or simply Hopkins, is a private research university based in Baltimore, Maryland, United States...
.
Accomplishments
Moore first worked in abstract algebraAbstract algebra
Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras...
, proving in 1893 the classification of the structure of finite fields (also called Galois fields). Around 1900, he began working on the foundations of geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
. He reformulated Hilbert's axioms
Hilbert's axioms
Hilbert's axioms are a set of 20 assumptions proposed by David Hilbert in 1899 in his book Grundlagen der Geometrie , as the foundation for a modern treatment of Euclidean geometry...
for geometry so that point
Point (geometry)
In geometry, topology and related branches of mathematics a spatial point is a primitive notion upon which other concepts may be defined. In geometry, points are zero-dimensional; i.e., they do not have volume, area, length, or any other higher-dimensional analogue. In branches of mathematics...
s were the only primitive notion
Primitive notion
In mathematics, logic, and formal systems, a primitive notion is an undefined concept. In particular, a primitive notion is not defined in terms of previously defined concepts, but is only motivated informally, usually by an appeal to intuition and everyday experience. In an axiomatic theory or...
, thus turning Hilbert
David Hilbert
David Hilbert was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of...
's primitive lines and planes into defined notions. In 1902, he further showed that one of Hilbert's axioms for geometry was redundant. Independently, the twenty year old R.L. Moore (no relation) also proved this, but in a more elegant fashion than E. H. Moore used. When E. H. Moore heard of the feat, he arranged for a scholarship that would allow R.L. Moore to study for a doctorate at Chicago. E.H. Moore's work on axiom systems is considered one of the starting points for metamathematics
Metamathematics
Metamathematics is the study of mathematics itself using mathematical methods. This study produces metatheories, which are mathematical theories about other mathematical theories...
and model theory
Model theory
In mathematics, model theory is the study of mathematical structures using tools from mathematical logic....
. After 1906, he turned to the foundations of analysis
Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
. The concept of closure operator
Closure operator
In mathematics, a closure operator on a set S is a function cl: P → P from the power set of S to itself which satisfies the following conditions for all sets X,Y ⊆ S....
first appeared in his 1910 Introduction to a form of general analysis. He also wrote on algebraic geometry
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
, number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
, and integral equations.
At Chicago, Moore supervised 31 doctoral dissertations, including those of George Birkhoff, Leonard Dickson, Robert Lee Moore
Robert Lee Moore
Robert Lee Moore was an American mathematician, known for his work in general topology and the Moore method of teaching university mathematics.-Life:...
(no relation), and Oswald Veblen
Oswald Veblen
Oswald Veblen was an American mathematician, geometer and topologist, whose work found application in atomic physics and the theory of relativity. He proved the Jordan curve theorem in 1905.-Life:...
. Birkhoff and Veblen went on to forge and lead the first-rate departments at Harvard and Princeton, respectively. Dickson became the first great American algebraist and number theorist. Robert Moore founded American topology. According to the Mathematics Genealogy Project
Mathematics Genealogy Project
The Mathematics Genealogy Project is a web-based database for the academic genealogy of mathematicians. As of September, 2010, it contained information on approximately 145,000 mathematical scientists who contribute to "research-level mathematics"...
, as of January 2011, E. H. Moore had over 14,900 known "descendants."
Moore convinced the New York Mathematical Society to change its name to 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...
, whose Chicago branch he led. He presided over the AMS, 1901–02, and edited the Transactions of the American Mathematical Society, 1899–1907. He 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...
, the American Academy of Arts and Sciences
American Academy of Arts and Sciences
The American Academy of Arts and Sciences is an independent policy research center that conducts multidisciplinary studies of complex and emerging problems. The Academy’s elected members are leaders in the academic disciplines, the arts, business, and public affairs.James Bowdoin, John Adams, and...
, and the American Philosophical Society
American Philosophical Society
The American Philosophical Society, founded in 1743, and located in Philadelphia, Pa., is an eminent scholarly organization of international reputation, that promotes useful knowledge in the sciences and humanities through excellence in scholarly research, professional meetings, publications,...
.
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...
established a prize in his honor in 2002.
See also
- Moore–Penrose inverse
- Moore–Smith sequence
- Moore matrix over a finite field
- Moore determinant of a Hermitian matrixMoore determinant of a Hermitian matrixIn mathematics, the Moore determinant is a determinant defined for Hermitian matrices over a quaternion algebra, introduced by ....
over a quaternion algebra