Eliakim Hastings Moore (; January 26, 1862 – December 30, 1932), usually cited as E. H. Moore or E. Hastings Moore, 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 ...

Life

Moore, the son of a Methodist minister and grandson of US Congressman

Eliakim H. Moore Eliakim Hastings Moore (June 19, 1812 – April 4, 1900) was an American politician who served one term as a United States House of Representatives, U.S. Representative from Ohio from 1869 to 1871. Biography Moore was born to David & Dolly (H ...

, discovered mathematics through a summer job at the

Cincinnati Observatory The Cincinnati Observatory is located in Cincinnati, Ohio, Cincinnati, Ohio (United States) on top of Mount Lookout, Ohio, Mount Lookout. It consists of two observatory buildings housing an 11-inch (28 cm) and 16 inch (41 cm) apertu ...

while in high school. He subsequently studied mathematics at

Yale University Yale University is a private research university in New Haven, Connecticut. Established in 1701 as the Collegiate School, it is the third-oldest institution of higher education in the United States and among the most prestigious in the wo ...

, where he was a member of

Skull and Bones Skull and Bones, also known as The Order, Order 322 or The Brotherhood of Death, is an undergraduate senior secret student society at Yale University in New Haven, Connecticut. The oldest senior class society at the university, Skull and Bone ...

and obtained a BA in 1883 and the PhD in 1885 with a thesis supervised by

Hubert Anson Newton Prof Hubert Anson Newton FRS HFRSE (19 March 1830 – 12 August 1896), usually cited as H. A. Newton, was an American astronomer and mathematician, noted for his research on meteors. Biography Newton was born at Sherburne, New York, and gradu ...

, on some work of

William Kingdon Clifford William Kingdon Clifford (4 May 18453 March 1879) 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 ...

and

Arthur Cayley Arthur Cayley (; 16 August 1821 – 26 January 1895) was a prolific United Kingdom of Great Britain and Ireland, British mathematician who worked mostly on algebra. He helped found the modern British school of pure mathematics. As a child, C ...

. Newton encouraged Moore to study in Germany, and thus he spent an academic year at the

University of Berlin Humboldt-Universität zu Berlin (german: Humboldt-Universität zu Berlin, abbreviated HU Berlin) is a German public research university in the central borough of Mitte in Berlin. It was established by Frederick William III on the initiative o ...

, attending lectures by

Leopold Kronecker Leopold Kronecker (; 7 December 1823 – 29 December 1891) was a German mathematician who worked on number theory, algebra and logic. He criticized Georg Cantor's work on set theory, and was quoted by as having said, "'" ("God made the integers, ...

and

Karl 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 ...

. On his return to the United States, Moore taught at Yale and at

Northwestern University Northwestern University is a private research university in Evanston, Illinois. Founded in 1851, Northwestern is the oldest chartered university in Illinois and is ranked among the most prestigious academic institutions in the world. Charte ...

. When the

University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park neighborhood. The University of Chicago is consistently ranked among the b ...

opened its doors in 1892, Moore was the first head of its mathematics department, a position he retained until his death in 1932. His first two colleagues were

Oskar Bolza Oskar Bolza (12 May 1857 – 5 July 1942) was a German mathematician, and student of Felix Klein. He was born in Bad Bergzabern, Palatinate, then a district of Bavaria, known for his research in the calculus of variations, particularly influe ...

and Heinrich Maschke. The resulting department was the second research-oriented mathematics department in American history, after

Johns Hopkins University Johns Hopkins University (Johns Hopkins, Hopkins, or JHU) is a private university, private research university in Baltimore, Maryland. Founded in 1876, Johns Hopkins is the oldest research university in the United States and in the western hem ...

Accomplishments

Moore first worked in

abstract algebra In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The term ''a ...

, proving in 1893 the classification of the structure of

finite fields In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subtra ...

(also called

Galois field In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subtra ...

s). Around 1900, he began working on the

foundations of geometry Foundations of geometry is the study of geometries as axiomatic systems. There are several sets of axioms which give rise to Euclidean geometry or to non-Euclidean geometries. These are fundamental to the study and of historical importance, but t ...

. He reformulated

Hilbert's axioms Hilbert's axioms are a set of 20 assumptions proposed by David Hilbert in 1899 in his book '' Grundlagen der Geometrie'' (tr. ''The Foundations of Geometry'') as the foundation for a modern treatment of Euclidean geometry. Other well-known modern ...

for geometry so that

point Point or points may refer to: Places * Point, Lewis, a peninsula in the Outer Hebrides, Scotland * Point, Texas, a city in Rains County, Texas, United States * Point, the NE tip and a ferry terminal of Lismore, Inner Hebrides, Scotland * Point ...

s were the only

primitive notion In mathematics, logic, philosophy, and formal systems, a primitive notion is a concept that is not defined in terms of previously-defined concepts. It is often motivated informally, usually by an appeal to intuition and everyday experience. In an ...

, thus turning

David Hilbert David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician, one of the most influential mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many a ...

's primitive lines and planes into defined notions. In 1902, he further showed that one of Hilbert's axioms for geometry was redundant. His work on axiom systems is considered one of the starting points for

metamathematics Metamathematics is the study of mathematics itself using mathematical methods. This study produces metatheories, which are mathematical theories about other mathematical theories. Emphasis on metamathematics (and perhaps the creation of the ter ...

and

model theory In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing statements about a mathematical structure), and their models (those structures in which the s ...

. After 1906, he turned to the foundations of

analysis Analysis ( : analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (38 ...

. The concept of a

closure operator In mathematics, a closure operator on a set ''S'' is a function \operatorname: \mathcal(S)\rightarrow \mathcal(S) from the power set of ''S'' to itself that satisfies the following conditions for all sets X,Y\subseteq S : Closure operators are dete ...

first appeared in his 1910 ''Introduction to a form of general analysis''. He also wrote on

algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...

, and

integral equations In mathematics, integral equations are equations in which an unknown function appears under an integral sign. In mathematical notation, integral equations may thus be expressed as being of the form: f(x_1,x_2,x_3,...,x_n ; u(x_1,x_2,x_3,...,x_n) ...

. At Chicago, Moore supervised 31 doctoral dissertations, including those of

George Birkhoff George David Birkhoff (March 21, 1884 – November 12, 1944) was an American mathematician best known for what is now called the ergodic theorem. Birkhoff was one of the most important leaders in American mathematics in his generation, and during ...

Leonard Dickson Leonard Eugene Dickson (January 22, 1874 – January 17, 1954) was an American mathematician. He was one of the first American researchers in abstract algebra, in particular the theory of finite fields and classical groups, and is also reme ...

Robert Lee Moore Robert Lee Moore (November 14, 1882 – October 4, 1974) was an American mathematician who taught for many years at the University of Texas. He is known for his work in general topology, for the Moore method of teaching university mathematics, ...

(no relation), and

Oswald Veblen Oswald Veblen (June 24, 1880 – August 10, 1960) was an American mathematician, geometer and topologist, whose work found application in atomic physics and the theory of relativity The theory of relativity usually encompasses two interrelat ...

. Birkhoff and Veblen went on to lead 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 The Mathematics Genealogy Project (MGP) is a web-based database for the academic genealogy of mathematicians.. By 31 December 2021, it contained information on 274,575 mathematical scientists who contributed to research-level mathematics. For a ty ...

, as of December 2012, E. H. Moore had over 18,900 known "descendants." Moore convinced the

New York 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, ...

to change its name to 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, ...

, 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 National Academy of Sciences (NAS) is a United States nonprofit, 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 Nati ...

, the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (abbreviation: AAA&S) 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 ...

, and the

American Philosophical Society The American Philosophical Society (APS), founded in 1743 in Philadelphia, is a scholarly organization that promotes knowledge in the sciences and humanities through research, professional meetings, publications, library resources, and communit ...

. He was an Invited Speaker at the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...

in 1908 in Rome and in 1912 in Cambridge, England. The American Mathematical Society established a prize in his honor in 2002.

Notes

References

Ivor Grattan-Guinness Ivor Owen Grattan-Guinness (23 June 1941 – 12 December 2014) was a historian of mathematics and logic. Life Grattan-Guinness was born in Bakewell, England; his father was a mathematics teacher and educational administrator. He gained his bac ...

(2000) ''The Search for Mathematical Roots 1870–1940''.

Princeton University Press Princeton University Press is an independent publisher with close connections to Princeton University. Its mission is to disseminate scholarship within academia and society at large. The press was founded by Whitney Darrow, with the financial su ...

. *

Karen Parshall Karen Hunger Parshall (born 1955, Virginia; ''née'' Karen Virginia Hunger) is an American historian of mathematics. She is the Commonwealth Professor of History and Mathematics at the University of Virginia with a joint appointment in the Corcora ...

and

David E. Rowe David E. Rowe (born August 11, 1950) is an American mathematician and historian. He studied mathematics and the history of science at the University of Oklahoma, and took a second doctorate in history at the Graduate Center of the City Univers ...

(1994) ''The emergence of the American mathematical research community, 1876–1900 : J. J. Sylvester, Felix Klein, and E. H. Moore'',

External links

* * *
David Lindsay Roberts, ''Moore´s early twentieth century program for reform in mathematics education'', American Mathematical Monthly, vol. 108, 2001, pp. 689–696Guide to the Eliakim Hastings Moore Papers 1899-1931
at th
University of Chicago Special Collections Research Center
{{DEFAULTSORT:Moore, E. H. 1862 births 1932 deaths 19th-century American mathematicians 20th-century American mathematicians Algebraic geometers Algebraists Geometers Mathematical analysts Members of the United States National Academy of Sciences Northwestern University faculty Number theorists People from Marietta, Ohio Presidents of the American Mathematical Society University of Chicago faculty Yale University alumni Yale University faculty

Life

Accomplishments

See also

Notes

References

External links