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# Eliakim Hastings Moore

Eliakim Hastings Moore (January 26, 1862, Marietta, Ohio – December 30, 1932, Chicago, Illinois) was an American mathematician.

He is a central source for much of 20th century American mathematical research activity. As a gross measure of Moore's influence, more than twice as many Ph.D. mathematicians were produced by his University of Chicago mathematics department during his tenure than were produced by any other single institution in the United States.[1]

Life

Moore, the son of a Methodist minister, 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.

Accomplishments

Moore first worked in abstract algebra, proving in 1893 that every finite field is a Galois field. Around 1900, he began working on the foundations of geometry. He reformulated Hilbert's axioms for geometry so that points 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,[2] 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.[3] 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 March 2010, E. H. Moore had over 14,300 known "descendants," almost as many as Weierstrass, who was 50 years older.

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.

See also

* Moore-Penrose inverse

* Moore-Smith sequence

Notes

1. ^ Roberts, David Lindsay: E. H. Moore's Early Twentieth-Century Program for Reform in Mathematics Education, American Mathematical Monthly, Mathematical Association of America, Volume 108,October 2001, p. 681 MAA.org

2. ^ Wilder, R. L. (1976). "Robert Lee Moore 1882-1974". Bull. AMS 82, 417-427. American Mathematical Society. http://www.discovery.utexas.edu/rlm/reference/wilder2.html. Retrieved 08:49, 10 July 2007.

3. ^ T.S. Blyth, Lattices and Ordered Algebraic Structures, Springer, 2005, ISBN 1-85233-905-5, p. 11

References

* Ivor Grattan-Guinness, 2000. The Search for Mathematical Roots 1870-1940. Princeton University Press.

* Parshall, K. H., and Rowe, D. E., 1994. The emergence of the American mathematical research community, 1876-1900 : J. J. Sylvester, Felix Klein, and E. H. Moore. Providence RI: AMS.

External links

* O'Connor, John J.; Robertson, Edmund F., "E. H. Moore", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Moore_Eliakim.html .

* E. H. Moore at the Mathematics Genealogy Project

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