E. H. Moore

Eliakim Hastings Moore ( born January 28, 1862 in Marietta, Ohio; † December 30, 1932 in Chicago, Illinois ) was an American mathematician.

Moore studied from 1879 at Yale University, Mathematics and Astronomy and received his PhD in 1885 with the thesis "Extensions of Certain theorem of Clifford and Cayley in the Geometry of n Dimensions" at Hubert Anson Newton ( 1830-1896 ). 1885 to 1886 he studied in Germany at Göttingen and Berlin, among others at Leopold Kronecker and Karl Weierstrass. He then worked as a tutor at Northwestern University and at Yale University before he became in 1892 professor of mathematics at the newly founded University of Chicago. From 1896 until his retirement in 1931, he headed the Department of Mathematics at the University. He took the two young German mathematician Oskar Bolza ( a specialist in the calculus of variations ) and Heinrich Maschke to the faculty, he made one of the centers of mathematical research in the United States. His students include Oswald Veblen, Leonard Dickson and Garrett Birkhoff.

1901 to 1902 he was president of the American Mathematical Society, which he also co-founded ( by convincing the New York Mathematical Society, to change their name ). He was a member of the National Academy of Sciences of the United States and the American Academy of Arts and Sciences.

Research

Moore first worked in the field of abstract algebra. A concept that took shape at that time, was that of the body, of which up to that point but only infinite structures were understood. Moore (about the same time Henry Weber) extended the term by he included also finite fields. He showed in 1893 that every finite fields as Galois Field (English: Galois field) can be represented. ( A Galois field is a finite field that is generated by means of a returning in Galois construction. Moore result because the terms body and finite Galois field are now often used interchangeably.)

In 1900 he began research on the foundations of geometry. He reduced the formulations of geometry axioms of David Hilbert extent that only points were needed as a primitive concept. Lines and planes, the Hilbert was also introduced as a primitive terms could be represented as derived constructs. Moore was also able to show in 1902 that the Hilbert axiom system is redundant. The work of Moore axiom systems are considered as the origin of meta-mathematics and model theory.

After 1906 Moore turned to the foundations of analysis. He also worked on algebraic geometry, number theory and integral equations.

Of practical importance are still the research results in linear algebra, where it has defined a so-called pseudo-inverse for non-regular matrices, called after him and Roger Penrose as Moore -Penrose inverse.

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