# Eliakim Hastings Moore

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

Moore studied mathematics and astronomy from 1879 at Yale University and received his doctorate in 1885 with the dissertation *Extensions of Certain Theorems of Clifford and Cayley in the Geometry of n Dimensions* with Hubert Anson Newton (1830-1896). From 1885 to 1886 he studied in Germany in Göttingen and Berlin , among others with Leopold Kronecker and Karl Weierstrass . He then worked as a tutor at Northwestern University and at Yale before becoming professor of mathematics at the newly formed University of Chicago in 1892 . From 1896 until his retirement in 1931 he headed the mathematics faculty at the university. He brought the two young German mathematicians Oskar Bolza (a specialist in calculus of variations) and Heinrich Maschke to the faculty, which he made one of the centers of mathematical research in the USA. His students include Oswald Veblen , Leonard Dickson , Garrett Birkhoff and Theophil Henry Hildebrandt .

From 1901 to 1902 he was president of the American Mathematical Society , which he also co-founded (by persuading the New York Mathematical Society to change its name). He was a member of the National Academy of Sciences of the USA and the American Academy of Arts and Sciences (both 1901).

## Research work

Moore initially worked in the field of abstract algebra. A term that emerged at that time was that of the *body* , which until then only meant infinite structures. Moore (at about the same time Heinrich Weber ) expanded the term by also including finite bodies . In 1893 he showed that every finite field can be represented as a Galois field (English: *Galois field* ). (A Galois field is a finite field that is generated by means of a construction going back to Galois . Because of Moore's result, the terms *finite field* and *Galois field* are often used synonymously today.)

Around 1900 he began research on the fundamentals of geometry . He reduced the formulations of David Hilbert's geometry axioms to such an extent that only points were needed as a primitive term. Lines and planes, which Hilbert had also introduced as primitive terms, could be represented as derived constructs. Moore proved in 1902 that the Hilbert system of axioms is redundant, and when he learned of the independently found proof of the (unrelated) mathematician Robert Lee Moore , a student at GB Halsted , he promoted it by writing his dissertation in Chicago made it possible. Moore's work on axiom systems is considered to be the origin of metamathematics and model theory .

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

His research results in linear algebra are still of practical importance today , where he defined a so-called pseudo inverse for non-regular matrices , which is called the Moore-Penrose inverse after him and Roger Penrose .

## Web links

- John J. O'Connor, Edmund F. Robertson :
*Eliakim Hastings Moore.*In:*MacTutor History of Mathematics archive .* - David Lindsay Roberts
*Moore's early twentieth century program for reform in mathematics education*, American Mathematical Monthly, Volume 108, 2001, p. 689

personal data | |
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SURNAME | Moore, Eliakim Hastings |

BRIEF DESCRIPTION | American mathematician |

DATE OF BIRTH | January 28, 1862 |

PLACE OF BIRTH | Marietta , Ohio , United States |

DATE OF DEATH | December 30, 1932 |

Place of death | Chicago , Illinois , United States |