Robert Lee Moore
Encyclopedia
Robert Lee Moore was an American
mathematician
, known for his work in general topology
and the Moore method
of teaching university mathematics.
and was of New England ancestry, he fought in the American Civil War
on the side of the Confederacy
. After the war, he ran a hardware store in Dallas, then little more than a railway stop, and raised six children, Robert being the fifth.
Moore entered the University of Texas
at the unusually low age of 16, in 1898, already knowing calculus
thanks to self-study. He completed the B.Sc.
in three years instead of the usual four; his teachers included G. B. Halsted
and L. E. Dickson
. After a year as a teaching fellow at Texas, he taught high school for a year in Marshall, Texas
.
An assignment of Halsted's led Moore to prove that one of Hilbert's axioms
for geometry was redundant. When E. H. Moore
(no relation), who headed the Department of Mathematics at the University of Chicago
, and whose research interests were on the foundations of geometry, heard of Robert's feat, he arranged for a scholarship that would allow Robert to study for a doctorate at Chicago. Oswald Veblen
supervised Moore's 1905 thesis, titled Sets of Metrical Hypotheses for Geometry.
Moore then taught one year at the University of Tennessee
, two years at Princeton University
, and three years at Northwestern University
. In 1910, he married Margaret MacLelland Key of Brenham, Texas; they had no children. In 1911, he took up a position at the University of Pennsylvania
.
In 1920, Moore happily returned to the University of Texas at Austin as an associate professor, and was promoted to full professor three years later. In 1951, he went on half pay, but continued to teach his habitual five classes a year, including a section of freshman calculus, until the University authorities forced his definitive retirement in 1969, his 87th year. In 1973, the University of Texas honored him by giving the name Moore Hall to a new building housing the physics, mathematics, and astronomy departments.
A strong supporter of the American Mathematical Society
, he presided over it, 1936–38. He edited its Colloquium Publications, 1929–33, and was the editor-in-chief, 1930–33. In 1931, he was elected to the National Academy of Sciences
.
, a topic he first touched on in his Ph.D. thesis. By the time Moore returned to the University of Texas, he had published 17 papers on point-set topology—a term he coined—including his 1915 paper "On a set of postulates which suffice to define a number-plane," giving an axiom system for plane topology. The Moore plane
, Moore's road space, Moore space
and the Moore space conjecture are named in his honour.
, John R. Kline, Mary Ellen Rudin
, Gordon Whyburn, R. D. Anderson, and Raymond Louis Wilder
. This attests to Moore's having been one of the most charismatic and inspiring university teachers of mathematics ever active in the United States
. Moore had a breathtaking ability to teach students who had never previously distinguished themselves in mathematics how to do proofs. He went out of his way to teach elementary and service courses every year, and actually forbade his students from consulting the mathematical literature.
It was while attending lectures at the University of Chicago
that Moore first hit on his original teaching methods. Finding these lectures rather boring, even mind dulling, he would liven up a lecture by running a race in his mind with the lecturer, by trying to discover the proof of an announced theorem before the lecturer had finished his presentation. Moore often won this silent race, and when he did not, he felt that he was better off from having made the attempt. It was at the University of Pennsylvania, while teaching a course on the foundations of geometry, that Moore first tried out the teaching methods that came to be known as the Moore method
. The success of this method led others to adopt it and similar methods.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician
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....
, known for his work in general topology
General topology
In mathematics, general topology or point-set topology is the branch of topology which studies properties of topological spaces and structures defined on them...
and the Moore method
Moore method
The Moore method is a deductive manner of instruction used in advanced mathematics courses. It is named after Robert Lee Moore, a famous topologist who first used a stronger version of the method at the University of Pennsylvania when he began teaching there in 1911.The way the course is conducted...
of teaching university mathematics.
Life
Although Moore's father was reared in New EnglandNew England
New England is a region in the northeastern corner of the United States consisting of the six states of Maine, New Hampshire, Vermont, Massachusetts, Rhode Island, and Connecticut...
and was of New England ancestry, he fought in the American Civil War
American Civil War
The American Civil War was a civil war fought in the United States of America. In response to the election of Abraham Lincoln as President of the United States, 11 southern slave states declared their secession from the United States and formed the Confederate States of America ; the other 25...
on the side of the Confederacy
Confederate States of America
The Confederate States of America was a government set up from 1861 to 1865 by 11 Southern slave states of the United States of America that had declared their secession from the U.S...
. After the war, he ran a hardware store in Dallas, then little more than a railway stop, and raised six children, Robert being the fifth.
Moore entered the University of Texas
University of Texas at Austin
The University of Texas at Austin is a state research university located in Austin, Texas, USA, and is the flagship institution of the The University of Texas System. Founded in 1883, its campus is located approximately from the Texas State Capitol in Austin...
at the unusually low age of 16, in 1898, already knowing calculus
Calculus
Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...
thanks to self-study. He completed the B.Sc.
Bachelor of Science
A Bachelor of Science is an undergraduate academic degree awarded for completed courses that generally last three to five years .-Australia:In Australia, the BSc is a 3 year degree, offered from 1st year on...
in three years instead of the usual four; his teachers included G. B. Halsted
G. B. Halsted
George Bruce Halsted was a mathematician who explored foundations of geometry and introduced Non-Euclidean geometry into the United States through his own work and his many important translations...
and L. E. Dickson
Leonard Eugene Dickson
Leonard Eugene Dickson 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 remembered for a three-volume history of number theory.-Life:Dickson considered himself a Texan by...
. After a year as a teaching fellow at Texas, he taught high school for a year in Marshall, Texas
Marshall, Texas
Marshall is a city in Harrison County in the northeastern corner of Texas. Marshall is a major cultural and educational center in East Texas and the tri-state area. As of the 2010 U.S. Census, the population of Marshall was about 23,523...
.
An assignment of Halsted's led Moore to prove that one of 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 was redundant. When E. H. Moore
E. H. Moore
Eliakim Hastings Moore was an American mathematician.-Life:Moore, the son of a Methodist minister and grandson of US Congressman Eliakim H. Moore, discovered mathematics through a summer job at the Cincinnati Observatory while in high school. He learned mathematics at Yale University, where he was...
(no relation), who headed the Department of Mathematics at 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...
, and whose research interests were on the foundations of geometry, heard of Robert's feat, he arranged for a scholarship that would allow Robert to study for a doctorate at Chicago. 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:...
supervised Moore's 1905 thesis, titled Sets of Metrical Hypotheses for Geometry.
Moore then taught one year at the University of Tennessee
University of Tennessee
The University of Tennessee is a public land-grant university headquartered at Knoxville, Tennessee, United States...
, two years at Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
, and three years 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....
. In 1910, he married Margaret MacLelland Key of Brenham, Texas; they had no children. In 1911, he took up a position at the University of Pennsylvania
University of Pennsylvania
The University of Pennsylvania is a private, Ivy League university located in Philadelphia, Pennsylvania, United States. Penn is the fourth-oldest institution of higher education in the United States,Penn is the fourth-oldest using the founding dates claimed by each institution...
.
In 1920, Moore happily returned to the University of Texas at Austin as an associate professor, and was promoted to full professor three years later. In 1951, he went on half pay, but continued to teach his habitual five classes a year, including a section of freshman calculus, until the University authorities forced his definitive retirement in 1969, his 87th year. In 1973, the University of Texas honored him by giving the name Moore Hall to a new building housing the physics, mathematics, and astronomy departments.
A strong supporter of 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...
, he presided over it, 1936–38. He edited its Colloquium Publications, 1929–33, and was the editor-in-chief, 1930–33. In 1931, 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...
.
Topologist
According to the bibliography in Wilder (1976), Moore published 67 papers and one monograph, his 1932 Foundations of Point Set Theory. He is primarily remembered for his work on the foundations of topologyGeneral topology
In mathematics, general topology or point-set topology is the branch of topology which studies properties of topological spaces and structures defined on them...
, a topic he first touched on in his Ph.D. thesis. By the time Moore returned to the University of Texas, he had published 17 papers on point-set topology—a term he coined—including his 1915 paper "On a set of postulates which suffice to define a number-plane," giving an axiom system for plane topology. The Moore plane
Moore plane
In mathematics, the Moore plane, also sometimes called Niemytzki plane is a topological space. It is a completely regular Hausdorff space which is not normal...
, Moore's road space, Moore space
Moore space (topology)
In mathematics, more specifically point-set topology, a Moore space is a developable regular Hausdorff space. Equivalently, a topological space X is a Moore space if the following conditions hold:...
and the Moore space conjecture are named in his honour.
Unusual teacher
Robert Lee Moore is known to have supervised 50 doctoral dissertations, almost all at Texas, including those of R. H. Bing, F. Burton JonesF. Burton Jones
F. Burton Jones was an American mathematician, active mainly in topology....
, John R. Kline, Mary Ellen Rudin
Mary Ellen Rudin
Mary Ellen Rudin is an American mathematician.Born Mary Ellen Estill, she attended the University of Texas, completing her B.A. in 1944 and her Ph.D. in 1949, under Robert Lee Moore. In 1953, she married the mathematician Walter Rudin. Following her mentor Moore, her research centers on point-set...
, Gordon Whyburn, R. D. Anderson, and Raymond Louis Wilder
Raymond Louis Wilder
Raymond Louis Wilder was an American mathematician, who specialized in topology and gradually acquired philosophical and anthropological interests.-Life:...
. This attests to Moore's having been one of the most charismatic and inspiring university teachers of mathematics ever active in the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
. Moore had a breathtaking ability to teach students who had never previously distinguished themselves in mathematics how to do proofs. He went out of his way to teach elementary and service courses every year, and actually forbade his students from consulting the mathematical literature.
It was while attending lectures at 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...
that Moore first hit on his original teaching methods. Finding these lectures rather boring, even mind dulling, he would liven up a lecture by running a race in his mind with the lecturer, by trying to discover the proof of an announced theorem before the lecturer had finished his presentation. Moore often won this silent race, and when he did not, he felt that he was better off from having made the attempt. It was at the University of Pennsylvania, while teaching a course on the foundations of geometry, that Moore first tried out the teaching methods that came to be known as the Moore method
Moore method
The Moore method is a deductive manner of instruction used in advanced mathematics courses. It is named after Robert Lee Moore, a famous topologist who first used a stronger version of the method at the University of Pennsylvania when he began teaching there in 1911.The way the course is conducted...
. The success of this method led others to adopt it and similar methods.
Political aspects
Moore's record as a teacher of mathematics has been tarnished by his attitude towards black students, which is considered extreme even for the standards of the then widespread anti-black racism in America. He was a virulent racist and explicitly refused to teach African Americans. He once famously walked out of a lecture once he realized the speaker was black.Quotations
- "That student is taught the best who is told the least." Moore, quote in Parker (2005: vii).
- "I hear, I forget. I see, I remember. I do, I understand." (Chinese proverb that was a favorite of Moore's. Quoted in Halmos, P.R. (1985) I want to be a mathematician: an automathography. Springer-Verlag: 258)
- "You are welcome to take my course but you start with a C and can only go down from there." Moore, in response to W.E. Hunt's intention to take a Topology course Moore taught, quote in S. W. Williams R. L. Moore: racist mathematician unveiled (2005). W.E. Hunt was black, and later went on to become a Professor of Mathematics.
Further reading
Biography, with extensive list of academic descendants of R. L. Moore and their publications.External links
The proximate source for this entry.- The Legacy of Robert Lee Moore Project.
- Links to biographical material and the Moore method.