Robert Lee Moore (November 14, 1882 – October 4, 1974) 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 ...

who taught for many years at the

University of Texas The University of Texas at Austin (UT Austin, UT, or Texas) is a public research university in Austin, Texas. It was founded in 1883 and is the oldest institution in the University of Texas System. With 40,916 undergraduate students, 11,075 ...

. He is known for his work in general topology, for the

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 The Un ...

of teaching university mathematics, and for his racist treatment of African-American mathematics students.

Life

Although Moore's father was reared in

New England New England is a region comprising six states in the Northeastern United States: Connecticut, Maine, Massachusetts, New Hampshire, Rhode Island, and Vermont. It is bordered by the state of New York to the west and by the Canadian provinces ...

and was of New England ancestry, he fought in the

American Civil War The American Civil War (April 12, 1861 – May 26, 1865; also known by other names) was a civil war in the United States. It was fought between the Union ("the North") and the Confederacy ("the South"), the latter formed by states th ...

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, of whom Robert, named after the commander of the Confederate Army of Northern Virginia, was the fifth. Moore entered the

at the unusually youthful age of 15, in 1898, already knowing

calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithm ...

thanks to self-study. He completed the B.Sc. in three years instead of the usual four; his teachers included

G. B. Halsted George Bruce Halsted (November 25, 1853 – March 16, 1922), usually cited as G. B. Halsted, was an American mathematician who explored foundations of geometry and introduced non-Euclidean geometry into the United States through his own work and ...

and

L. E. 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 remem ...

. After a year as a teaching fellow at Texas, he taught high school for a year in

Marshall, Texas Marshall is a city in the U.S. state of Texas. It is the county seat of Harrison County, Texas, Harrison County and a cultural and educational center of the Ark-La-Tex region. At the 2020 United States census, 2020 U.S. census, the population of M ...

. An assignment of Halsted's led Moore to prove that one of Hilbert's axioms for geometry was redundant. When

E. H. Moore Eliakim Hastings Moore (; January 26, 1862 – December 30, 1932), usually cited as E. H. Moore or E. Hastings Moore, was an American mathematician. Life Moore, the son of a Methodist minister and grandson of US Congressman Eliakim H. Moore, di ...

(no relation), who headed the Department of Mathematics at 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 ...

, 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 (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 ...

supervised Moore's 1905 thesis, titled ''Sets of Metrical Hypotheses for Geometry''. Moore then taught one year at the

University of Tennessee The University of Tennessee (officially The University of Tennessee, Knoxville; or UT Knoxville; UTK; or UT) is a public land-grant research university in Knoxville, Tennessee. Founded in 1794, two years before Tennessee became the 16th state, ...

, two years at

Princeton University Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...

, and three years 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 ...

. 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 The University of Pennsylvania (also known as Penn or UPenn) is a private research university in Philadelphia. It is the fourth-oldest institution of higher education in the United States and is ranked among the highest-regarded universitie ...

. In 1920, Moore 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 five classes a year, including a section of freshman calculus, until the University authorities forced his definitive retirement in 1969, his 87th year. A strong supporter of 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, ...

, he presided over it, 1936–38. He edited its

Colloquium Publications Colloquium may refer to: *An academic seminar usually led by a different lecturer and on a different topic at each meeting or similarly to a tutorial led by students as is the case in Norway. *A form of testing and assessing students' knowledge i ...

, 1929–33, and was the editor-in-chief, 1930–33. In 1931, 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 ...

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

topology In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such ...

, 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 In mathematics, general topology is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. It is the foundation of most other branches of topology, including differential topology, geomet ...

—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 Plane(s) most often refers to: * Aero- or airplane, a powered, fixed-wing aircraft * Plane (geometry), a flat, 2-dimensional surface Plane or planes may also refer to: Biology * Plane (tree) or ''Platanus'', wetland native plant * ''Planes' ...

. The Moore plane, Moore's road space, Moore space, and the normal Moore space conjecture are named in his honor.

Unusual teacher

Robert Lee Moore is known to have supervised 50 doctoral dissertations, almost all at Texas, including those of

R. H. Bing R. H. Bing (October 20, 1914 – April 28, 1986) was an American mathematician who worked mainly in the areas of geometric topology and continuum theory. His father was named Rupert Henry, but Bing's mother thought that "Rupert Henry" was too ...

F. Burton Jones Floyd Burton Jones (November 22, 1910, Cisco, Texas – April 15, 1999, Santa Barbara, California) was an American mathematician, active mainly in topology. Jones's father was a pharmacist and local politician in Shackelford County, Texas. As the ...

John R. Kline John Robert Kline (December 7, 1891 – May 2, 1955) was an American mathematician and educator. One of three children born to Henry K. Kline (1862–1923) and Emma M. Kline (1869–1948), he was Professor of mathematics at the University of Pen ...

Edwin Evariste Moise Edwin Evariste Moise (; December 22, 1918 – December 18, 1998) was an American mathematician and mathematics education reformer. After his retirement from mathematics he became a literary critic of 19th-century English poetry and had severa ...

, Mary Ellen Rudin,

Gordon Whyburn Gordon Thomas Whyburn (7 January 1904 Lewisville, Texas – 8 September 1969 Charlottesville, Virginia) was an American mathematician who worked on topology. Whyburn studied at the University of Texas in Austin, where he received a bachel ...

Richard Davis Anderson Richard Davis Anderson, Sr. (February 17, 1922 – March 4, 2008) was an American mathematician known internationally for his work in infinite-dimensional topology. Much of his early work focused on proofs surrounding Hilbert space and Hilb ...

, and

Raymond Louis Wilder Raymond Louis Wilder (3 November 1896 in Palmer, Massachusetts – 7 July 1982 in Santa Barbara, California) was an American mathematician, who specialized in topology and gradually acquired philosophical and anthropological interests. Life Wilde ...

. Moore has been described as having been one of the most charismatic and inspiring university teachers of mathematics ever active in the United States. Accounts have been given of his 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 pre-doctoral level students from consulting the mathematical literature. It was while attending lectures at the

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

. The success of this method led others to adopt it and similar methods.

Prejudice

Moore's record as a teacher of mathematics has been tarnished by his racism towards black students. Most of Moore's career was spent in a racially segregated part of the United States. African-American students were prohibited from even enrolling at the University of Texas until the late 1950s, and Moore himself was strongly in favor of segregation.. After the University of Texas began admitting African-American students, he refused to allow them into his classes, even for mathematics graduate students such as

Vivienne Malone-Mayes Vivienne Lucille Malone-Mayes (February 10, 1932 – June 9, 1995) was an American mathematician and professor. Malone-Mayes studied properties of functions, as well as methods of teaching mathematics. On one occasion he walked out of a talk by a student, his academic grandchild, after discovering that the speaker was African-American. Moore was also known for repeatedly claiming that female students were inferior to male students, and, though "less pronounced than his racism", for his

antisemitism Antisemitism (also spelled anti-semitism or anti-Semitism) is hostility to, prejudice towards, or discrimination against Jews. A person who holds such positions is called an antisemite. Antisemitism is considered to be a form of racism. Antis ...

. However, while Moore's racism is confirmed by several first-hand accounts of his refusal to teach African-American students, the often-repeated description of him as a misogynist and antisemite is based largely on his oral remarks. Some of the sources reporting these remarks, such as Mary Ellen Rudin, also point out that in fact he encouraged females who showed mathematical talent and that he had Jewish students, such as

Edwin E. Moise Edwin Evariste Moise (; December 22, 1918 – December 18, 1998) was an American mathematician and mathematics education reformer. After his retirement from mathematics he became a literary critic of 19th-century English poetry and had severa ...

(who was asked about Moore's anti-Semitic reputation in an interview) and Martin Ettlinger, and close colleagues, such as Hyman J. Ettlinger. His encouragement of Rudin and other white female students is documented and between 1949 and 1970 (the earliest period when national data are known) 4 of Moore's 31 doctoral students (13%) were female, while nationally 175 were female out of 2646 doctoral graduates in mathematics and statistics (7%).

Honors

* The

Robert Lee Moore Hall Physics, Math, and Astronomy Building (abbreviated PMA; formerly known as Robert Lee Moore Hall or RLM) is a high rise building on the University of Texas at Austin campus, in the U.S. state of Texas. The building was completed in 1972, and houses ...

, a classroom building at the University of Texas, was named after Moore from its construction in 1972–2020. In 2020, following complaints and petitions in 2019 and then the 2020

George Floyd protests The George Floyd protests were a series of protests and civil unrest against police brutality and racism that began in Minneapolis on May 26, 2020, and largely took place during 2020. The civil unrest and protests began as part of internati ...

and

Black Lives Matter Black Lives Matter (abbreviated BLM) is a decentralized political and social movement that seeks to highlight racism, discrimination, and racial inequality experienced by black people. Its primary concerns are incidents of police bruta ...

movement, it was renamed to the "Physics, Math and Astronomy Building".

Quotations

*"That student is taught the best who is told the least." Moore, quote in Parker (2005: vii).Parker, John, 2005
''R. L. Moore: Mathematician and Teacher''
Mathematical Association of America. . *"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)

Notes

References

* Jones, F. Burton, 1997,
The Beginning of Topology in the United States and the Moore School
in C. E. Aull and R. Louwen, eds., ''Handbook of the History of General Topology, Vol. 1''. Kluwer: 97–103. *Lewis, Albert C., 1990,

in ''Dictionary of Scientific Biography, vol. 18''. Charles Scribner's Sons: 651–53. *Moore, R. L., 1970 (1932). ''Foundations of Point Set Theory''. Vol. 13 of the AMS Colloquium Publications. American Mathematical Society. * Wilder, R. L., 1976,
Robert Lee Moore 1882–1974
" ''Bulletin of the AMS 82'': 417–27. Includes a complete bibliography of Moore''s writings.

External links

* *

to biographical material and the Moore method. {{DEFAULTSORT:Moore, Robert Lee 1882 births 1974 deaths 20th-century American mathematicians Members of the United States National Academy of Sciences Northwestern University faculty People from Dallas Presidents of the American Mathematical Society Princeton University faculty Topologists University of Chicago alumni University of Pennsylvania faculty University of Texas at Austin College of Natural Sciences alumni University of Texas at Austin faculty Mathematicians from Texas