Celebratio Mathematica

Robert Lee Moore

Robert Lee Moore

by Steve Armentrout

R. L. Moore was a lead­ing re­search math­em­atician whose work in point-set to­po­logy early in the twen­ti­eth cen­tury was in­stru­ment­al in lay­ing the found­a­tions of that emer­ging top­ic of to­po­logy. Over the next half cen­tury, he and his stu­dents de­veloped this top­ic ex­tens­ively. He was elec­ted to the Na­tion­al Academy of Sci­ences in 1931.

He was also an out­stand­ing teach­er of math­em­at­ics, and in his ca­reer he su­per­vised the Ph.D. theses of fifty stu­dents, many of whom went on to be­come out­stand­ing re­search math­em­aticians and teach­ers. His goal was to de­vel­op a re­search abil­ity, not know­ledge alone. Bey­ond cal­cu­lus there were no lec­tures; he chal­lenged each stu­dent to prove the the­or­ems of the course — easy or hard — on his or her own, without help from texts or oth­ers. His ap­proach was called “The Moore Meth­od,” and it of­ten gen­er­ated strong neg­at­ive re­ac­tions from those who ad­voc­ated more con­ven­tion­al meth­ods.

R. L. Moore’s fath­er, Charles, was des­cen­ded from a long line of New Englanders, the first be­ing one John Moore who emig­rated from Eng­land to Mas­sachu­setts in 1642. R. L.’s pa­ternal grand­fath­er, a phys­i­cian in Con­necti­c­ut and Ver­mont, took his fam­ily to North Car­o­lina in the mid-1850s so he could study nat­ur­al drugs and rem­ed­ies used by Nat­ive Amer­ic­ans. When the fam­ily re­turned to Con­necti­c­ut, the eld­est son Henry stayed and soon moved to Ken­tucky. Charles joined him in 1858. When the Civil War broke out, both broth­ers joined the Con­fed­er­ate Army. They sur­vived the war, but the units they served in of­ten suffered heavy cas­u­al­ties.

After the war, the broth­ers came in con­tact with a fam­ily in Vir­gin­ia named Moore, and the broth­ers mar­ried sis­ters in this fam­ily. The so­cial, eco­nom­ic and polit­ic­al dis­rup­tion in the South led Charles to con­sider mov­ing. At this point, he con­sidered him­self a South­ern­er, un­able to re­turn to the North, in part be­cause two of his broth­ers had fought in the Uni­on Army in the war.

In 1877, Charles Moore and his fam­ily of four chil­dren moved to Dal­las, Texas, where he opened a hard­ware, grain and gro­cery store near the town square. Robert Lee Moore was born in Dal­las on Novem­ber 14, 1882, the fifth of six chil­dren.

At the time, Dal­las was a rap­idly grow­ing fron­ti­er town, and pub­lic edu­ca­tion in Dal­las was prac­tic­ally nonex­ist­ent. When he was eight, R. L. was en­rolled in a private school at­ten­ded by two of his older broth­ers. He did well in school, early on show­ing a strong in­terest in math­em­at­ics, and mak­ing straight As in the sub­ject. He was en­cour­aged to at­tend the Uni­versity of Texas, which had opened in 1883.

R. L. de­cided to go there and, in pre­par­a­tion for this, study cal­cu­lus on his own. He ob­tained a copy of the text­book used by the Uni­versity. One of his goals in study­ing cal­cu­lus was to prove the the­or­ems of the course for him­self. He would read the state­ment of the the­or­em, the proof covered with a sheet of pa­per, and try to prove the the­or­em. If, after a time, he hadn’t pro­gressed, he un­covered the first line of the proof, read it, and thought about how to con­tin­ue. If he had to un­cov­er sev­er­al lines of the proof, he felt that he had failed. He mastered cal­cu­lus to the ex­tent that, when he en­rolled in cal­cu­lus at the Uni­versity, he was quickly ad­vanced to the next course.

Moore entered the Uni­versity in 1898, shortly be­fore his 16th birth­day. There, he came un­der the in­flu­ence of G. B. Halsted, head of the De­part­ment of Math­em­at­ics. One of Halsted’s in­terests was the found­a­tions of geo­metry, and he taught Moore non-Eu­c­lidean geo­metry. Moore re­ceived his B.A. and M.A. in 1901, and spent the next year as a teach­ing as­sist­ant at Texas.

Hil­bert’s book, Grundla­gen der Geo­met­rie, had ap­peared re­cently (the first edi­tion was trans­lated by Halsted). Halsted sug­ges­ted to R. L. that he try to prove that a cer­tain one of Hil­bert’s ax­ioms was re­dund­ant. R. L. quickly did this, and it was writ­ten up and pub­lished by Halsted. It came to the at­ten­tion of E. H. Moore (no re­la­tion), head of the De­part­ment of Math­em­at­ics at the Uni­versity of Chica­go, who had ob­tained the same res­ult earli­er. However, R. L.’s ar­gu­ment was short­er and, in the words of E. H. Moore, “de­light­fully simple.”

R. L. spend the next year teach­ing math­em­at­ics in a high school in Mar­shall, Texas. E. H. Moore ar­ranged for R. L. to come to Chica­go for gradu­ate study. Chica­go had es­tab­lished a gradu­ate pro­gram in math­em­at­ics in the 1890s, one of the first in the United States. E. H. Moore was a cha­ris­mat­ic teach­er and a lead­er who built a strong de­part­ment and de­veloped many of the first gen­er­a­tion of math­em­aticians trained in the United States.

R. L. Moore spent the years 1903–1905 at Chica­go. One of E. H. Moore’s main in­terests was the found­a­tions of geo­metry, and R. L. Moore’s Ph.D. thes­is, Sets of met­ric­al hy­po­theses for geo­metry, was dir­ec­ted by Os­wald Veblen, who had got­ten his Ph.D. un­der E. H. Moore just two years earli­er. No doubt E. H. Moore was the ma­jor in­flu­ence on both Veblen and R. L. Moore.

For the next 15 years, R. L. taught at four dif­fer­ent uni­versit­ies: Ten­ness­ee 1905–1906, Prin­ceton 1906–1908; North­west­ern 1908–1911; and Pennsylvania 1911–1920. At Pennsylvania, he had his first Ph.D. stu­dents, and among them, his first wo­man Ph.D. stu­dent.

Moore re­turned to the Uni­versity of Texas in 1920, and was pro­moted to full pro­fess­or in 1923. He taught un­til 1969; in most of these years he taught five courses: cal­cu­lus, a se­quel to cal­cu­lus, a two-year se­quence in gradu­ate-level point-set to­po­logy, and a re­search sem­in­ar.

Sev­er­al of Moore’s early pa­pers were on geo­metry. In the peri­od 1916–1919, he de­veloped ax­io­mat­ic to­po­lo­gic­al char­ac­ter­iz­a­tions of the plane and the 2-sphere. He made nu­mer­ous con­tri­bu­tions to the the­ory of con­tinua and to the study of con­tinu­ous curves (loc­ally con­nec­ted, com­pact con­nec­ted met­ric spaces). He in­ven­ted the no­tion of up­per-semi­con­tinu­ous de­com­pos­i­tions, and proved a sem­in­al the­or­em con­cern­ing such de­com­pos­i­tions of the plane, and an ana­log­ous res­ult for the 2-sphere.

In 1929, Moore gave the Col­loqui­um Lec­tures of the Amer­ic­an Math­em­at­ic­al So­ci­ety, and his volume in the AMS Col­loqui­um series, Found­a­tions of point set the­ory, ap­peared in 1932. In this volume, he gives an ex­tens­ive de­vel­op­ment of ba­sic point-set to­po­logy and a de­tailed treat­ment of the to­po­logy of the plane and the 2-sphere. In 1964, a re­vised and much ex­pan­ded ver­sion of this volume ap­peared.

Moore was act­ive in the af­fairs of the Amer­ic­an Math­em­at­ic­al So­ci­ety, serving as pres­id­ent from 1937 to 1938. He en­cour­aged his stu­dents to serve the math­em­at­ic­al com­munity, and many of his stu­dents fol­lowed his ad­vice. Three of his stu­dents be­came pres­id­ents of the AMS, five of the MAA, and many served as elec­ted of­ficers of math­em­at­ic­al or­gan­iz­a­tions and in nu­mer­ous oth­er po­s­i­tions in the math­em­at­ic­al com­munity.

Moore’s teach­ing tech­nique seems to have been based on his strongly felt need to work out proofs of res­ults for him­self, with no out­side help. E. H. Moore’s teach­ing style was some­what un­con­ven­tion­al, and this may have en­cour­aged R. L. Moore to move away from the tra­di­tion­al lec­ture meth­od. Moore’s teach­ing stressed the stu­dent’s in­di­vidu­al­ity and self-re­li­ance, re­fined the stu­dent’s in­tu­ition, and de­veloped his or her con­fid­ence. He fostered strong com­pet­i­tion in his classes, and there was al­ways a race to see who could prove the the­or­ems the fast­est.

Be­cause the re­tire­ment sys­tem for pub­lic em­ploy­ees in Texas was late in be­ing es­tab­lished, the Uni­versity of Texas al­lowed fac­ulty bey­ond the age of 70 to go on “mod­i­fied ser­vice” — half-time ser­vice and half pay. When Moore went on mod­i­fied ser­vice in 1951, he in­sisted on con­tinu­ing to teach his five courses each year un­til his re­tire­ment. He was forced to re­tire in 1969. He died in 1974 at the age of 92.

In Oc­to­ber 1973, the new math­em­at­ics build­ing at U. T. Aus­tin was ded­ic­ated and named Robert Lee Moore Hall. A ded­ic­a­tion con­fer­ence was held and six of his math­em­at­ic­al grand­sons spoke: James Can­non (C. E. Bur­gess), Daniel Mc­Mil­lan, Jr. (R H Bing), Thomas Chap­man (R. D. An­der­son), John Kel­ley (Gor­don Why­burn), Frank Ray­mond (R. L. Wilder), and Ro­bi­on Kirby (El­don Dyer).

Moore mar­ried Mar­garet MacLel­lan Key in 1910. She sur­vived him by one year. Throughout all of their Aus­tin years, they lived on W. 23rd St. just a few blocks from cam­pus. Mrs. Moore served as a gra­cious host­ess for small so­cial events at home, where of­ten a few gradu­ate stu­dents were in­vited. R. L. Wilder has said of her that “it can only be sur­mised how much her strong de­vo­tion to R. L. and his work con­trib­uted to his suc­cess.”