Celebratio Mathematica

Robert Lee Moore

Christmas in Big Lake

by Sam Wayne Young

It was the spring of 1959, and I had struggled that school year to catch on to the the­or­em-prov­ing courses of Fitzpatrick and Wall. It was com­ing to­geth­er for me to some ex­tent, al­though I was not do­ing nearly as well as many of the oth­er stu­dents, such as my friend Harvy Baker, for ex­ample. I do re­mem­ber that I man­aged to give an ep­si­lon-delta proof of the fun­da­ment­al the­or­em of cal­cu­lus. But Harvy came up with a de­scrip­tion of a set of real num­bers which we now know as the Can­tor set, and I thought that there was no such thing. I tell you this so you will know about where I stood in my newly chosen ma­jor of math­em­at­ics.

By that spring, Harvy and I and oth­er class­mates had heard stor­ies about R. L. Moore and his fam­ous MH688 course. We were curi­ous to find out if we could, or should, sign up for it the fol­low­ing Fall semester. We were un­der­gradu­ates, and would have to get spe­cial per­mis­sion, and we were not sure it was the right thing to do. So we went to talk to Ben Fitzpatrick and asked for his ad­vice. I re­mem­ber that Ben warned us that it would be very dif­fer­ent from any­thing we had ex­per­i­enced be­fore. And I guess he gave us the ad­vice of go­ing ahead and sign­ing up, be­cause in Septem­ber we were there.

Dr. Moore began the course by stat­ing Ax­iom 0 (“Every re­gion is a point set”) and some defin­i­tions and the first few the­or­ems. The un­defined terms were “re­gion” and “point.” On the second day of class Dr. Moore asked who could prove The­or­em 1. Ac­tu­ally, he may have star­ted down the class roll, and asked stu­dents one at a time if they could prove The­or­em 1. There were plenty of stu­dents who could prove the first few the­or­ems, which were ele­ment­ary con­sequences of the defin­i­tions. But I did not un­der­stand how to prove the the­or­ems, and I did not un­der­stand the proofs that were giv­en. Look­ing back on it now, I think that I failed to un­der­stand that the the­or­ems were in­de­pend­ent of the mean­ing of the un­defined terms. I was la­bor­ing un­der the as­sump­tion that the stu­dents who went to the black­board to present a proof knew more about “re­gions” than I did.

I was con­fused about some oth­er things too, but it does not mat­ter why; I was simply baffled and flustered by the en­tire pro­cess. I con­tin­ued to take notes me­tic­u­lously, and this habit turned out to be a con­trib­ut­or to my even­tu­al sal­va­tion. I would write down the words of a proof, and copy the draw­ings that stu­dents were put­ting on the board, and then I would copy it all again neatly in­to a spir­al note­book. After a few weeks we got to some of the more dif­fi­cult the­or­ems, or so it seemed to the class. To me, they were all im­possible. I con­tin­ued to copy the proofs which were just so much gib­ber­ish to me.

Dr. Moore’s meth­od of call­ing on stu­dents for proofs in­volved call­ing first on the per­sons who had con­trib­uted the least. My name rose to the top of the list. The class met at 9:00 am on Tues­day, Thursday and Sat­urday, and my day would usu­ally be­gin the same way. Dr. Moore would take his place in front of the classroom, and might make a few com­ments or re­mind us of where we were in the ma­ter­i­al yet to be done. Then he would look at me and ask the same ques­tion, “Mis­ter Young, can you prove the next the­or­em?” It was a bit ter­ri­fy­ing and hu­mi­li­at­ing, but I felt no neg­at­ive feel­ings to­ward him. After all, I knew how to ex­tract my­self from the situ­ation. I had to prove a the­or­em and get the pres­sure off of my­self. But my an­swer was al­ways the same, “No sir, I can­not.” It sounds cruel as I de­scribe it now, but there were no hurt feel­ings. It was as much com­ic­al as cruel. Someone had to be the worst stu­dent in class, and it was me.

In those days, the Fall semester did not end un­til after the Christ­mas break. Our class would meet three or four times after we got back from Christ­mas. On the last class meet­ing be­fore Christ­mas, Dr. Moore spent the en­tire hour stat­ing the­or­ems and defin­i­tions. He really loaded us up with work to do. I took my notes and went to be with my par­ents for Christ­mas. My par­ents had moved that year from San An­gelo to Big Lake, Texas, a small oil-town 80 miles to the west. They lived in a met­al build­ing which had been con­ver­ted from the of­fice of a weld­ing shop in­to liv­ing quar­ters. I knew prac­tic­ally no one in the town, and so I was as isol­ated and un­dis­trac­ted as I could pos­sibly be for the task be­fore me. I be­lieve that I began as usu­al to make good cop­ies of the latest proofs that were giv­en in class.

This time, as I read the proof of The­or­em 25 (I am not sure if 25 is the num­ber) that my class­mate had presen­ted, I some­how man­aged to un­der­stand the ar­gu­ment. I saw how he had made use of a pre­vi­ous the­or­em and the defin­i­tions which were in­volved. I was as­ton­ished! I was un­der­stand­ing one of the proofs for the first time. I went to the proof of The­or­em 24 and I man­aged to un­der­stand that one too. I re­mem­ber think­ing that per­haps I could proved some of those the­or­ems my­self. I worked my way back through the the­or­em se­quence, and proved al­most all of the the­or­ems in my own way, and wrote my own proofs in my spir­al note­book, in­clud­ing those very ele­ment­ary the­or­ems at the be­gin­ning. I worked all day, every day, through Christ­mas do­ing this. Fi­nally, with a few days left be­fore head­ing back to Aus­tin, I was ready to look at the work that Dr. Moore had giv­en us to do dur­ing the break.

I wish that I had the abil­ity to de­scribe the ex­hil­ar­a­tion that I felt to the core of my ex­ist­ence when I put to­geth­er a proof of The­or­em 26. I marched for­ward prov­ing the next the­or­em, and the next. I am not say­ing that it was easy; it was ex­haust­ing work. I would get up early in the morn­ing, and work all day. I won­der what my moth­er thought about all this. She prob­ably thought that her son who went off to col­lege had to study. She could not have known that what I was do­ing went well bey­ond study­ing. She could not have known that her son be­came a math­em­atician that Christ­mas.

The time came to go back to Aus­tin, and a great fear came over me as I visu­al­ized the in­ev­it­able scene that would un­fold in the classroom. I was ready and con­fid­ent with proofs of sev­er­al of the up­com­ing the­or­ems, but I was scared to death. I had nev­er “been to the board.” When the time came, Dr. Moore looked at me and asked the usu­al “Mis­ter Young, can you prove The­or­em 26?” I am pretty sure that my ex­act an­swer was “Yes, sir, I can.” I had learned that he did not like for any­one to say “Yes, I think I can.” The fear that I felt at that mo­ment is in­des­crib­able, but I want to re­peat that I was con­fid­ent that my proof was cor­rect. The fact that I knew I had it, the fact that I was con­fid­ent in spite of the aw­ful fear of the mo­ment is a trib­ute to the Moore meth­od of teach­ing. I went to the board and presen­ted my proof. He asked if any­one had any ques­tions. Thee were none and I took my seat.

My friends who have had courses from Dr. Moore are al­ways sur­prised when I tell them what happened next. He nev­er called upon the same per­son who had just presen­ted a proof. It was just not done. He would turn the pres­sure on someone else. But I dis­tinctly re­mem­ber that he looked around the room as if try­ing to de­cide whom to call upon. He eyes fell upon me again and he asked “Mis­ter Young, can you prove The­or­em 27?” I said that I could, and went to the board again. When I fin­ished I sat down again and again he looked around pre­tend­ing to de­cide and said “Mis­ter Young, can you prove The­or­em 28?” This imp­ish routine con­tin­ued for an hour, and star­ted again at the next class meet­ing. In fact, no one else was called upon for the re­mind­er of the term. I proved all of the the­or­ems that we had time for.

Un­for­tu­nately, I was not able to con­tin­ue with my class that next semester, be­cause of a con­flict with the only sec­tion of Rus­si­an that was offered, and I had to have the Rus­si­an class to gradu­ate. I re­sumed the MH688 course the next year as a gradu­ate stu­dent, and took the MH689 course the year after that. I also took Dr. Moore’s meas­ure the­ory course. Along the way, I be­came a stu­dent of H. S. Wall and chose that route for my Ph.D. work. I will al­ways re­mem­ber that Christ­mas in Big Lake, and the feel­ing of tri­umph that res­ul­ted — a meas­ure of suc­cess for the Moore teach­ing meth­od, and suc­cess for my­self which pro­pelled me to­ward a ca­reer in math­em­at­ics. Of course, I will al­ways treas­ure the in­flu­ence that he had upon me. I like to think that maybe, just maybe, he nev­er for­got me either.

Ope­lika, AL
March 5, 1998