A Reminiscence of Bill Mahavier
by Michel Smith
I’m a student of William S. Mahavier, having completed my degree under his direction at Emory University in 1974. I first met Bill by telephone in Spring of 1969; I was an undergraduate senior at the University of Texas and I had applied to Emory, where Bill taught, for graduate school. Several other students from UT, in the wake of R.L. Moore’s forced retirement, were also applying to Emory. Bill was visiting Texas and wanted to meet some of these students. I had taken courses from Moore and H. S. Wall, and so Emory was one of the places to go to for graduate school since it had students of Moore and Wall teaching there (and using the Moore method, which was particularly important to us). Bill has a deep rich voice and on the telephone he sounded like a seven-foot-tall Texas Ranger. If this image of stature could be reinterpreted in a teacher of mathematics, then my original image was pretty much on the mark.
As anyone who has met Bill knows, he was a staunch advocate and user of the Moore method, also called the Texas method, in his teaching. Back in those days it was mostly called the Texas method because both Moore and Wall at Texas, and their graduate students, used it. In my first year at Emory I took classes from Mahavier and John Neuberger, students of Moore and Wall respectively. I had taken 688 from Moore back at Texas (many who read this will know what that is - it was the first topology course that Moore taught. It was called (I think) Foundations of Mathematics).
Although I didn’t know any of the theorems from the class by name I knew them by the theorem number by which Moore identified them. Thus I still know Zorn’s lemma as Theorem 39. (I found out it was called Zorn’s lemma years later.) Between the time when Bill took 688 and the time I took it, Moore had published a new edition of his Foundations book. Thus, Bill referred to his original numbering as the “King James” version and the numbering that the new students used as the “Revised Standard” version. I conjecture that he had copies of both; certainly he was comfortable with our numbering. I think the important thing was that each of us (those who had come from UT) had either proven or tried to prove these theorems in Moore’s class and Bill picked up where we left off with Moore in the Revised Standard Version.
Regarding theology, I don’t recall having any theological discussions with Bill, though I have a pretty good guess of his theological inclinations. When I was at Emory, there was a student working under his direction at the tail end of the Ph.D. process who completed the degree a few years before I did. This student was very religious and, Bill told me, in the acknowledgements section of the dissertation thanked Jesus Christ - saying something like, “I couldn’t have done the dissertation without His [Jesus Christ’s] help.” I distinctly remember Bill’s saying something like, “If I thought [so and so] had any outside help with the dissertation, I’d never have signed off on it.”
I interpret this story as his way of emphasizing and reminding me of his view of the solitary nature of a student’s work in the Moore method technique. We well understood that we were not to get any outside help at all, be it from books, articles or other students, in our attempts to prove theorems for presentations in his class. (Apparently divine inspiration was okay - certainly we all have probably experienced something of this sort: the sudden “eureka” moment.) His course was very competitive and we all wanted to be the one to be asked to present the next theorem; such presentations had to be 100% our own work. (I remember attempting to present a proof once where I bombed terribly; I heard him commenting (within earshot of me) “I don’t think Smith thought he really had the proof” - he was right; he had an uncanny ability to read students.)
The story also says something else about Bill’s approach to teaching mathematics: anything not relevant to the understanding of mathematics, be it race, religion, sex or any other culturally used labels, was not important to his teaching and did not in any way affect his relationship to his students. All you had to do was solve problems and prove theorems and he would be delighted to guide you.
Despite our never having talked theology, I have always regarded Bill Mahavier as one of the most ethical human beings that I’ve ever met. He was true to his word, always! So, with himself as an example before us, we students had to follow suit. Near the end of my graduate studies, at the point where I was starting to write up my work, Bill told me that he was going on a sabbatical to the University of Houston. He suggested that I should go too; well, I had made friends at Emory, had a girlfriend there and wasn’t too excited about leaving and expressed as much to him. He asked me if I would go there if he could obtain a graduate teaching appointment for me there. I must have said something like, “I guess so.” A couple of weeks later there was a note from him in my department mailbox stating: “You have accepted a graduate teaching assistantship at the University of Houston.” So I went. (He was correct to have me go there; it was a great mathematical experience - I met some excellent mathematicians there.)
Bill once described to me one of his favorite Snuffy Smith comic strips. It seems that someone (let’s say it was Barney Google - I can’t remember who he said it was) was coming up to Snuffy’s house.
Snuffy says: “Why, Barney Google, I haven’t seen you in coon’s age.”
Barney: “Well I haven’t come around since that really bad argument we had. Do you remember what it was all about?”
Snuffy: “No, not a bit. Do you?”
Barney: “No, I’ve forgotten all about it too, (laughing) har, har!”
Snuffy: “Well, do you remember what I said that last time?” (Picture Snuffy with a big smile.)
Barney: “Yes, Har Har (laughing again). You said to me, har, har, ‘don’t ever come across my land again or I’ll take a shotgun to ya.’”
Snuffy: “I remember that too and I gots to keep my word!”
The last frame has Snuffy chasing Barney with a shotgun.
One of his favorite expressions that he used in response to situations where things didn’t workout quite right, was “and if frogs had wings they wouldn’t hit their butts on the ground.”
I did not have a car when I first arrived at Emory and got around everywhere by bicycle; as a poor graduate student I didn’t have enough money for a “real” pair of wheels. Around my second or third year I scraped up enough money from a summer appointment to do just that: get myself (literally) a pair of wheels. I bought a motorcycle! And shortly thereafter I learned that Bill too was a motorcycle enthusiast - and that this had also been his means of transportation as a graduate student at Texas. So we had several motorcycle talks over the years. One of the earliest ones that I recall occurred when he gave advice to me as a novice: “If you’re really careful and make it through the first 10,000 miles you’ll be fine; but you have to watch out that you don’t get cocky after 30,000.” We compared wrecks and mishaps that we had had.
Bill has told the following story a thousand times and I’m sure anybody who knew him remembers some version of it. I’ll recall my version. Apparently Bill is irritated one day while leaving Benedict Hall, the Mathematics building at UT, probably after seeing Dr. Moore; perhaps his presentation to Moore didn’t go well. He goes to his motorcycle and attempts to kick-start it; as anyone who has owned a bike knows, engines can be persnickety and one learns what one’s bike engine “likes” in order to persuade it to respond.
Because of a combination of his mood and the stubbornness of the engine, the bike just will not start. So he kicks down on the starter pedal over and over again till the engine finally starts (picture Bill telling this story over a beer and holding onto imaginary handlebars and kicking down with a foot.) His irritation now magnified by his stubborn bike, once the engine kicks in and does finally start, he takes off “like a bat out of hell.” Now the motorcycle parking area is just outside Benedict Hall and can be seen from the window in Dr. Moore’s office. The next time he sees Dr. Moore, Dr. Moore asks him, “Is it the case that the reason one drives so fast on a motorcycle is to make up for the lost time it takes to start it?”
By the time I got my motorcycle I was presenting my work to him in his office; between the bicycle and motorcycle, I took to carrying around a wrench and pair of pliers in my back pocket; after I had graduated he passed on to me that he noticed this fact one day and had told Neuberger (I think) that “anyone presenting a proof with a wrench in his back pocket can’t be all bad.” I feel that this symbolized his appreciation of a common sense-ical, jack-of-all-trades, roll-up-your-sleeves-and-get-your-hands-dirty approach to mechanical (or whatever) day-to-day problems that need to be solved.
Though an excellent theoretician, it seemed to me that he used his Moore method approach to everyday issues: namely he would figure out a solution (to whatever practical problem needed solving) himself. The year during which Bill and I were at Houston was the year when there was the gas-rationing, embargo, or whatever problem; it was so long ago that all I can remember about it was that obtaining gas was potentially problematic.
That year the Topology Conference was in Charlotte, North Carolina - so, before we left, Bill packed up his old station wagon with two extra gas tanks that he had filled up from his boat (I think his wagon had the “slant six” engine; in any case, I learned what that was from him). We picked up Ben Fitzpatrick at Auburn on our way up. I remember that we drove (probably on the way back) on Sunday and were amazed at the number of gas stations that were still open. (I was, anyway. Bill was pretty sure that capitalism would win out and encourage the human propensity to make money, and so was not so surprised - but he still wanted to make sure that he had plenty of gas, knowing that we would be traveling on a Sunday.)
We never had to use the extra gas tanks. And so I rode in the back seat of the station wagon right in front of two full tanks of gasoline, confident in Bill’s driving skills whether or not he had had a beer. (Bill maintained that he was a good drunk driver and that he knew which eye to put his hand over when he saw double. Having had many conversations with him over many beers, I’m confident that the real situation was that he well understood his limits and never went over them - well, at least not when he drove and I rode with him.)
He once described to me a notion that he had for a measurement of humans that he called the “Ape Factor”. The Ape Factor was the ratio of the distance from fingertip to fingertip of the arms stretched out horizontally to one’s height. The larger the Ape Factor, the more ape-like one was. Apparently he had a particularly high Ape Factor and I think he was proud of the fact that a mathematician could have such a large one. I never compared mine to Bill’s; I’d rather like to think that mine’s high, too, and thus follow him in this Ape Factor-mathematician anomaly.
After I had graduated I would see Mahavier regularly at meetings, at the annual Topology Conferences in particular; and we’d discuss just about anything, but in particular the Texas/Moore method. Not too many years ago, we were discussing directing Ph.D. graduate students; this was after things got pretty bad for him at Emory and he didn’t have any more graduate students.
One of the things that he told me was that he used to keep a list of potential problems for his next set of Ph.D. students to work on. He said that if he didn’t get any more students, he’d start working on them himself. Apparently one of these topics was that of inverse limits with upper semi-continuous bonding maps. And indeed a few years ago he started to work in this area; he connected up with Tom Ingram about this and the two of them published some results in the area.
My dissertation was on a generalized inverse limit, too (generalized to uncountable index sets); and so I was very excited about these papers. I worked through various parts of them (a graduate in the Moore method pedagogy must approach reading papers in a unique way) and then defined the concept to one of my own graduate students, Scott Varagona - who was able to obtain some interesting new results on his own. So, Bill’s list of potential problems did indeed end up being used by one of his mathematical grandchildren.
Bill Mahaiver was very much like a second father; he guided me through my mathematical studies. I respected him so much that I would listen to his advice on all sorts of things besides mathematics: how to keep a car in repair, how to raise a family, how to build a house and, of course, how to teach. I would often get discouraged with my own classes, but a discussion with him (usually at a mathematics conference) on the issue would always re-inspire me. And he always had a topology puzzle or problems to challenge us/me or whoever was around the table.
I loved his stories and puzzles - I think there is something archetypical about sharing stories and challenges that dates back to pre-civilized days when we sat around campfires and knowledge was conveyed by stories. The corresponding modern-day activity among topologists would be the beer party. And I know that these stories will live on to carry his memory; for we continue to share them, as this short memoir indicates. Bill’s presence continues to influence my mathematical children as well as my biological children. His example was not just on how to teach and learn mathematics but on how to live an exemplary life.