Saturday, January 24, 1976

Court Real Palacio del Rio

San Antonio, Texas (Hilton Hotel)

*(Transcript of a cassette tape made at the presentation breakfast by Lucille Whyburn. Unfortunately a portion of the tape near the beginning was erased but it has been reconstructed through the kindness of Professor Bing.)*

**DR. BING:** Greetings Texans! I am amazed! I prophesied utter chaos for today with people coming in for breakfast at 7:30, at 7:45, and some even at 8:00 o'clock. My opening remarks were to suggest that you continue eating. But now that it is time to begin, everyone has been served, the tables have been cleared, and we are ready to begin. You arrived on time so early in the morning. I am amazed.

The University of Texas at Austin Mathematics Award was made possible by a gift from Professor Emeritus H.J. Ettlinger. Professor Ettlinger was a professor at The University of Texas for many years and has remained a staunch booster. Professor Ettlinger is with us today. (*applause*)

The award is to honor two of the Department of Mathematics' most famous members -- Professors R.L. Moore and H.S. Wall.

Members of the Selection Committee were myself, Professors Hyman Bass of Columbia University, Joe Diaz of Rensselaer Polytechnical Institute, George Lorentz of The University of Texas at Austin, Deane Montgomery of the Institute for Advanced Study, C. B. Morrey of the University of California, Berkeley, and Stan Ulam of the University of Colorado.

The Selection Committee realized early that with so many good papers to consider, there was no assurance that we could select the very best. Opinions would differ as to the very best paper and although a choice by the Selection Committee might not be one which all would agree was the very best paper of the lot, it would be a worthy paper. There were 91 papers submitted for our consideration and some of these were excellent.

I want to run this like a beauty contest so I'll tell you who the finalists were. These finalists may not actually be the very best of the papers, but they are those that were still being considered by the Selection Committee during last November.

I will include the winner's name among the finalists, and then you will find out later who the winner is. I have not told the winner that he or she will win the prize. The finalists were:

Professor Sterling Berberian for his book on *Baer *-Rings* published in 1972.

Professor James Daniel for his joint book with Ramon E. Moore, *Computation and Theory in Ordinary Differential Equations* (1970).

I might tell you frankly that the Selection Committee favored single-authored papers over joint ones but as of November 15, we were still considering this book by Professors Daniel and Moore: *Computation and Theory in Ordinary Differential Equations*. I thought Professor Daniel would be here this morning, but -- (*Bing then sees Daniel*). Would you stand up? (*applause*)

Another one of our finalists is: Professor Bill Eaton for his research paper on "The Sum of Solid Sphere," *Michigan Mathematics Journal* (1972). Bill, will you and Ann stand up? (*applause*)

Another one of our finalists is: Professor Ed Hewitt for his book with Kenneth Ross on *Abstract Harmonic Analysis*, Vol. II, (1970). I talked with Professor Hewitt on the phone this week. He is now in Europe and expressed disappointment at not being with us today.

Another finalist is: Professor Elton Lacey for his book on *The Isometric Theory of Classical Banach Spaces* (1974). Elton, will you and Bonnie stand up? (*applause*)

We had a problem on the next. We were considering two of the books of W.T. Reid of the University of Oklahoma. One of his books is: *Ordinary Differential Equations* (1971) and the other is: *Ricatti Differential Equations* (1972). Professor Reid is here with his wife Idalia. Professor Reid, will you and Idalia stand up? (*applause*)

Another of our finalists is Mary Ellen Rudin and here we had problems again since we were trying to decide between two of her very superior papers. One was her paper: "A normal Moore space X for which X I is not normal," published in *Fundamenta Mathematicae* (1970-71), and the other was *Lectures in Set Theoretic Topology*, CBMS Regional Conference Series in Mathematics (1975). Mary Ellen, will you and Walter stand up? (*applause*)

Next, we will hear from Professor R.L. Wilder. Of those here today, he is probably the first to get a Ph.D. at Texas. When did you get your degree?

**DR. WILDER:** 1923.

**DR. BING:** Did anyone here get their degree before 1923? (*no response*) Professor Wilder is going to make a few comments about R.L. Moore and Mathematics. (*applause*)

**DR. WILDER:**: I was telling President Rogers this morning that I was either the fifth or sixth Ph.D., I think, at The University of Texas. In '23 there were two of us who got doctorates. One was a lady in history and I was the other one. I accorded her the privilege of being fifth and I, the sixth, (*laughter*) I guess. I was Moore's first Ph.D. at Texas. He had three Ph.D.'s at Pennsylvania: J. R. Kline, Anna Mullikin, (who only died a couple of years ago), and a third one, George Hallett.

I might say that I very nearly missed this opportunity. In fact I very nearly missed it back in the fall of 1921. (*laughter*) I came to Austin to study actuarial mathematics with Professor E.R. Dodd, and, after talking with Dodd awhile, I decided I wanted to take a course in pure mathematics, too. I came here from Brown. "Well," he said "you might take Moore's course." I asked, "Where'll I see Moore?" He replied, "Moore always has a table at the Registration building, and you might talk with him." I went over to the Registration Building and introduced myself to Moore, and I soon realized that he was very negative about my enrolling in his course. I know I've told some of you about this before. I had two counts against me, as I analyzed it later. One was that I was a Yankee. The second was that I was an actuarial student, and what in the world was an actuarial student doing taking a course from Moore? Well, this went on for some time, and I didn't want to give up. He finally made the mistake of asking me, "What is an axiom?" I had pretty good training at Brown, and I knew what an axiom was. His guard was down, and I think he, in utter frustration, said, "OK, go ahead, and take the course." Actually, I wasn't really in the course until I proved what we called Theorem 15 in those days. (*laughter*) I didn't know that at the time. (*laughter*)

I also had a great privilege one year when Dodd went to Williams College to teach. I had the great privilege of occupying his office which was with Moore. We had one of the offices up in the old Main Building which consisted of a sort of a set of boxes along the side walls of the old theater. I know Professor Ettlinger remembers this well; he was in one of those boxes. They had taken off the side rows of seats in the theater and built these boxes along the wall. Of course, they were anything but soundproof. In many ways, this old theater was convenient. When your students came to interview you they could sit out in the middle of the theater in the seats while they waited to talk with you. I have never forgotten A. A. Bennett, who established the Bennett Calculus Prize, which I think is still in existence at Texas. He was in the office next to Moore and me. And R.L. delighted in baiting Bennett. When we found that we were in agreement (Moore and I on something), he'd say, "Let's raise our voices." (*laughter*) We'd raise our voices and in about two minutes you'd hear Bennett's chair scraping. He was sure a fast walker. He'd come trotting around and knock on the door. We'd say, "Yes, come in." "Gentlemen, I'm sorry, I wasn't eavesdropping, but I couldn't help but overhear what you were saying, and I wanted to take issue with you." (*laughter*) We always chose something, of course, with which we knew he would take issue. (*laughter*)

Well, I suppose I should say something about what I think Moore's influence on Mathematics was. I know very well what his influence on me was. As you all know he had fifty doctoral students in all, and I think that through his own publications and his doctoral students', he must be accorded the right to being cited as one of the greatest influences on American mathematics in the current century. I have just written his obituary for the *Bulletin*. It should be out in either the next issue or the issue after that; I've already done the galley proofs over a month ago. I've estimated he had at least five hundred and fifty descendants and probably around six hundred mathematical descendants. Among these descendants there are two presidents of the American Mathematical Society, four presidents of the Mathematical Association and three members of the National Academy of Sciences and one present member of the National Science Board.

It's a curious thing, but statistics show that it was much easier to get a Ph.D. with Moore than it was to get a Master's degree. Moore had only four master's degrees. I knew them all. One of them was in the same class with me in that Fall of 1921. I won't name her. It's a lady. But at the end of her year when she took her degree she decided it was better to get married than to go on for her doctorate. Whereupon Moore made a solemn vow in my presence: "I'll never take on another woman student!" What do you think of that, Mary Ellen Rudin? (*laughter*) Moore, of course, broke his vow in the early 1940's, and I must say that I think Mathematics is very fortunate in his having broken his vow at that time. Moore didn't normally break a vow. As I say, he had four master's degree candidates. One of them did go on and take his doctorate.

There are many other things I could tell about Moore and some of the controversies I had with him. You know very well it was easy to have a controversy with Moore; he loved controversy, and he never liked trite remarks. I was in Austin -- I don't know whether it was the early forties perhaps -- and walking across the campus with Moore. I don't know what he said, but I made the trite remark, "Oh," I said, "I suppose there's something good in everybody." Oh boy! (*laughter*) Just at this moment, Dean Harper, he of the red bow tie, came across our path and Moore stopped him. He said, "Dr. Harper, Wilder here has just said to me, 'There's some good in everybody,' but you'll agree, won't you, there's no good in a horse thief?" (*laughter*) Harper thought for a moment. "Well," he said, "you know, when I was a pharmacist in West Texas (or some place, I forget where), back in such and such a day, among my best customers were the James boys." (*laughter*) Harper came to my assistance, bless his heart. I learned during the process -- and I'll stop here; don't worry any further. During the process of writing the obituary, I discovered that Moore was only two generations from being a Vermont Yankee. His grandfather Moore was a Vermont physician who went South to the Carolinas, I guess, to study the herbs used by the Indians and others, and, when he left there, he left two sons to the South. One of them was Moore's father. Later, of course, the not uncommon situation developed where these two brothers were fighting their brothers in the North during the Civil War. Thank you. (*applause*)

**DR BING:** We have Professor Walter Scott, who will say a few words about H.S. Wall and Mathematics.

**DR. SCOTT:** It's good to be here in Texas. It's a homecoming for me, though I'm not a graduate of The University of Texas. I went to a small school a couple of hundred miles east of here. But as you know, when we get out of the state, we all become Texans -- professional Texans. (*laughter*) I think Professor Bing knows this well from his years at Wisconsin.

My association with Hubert Wall began in 1938 and is one for which I'm very grateful. We worked together in a number of areas. We corresponded, and we tried to keep each other informed of what our students were doing.

I'd like to start with a bit of biographical material. Wall was born in Iowa in 1902, and he went to high school there. His college work was at Cornell College in Mount Vernon, Iowa and in 1924 he received both his bachelor's and master's degree. During the Cornell years he had a professor, Professor Elmer Moots, who was a strong influence on him, and one of his subsequent papers, an important one, was dedicated to Professor Moots. After leaving Cornell College, he went to the University of Wisconsin at Madison and worked under E. B. VanVleck where it was quite natural that he acquired an interest in continued fractions, Pade tables, moment problems, and related subjects. When he received his doctor's degree in 1927, he went to Northwestern University and remained there until 1944. At that time he went to the Illinois Institute of Technology for two years and in 1946 came to The University of Texas. Indeed, I remember soon after his arrival in Texas, he gave me a hard time about not making him believe all of those lies I had been telling about Texas! He really felt when he came to Texas, that it was in fact, a homecoming for him.

Now during the years 1939 to 1944, Wall had worked with Professor Ernst Hellinger, and they had collaborated on an analysis seminar in which they used very brief hints and asked the students to provide proofs of the theorems. This was, let's say, the beginning of the seminar method which he later developed more fully at The University of Texas. The origin of that seminar was a non-credit course, really, designed originally just to read papers in which people were interested. It had one great attraction, though. Following the regular seminar there was a delayed seminar where everyone adjourned to have a beer or two, and this was a traditional Wednesday evening affair. Now, when Wall came to The University of Texas, it was natural for him to utilize the seminar method of instruction even more fully, and this he did. I think there are many of you here who had seminars with Wall. His book, *Creative* *Mathematics*, was written to try to explain his methods and how he hoped to develop creative talents in his students. And, I might add, in looking at some of the letters, I had a few of them, his enthusiasm for what his students were doing was amazing. He characterized a student as a potential Hardy or a potential F. Riesz on the basis of his proofs of a theorem or two in seminar, and this enthusiasm certainly had an effect on his students -- there's no doubt.

Wall's interest was primarily continued fractions and continued fraction-related concepts. He did write one paper in algebra, a paper on hyper-groups. That was the result of a year he spent at the Institute for Advanced Study. I don't know whether he ever really worked in this area again. I found one paper by Oystein Ore as a follow-up on this, but where the subject is now, we would have to ask an algebraist. He wrote a book called *The* *Analytic* *Theory* *of* *Continued* *Fractions*, which is really a standard reference in this field, the field of continued fractions.

His research contributions are substantial, and I'll try to briefly explain what went into each. Continued fractions, in general, is a very difficult area because there are computational difficulties. You want to test an idea, and you can't even get an example or a counterexample. What Wall did to the theory of continued fractions was to synthesize a large part of it. The major item, I would say, was the theory of positive, definite-continued fractions, including J-fractions. Now the first step in this direction came in a joint paper with Hellinger in 1943, and subsequent developments followed fairly quickly so that the theory was relatively complete by about 1948. The viewpoint used was one that certainly strengthened the repertoire of everyone working in the area. He used a double-edged sword, the continued fraction, as a sequence of linear fractional transformations and also as an infinite linear system. These result were quite startling.

In another area, there were the convergence results for continued fractions. Let me give an example, what is called the convergence region problem: within what region can the elements of a continued fraction of a certain type vary while preserving convergence and vary independently? Up to 1940, the best region that was known was a small circle in the complex plane, center at the origin, radius one-fourth. Then came the first of the Parabola Theorems in which it was shown that any bounded portion of a parabola with center at the origin, symmetric about the real axis, vertex at minus one-fourth, was the best possible such symmetric region and that any bounded portion of the parabola was a convergence region. This represented a vast change. Now there were other theorems, I don't want to get specific, but other theorems of this nature including the rotated parabola theorems and the associated value region problems.

A third area in which Wall made a very substantial contribution was the characterization of Hausdorff Moments by means of continued fractions, and also some continued fraction transformations which enabled him to obtain inclusion relations for Hausdorff Summability Methods. A fourth area was the area of Harmonic Matrices and the continued fraction integral (or continuous continued fraction), and in this he reworked and generalized results that correspond to the differential analog of the linear equations that go into the Jacobi matrix.

A fifth area is one in which he didn't publish anything and yet in which he had a substantial research interest, and that is the Hollinger Integral. I know that many of his students worked in this area. I'm looking at some of them now. This was characteristic of Wall or, I should say, of the two periods in his life. The first portion, in which he published very prolifically; the second period, in which he devoted himself to his students. He had a total of sixty-two doctoral students and most of those, all except five, were at The University of Texas. I remember in talking with him he said that he really felt his students were a much more important contribution to mathematics than was his own research. I think the vote is still being taken -- both are important. Thank you. (*applause*)

**DEAN OLUM:** R.H. doesn't want to introduce me. (*laughter*) Unlike many of you in this room, I have not had the privilege of knowing Dr. Moore and Dr. Wall. I am a relative newcomer to The University and the state of Texas, but I must say that this is a most impressive gathering -- a tribute to their memory and a great pleasure to be part of it. I know, of course, both of them by their great reputations, and I think it is a wonderful thing that Professor Ettlinger has done in organizing all of this and giving this prize in memory of these two great Texas mathematicians. I would like to personally pay my own tribute to Dr. Ettlinger, whom I have gotten to know in the course of the past year-and-a-half that I have been here, and I cherish Dr. Ettlinger, whom I did not know before, as a new-found friend.

It is my own particular pleasure to be able to introduce to you the President of The University of Texas at Austin. Dr. Rogers is a scientist, a biochemist, who received her Ph.D. from The University of Texas, and is now a professor at The University as well as President of the University. As a professor, she is a professor in the College of Natural Sciences of which I am the Dean, which, I think, makes me her boss, (*laughter*) but it's not a distinction on which I ordinarily insist. (*laughter*)

I hope you won't think that it's a terrible sexist statement for me to call your attention to the evident fact that Dr. Rogers is a woman. (*laughter*) Those of you who read the papers or listen to the radio will know that black leaders in the United States have recently begun to protest at the notion of being labeled as "black" leaders. You don't call white leaders, "white" leaders, and no one would call Derek Bok the "male" president of Harvard University. (*laughter*) Dr. Rogers is the President of The University of Texas, but the distinction is so rare and unusual that it's worthy of comment. Dr. Rogers is the first, and I believe still the only, president of a major American university, who is a woman. I hope she won't feel I'm pressing it too far when I say that The University of Texas is her total dedication and her whole life. Everything that concerns the University concerns President Rogers. Her presence here, in fact, is typical evidence of that statement.

Running a university of forty-two thousand students would be difficult in any case. Running The University of Texas is even more difficult. (*laughter*) No other university, even with that many students, imposes such a burden on its president. It's a large and complex university and a faculty with many and divergent interests. The President of The University has to deal not only with all of that but with a System's Administration which does not always understand all of our problems, with a Board of Regents who are by no means shy and retiring about what happens at The University, (*laughter*) a Coordinating Board and the State Legislature.

The fact that with all of that she finds time to come here and join us in the awarding of this prize, as I said, is a remarkable thing, but it is typical of Dr. Rogers. I think that wherever the needs, the purposes, the activities, the future of The University of Texas at Austin is at stake, Dr. Rogers will be there. It is a pleasure to present her to you. (*applause*)

**DR. ROGERS:** Thank you very much, Paul. We don't argue over who's boss!

I do consider it a real privilege to be here today, both for the honor of being able to present this award, and also for the opportunity to pay my personal tribute to at least two of the professors who are involved in this award today. I didn't have the privilege of knowing Professor Wall, but I've known Professor Ettlinger and Professor Moore almost from the day I first came to The University of Texas, and that was a long time ago. I first came here in 1937 when my husband came to work on his doctor's degree in Chemistry. During that period, since I'm a great music lover as was my husband, we attended every musical concert that we could. I don't remember ever going to one of those but what I saw Professor Ettlinger and his gentle wife and his very precocious son, Martin, also at the concerts. He has been a real and vital part of The University of Texas for many, many years; and this award that he has set up, that's being presented today, is further evidence of his devotion to this institution and to the discipline of mathematics. He has made contributions all through the years and continues to make them. So I want to say, "Thank you," for myself as well as for The University of Texas, Professor Ettlinger, for what you have done and what you're continuing to do. (*applause*)

And now if you'll indulge me just a little further I want to talk about at least three associations that I've had with, that I did have with Dr. Moore through the years. My undergraduate degree was in English literature, which I got before I was married. After my husband's death, I decided that I would like to study chemistry. But the thing that frightened me most was that during those years when my husband was a graduate student here, I heard him and his friends talk about how difficult calculus was. I thought I could learn chemistry. I wasn't sure that I could pass the calculus course that was a required part of that chemistry program. I decided to embark on this anyway, and, fortunately for me, when I started to take solid geometry, I got into Dr. R.L. Moore's class. He had us learning calculus before I even knew we were out of solid geometry. It wasn't hard at all. And I consider one of the real triumphs of my student career, the fact that when I finished that calculus course, Dr. Moore called me in and tried to convince me that I would find mathematics more interesting than I would find chemistry. And that was also in the early '40's when he had gone back on that pledge that he made to you (*looking at Wilder*). (*laughter*) He pointed out to me that he could see to it that I had a Teaching Assistantship if I wanted to change over.

I didn't change; I stayed in chemistry, but when I came back here on the faculty and started attending faculty meetings, I saw another side of Dr. Moore. (*laughter*) He, as those of you who knew him will remember, was one of the giants among the faculty. He took his citizenship responsibilities seriously; he attended the faculty meetings. If there was a controversial subject, he always spoke his mind on the subject, and because he was such a great scholar and great thinker, people listened to him. They had great respect for him, and he was very persuasive. During the later years of his life, when he was well up into his 80's, one of our articulate faculty members was still trying to get the calendar changed to the calendar that we do now have: where we finished up the Fall semester before Christmas. Dr. Moore didn't think that was academically sound. He was very much opposed to it. He had talked it down several times, and then it was brought up again, and Dr. Moore went to that general faculty meeting. I attended that meeting with a very young professor who hadn't known Dr. Moore at all until he saw him there that day. Dr. Moore got up, and his knees were shaky, and he was a little bit doddering, and he stood there and just talked in general -- not about the calendar -- but he just sort of rambled around for about three or four minutes. But he got all of his thoughts together, and then he slapped down every argument that the articulate faculty member had made and won the day, and the calendar didn't pass. That young faculty member who was with me was so impressed that he still talks about it every time I see him.

The other association that I had with Dr. Moore was when I was serving as Associate Dean of the Graduate School. Again, this was in the period when he was in his eighties. He was very impatient with regulations that he didn't see any sense in, and one of the regulations that had come about by that time was that we have formula funding for The University. We get a higher rate for graduate courses than we do for undergraduate courses. But the Coordinating Board, and the Legislature says if you have one undergraduate student in that graduate course, then you get undergraduate funding, instead of graduate funding. Dr. Moore thought this was completely ridiculous. As you know, he had students that he saw possibilities in, and he carried those students along just as rapidly as he could. When I was in the graduate school, I would find every now and then that Dr. Moore had three undergraduate students in his graduate class, and I would call Dr. Moore and say, "Dr. Moore, you're going to keep us from getting the proper kind of funding." "That's silly," he'd say. He just wasn't going to pay any attention to it. And he didn't! And he won that argument, too. I never did convince him that he shouldn't have those students in that class.

Well, so much for my association with Dr. Moore. He, as I said, was one of the real giants of this campus and one whose influence will continue to go on and on through all of these academic children and grandchildren that he has.

It's now my privilege to reveal to you the winner of this $3,000 award. I have the check all made out here, and I understand that the winner is an academic grandson of Dr. Moore, which makes this event even more meaningful than it might be otherwise. The winner of the award, and I will ask him to come forward so that I can present the check, is William T. Eaton. (*applause*)

(*Long pause. Eaton goes over and shakes hands with Dr. H.J. Ettlinger and Dr. Ed Burgess before coming to the speaker's stand.*) I've never seen one so reluctant to accept money! (*laughter*) What's funny is that he didn't grab the check first! (*laughter*) Since I've stayed in chemistry instead of mathematics, I can't really say anything about the paper, though I did read some comments on it. The only thing I can tell you, it's on topology, and the critics considered it clean. (*laughter*)

**DR. EATON:** I'm kind of nervous here, but I do think that breakfast is beginning to taste better and better. (*laughter*) I notice they have the decimal point in the right spot! (*laughter*) Thank you all very much for coming. (*applause*)

**DR. BING:** I might read this comment, this "clean" comment. The paper for which the award is given is "The Sum of Solid Spheres," and one of our people who commented on this says, "Eaton's results are clean. The proofs are delicate and difficult. The consequences are rich, interesting, and surprising." I think that I'll leave it at that. (*laughter*) You're dismissed. (*applause*)

-END OF CEREMONY-

*Transcribed in the Department of Mathematics, February 1976.*