This is Ben Fitzpatrick. I'm with Richard D. Anderson in New York City. It's the 29th of June, 1998, and we're going to talk about our meetings with Edwin Moise and Gail Young.
Ben Fitzpatrick: Good morning, Dick.
R. D. Anderson: Good morning, Ben. We had quite an interesting day yesterday visiting for about two and a half hours with Ed Moise and with Mary Moise, his wife or former wife, who helps take care of him, I believe. I've known Ed for a long time, for I first went to The University of Texas in the fall of 1941, and I was in a class with Ed Moise and Gail Young, and also with Joe Diaz, a class taught by Vandiver, a distinguished mathematician there who eventually was on the serious outs with R. L. Moore. It was an interesting class. I got to know both Gail and Ed fairly well and other classmates as well as fellow students in a fairly small environment of students. There may have been a total, I'm sort of guessing, of ten or twelve of us around. There were four beginning students in class with me, and there were a number, maybe as many as 15 students, who would be identified as part of the system at that time. Those were all the various levels of graduate work in the math department. Ed was a very bright guy. He had been an undergraduate at Tulane, and there are interesting stories in the record about how he was identified as a very promising undergraduate, and was essentially sent to work with R. L. Moore. His brother-in-law, Gail Young, (Gail had married Ed's sister) was an earlier, a year or so ahead of Ed in school, and Gail had come over to Texas to work with Moore and to have a half time instructorship as a senior finishing his degree and going ahead and working toward a doctorate with Moore. It was through Gail, I believe, that Ed came over, and the two are still close friends. They still see each other, in fact, they are going to be seeing each other today. Ed lives in downtown Manhattan, and Gail lives north along the Hudson River, and they do get together occasionally, and continue to be close friends. Neither one is in good health. Ed has had several strokes, and has a difficult time communicating. You have to work hard to understand the words he's trying to state. He also has difficulty writing at this stage, so I think it was a very good thing that we were able to come up and interview him on this occasion. It was a pleasure also to see Mary, who is in pretty fair shape, who was also present. I've known Mary off and on since graduate student days when she was married to Ed and I was married to Jeanette. We had one child, and our second child and their first came about the same time, shortly after the war. Gail is also not in good shape. He's in better shape than Ed, but Gail has apparently had some serious heart problems. He's taking a great deal of medication, and I think he mentioned to us something like $400 a month spent on pills. We can talk with him rather freely, but he and we agreed he should not personally be taped. We would simply report on our understandings of what he was saying. We could direct some questions and suggestions to him. This made more sense than trying to tape somebody who has some difficulty recalling names of people, perhaps under the influence of medication.
Ben Fitzpatrick: I might begin by saying that we sent Ed Moise and Gail Young some topics and possible questions that they might want to address, and Ed supplied written responses to some. I might just read those out now so they'll be in the record.
This question is from Dave Roberts who communicated it to Albert Lewis: In what ways, if any, did studying with R. L. Moore influence Moise's involvement with reform of math education and the substance of his reform ideas?
Moise's response: I always respected teaching and thought it required my best efforts. This is true of every Moore student I know of. But, my conception of mathematics and of teaching was always different from his.
Question 2 from Roberts: Did Moise ever discuss his education reform activities with Moore? Did Moore ever express any opinions on SMSG (School Math Study Group) or the new math generally?
Response from Moise: Never.
Question 3: From my reading it seems clear that Moise and Morris Kline were antagonists regarding the new math and SMSG in particular. See, for instance, Five Views of the New Math published by the Council for Basic Education in 1965 to which both Moise and Kline contributed. (I want to interject that Morris Kline is not the Moore student, J. R. Kline.) Would it be true to say that other R. L. Moore students would have been more likely to side with Moise than with Kline at the time? ( I'm not going to read the rest of that question. I'll attach it as an addendum to the report.)
Moise's answer is amusing in a sense: This paragraph (with the question) suggests that he takes Kline seriously. If so, he should look more carefully. For example, he should note what the statement of the 74 actually said.
[Editor's Note: Morris Kline was a leading critic of the activities of SMSG. He devotes Chapter 5 of his Book "Why Johnnny Can't Add" (St. Martin's Press, New York 1973) to criticism of the Moise approach to geometry without mentining him by name.Kline also includes a critique of mathematics reform published in the American Mathematical Monthly and in the Mathematics Teacher in March 1962 signed by 74 eminent mathematicians active in research in a variety of specialties. It seems fair to say that no constructive alternative was offered.]
Question 4: In Five Views cited above, Moise laments the dismal image of the mathematician in popular culture. Would it be fair to say that a good deal of Moise's motivation for involvement in education reform was to rectify this image? Does he believe that he and other reformers effected any improvement in this regard?
Response: I was trying to improve teaching. Improving the popular conception of mathematics was not my proximate objective. I think that the new math was a mixed bag. Mainly it was an improvement. Mainly it differed from the old math by insisting that mathematics is a form of knowledge, not a repertoire of conditioned responses. SMSG had defects. It was often over-formal and it used too many big words. Max Beberman said that a student should not be taught a word unless the word is the name of an idea that the student understands. Continuing with Moise's response…Long ago the SMSG books ceased to be used. If a school book needs to be revised to survive, that is not news. If an experimental text needs to be polished up, that is not news. But the SMSG had another handicap. It required intellectual effort. Students ceased to like such effort. Now they do not want to understand mathematics or French or German or even English. That is why Harvard offers remedial courses. The intellectual motivation of students lasted through my time but only barely. After me, the deluge.
Anderson: I would like to add something as someone also involved with SMSG, much less involved and certainly not publicly like Ed Moise was in controversies with Morris Kline and others. My own reading of SMSG and its successes and its failures is that the school math study group had some very good ideas about reforming some of what was traditional math. For example, the word "line" was used in many geometry texts in about seven different ways, depending on what context the author wanted. When Moise wrote his geometry text, he was rather careful to use it in a single way, or possibly two ways, that which was drawn or the abstract entity that it represented. And to make distinctions between ray, a half line so to speak, and a segment, and to think much more cleanly in terms of the concepts associated with geometry. He used the language to assist that. That was one of the reasons why Moise's geometry book was one of the more successful outgrowths of the new math. From my own perspective, however, a major reason the new math did not work as well with many students was that there was nothing to leave out of the curriculum. Back in the 60's the inexpensive hand held calculator had not been invented. There may have been a handful of special ones for specialists, but with calculation absolutely needed and paper and pencil techniques needed for most people, there was almost nothing to leave out of the traditional curriculum. The better students, the top 15 – 20% perhaps, I'm guessing at the number, were challenged by the new math and learned a lot more. They were sort of eager for more intellectual challenges. The slower learners and the memorizers sort of got swamped when they had that much more to do. That is one of the reasons that the new math fell into disfavor, because people who were not the high level performers were having difficulty with a much broader spectrum of both concepts and techniques. Enough on the new math.
Fitzpatrick: Let's turn to Moise's relationship with Moore. I believe Dick asked Moise point blank, 'Are you glad that you were a Ph.D. student of R. L. Moore.'
Anderson: And Ed gave a clean answer, he said, Yes, he was glad he had worked with Moore, as I recall it.
Fitzpatrick: He went on to give a wonderful quote that I don't think ought to be in the record. Do you want to say this?
Anderson: He said that he considered himself and Moore to be oddballs in the same way. That is to say, each of them liked to think but not to study.
Fitzpatrick: That's a good …
Anderson: We think that's a very apt quote, apt for Moise, and in the same sense, apt for Moore because he liked to do mathematics rather than study about mathematics, at least in the years when we knew him. He may have done a lot of studying earlier, but from '40 on he didn't study very much mathematics. He did study a great deal about teaching of mathematics because he put great effort into his students' learning, learning to think.
Fitzpatrick: We asked Moise about his own work in topology, and he indicated that he was on leave from Michigan at the Institute for Advanced Study as kind of a protégé of Deane Montgomery when he achieved his triangulation of three manifolds theorem which is probably his most notable success in mathematics, and a very important achievement it was indeed.
Anderson: It helped redirect (mathematical) topology, particularly toward three-dimensional topology, as distinct from plane topology which had been two-dimensional topology before Moise and some others came along.
Fitzpatrick: Moore and some of his contemporaries had pretty much developed the topology of the plane, and it was left to, in large part, Moise and to R. H. Bing, whose three dimensional work was subsequent to his, to plow the new ground of doing three-dimensional manifold topology. After that work on three manifolds, Moise turned his attention to the Poincare' Conjecture and worked very hard on that for a number of years. He finally realized he wasn't going to crack it, and I guess it was at about that time that he decided to change his attention to mathematics education.
Anderson: That was my understanding, both chronologically and with what we got from our conversation with Moise. We asked him a good many other questions. One of the issues that face people thinking about Moore and his effect, is the sort of brotherhood of ex-students of Moore, or if not ex-students, at least descendants of Moore, mathematical descendants of Moore. I was trying to probe to see what kind of relationships he had with other ex-students. I think he had somewhat less than most of us did in the sense that, for example, the year before I came to Texas three people had graduated: Harlan Miller, Swain, and Sorgenfrey. Harlan Miller was a female who went to Texas Woman's University, Swain went to Wisconsin, and Sorgenfrey went to UCLA. Moise had hardly any relationship with any of them after he graduated later. He just didn't see them much.
Fitzpatrick: In fact they would avoid him if they happened to be at the same meeting or something.
Anderson: Yeah, they might have, yes. Whereas, as an ex-student of Moore, when I would see Miller or Swain each of them would sort of automatically start apologizing to me as a fellow Moore student for their lack of doing research. It was the building up of a kind of guilt complex in some of his students who didn't do research that was a consequence of Moore's manner of teaching and manner of valuing what people do. He would praise his successful students in class intentionally and cite them for a variety of their accomplishments, and that had a tendency, I believe, to make those who didn't have accomplishments feel that they were sort of on the out. We asked him what he thought about the statement that F. B. Jones, who was a friend of all of us, made. (He got out in the mid-thirties and was at Texas for fifteen years on the faculty and then went to a number of other places, North Carolina and then Riverside, and had a number of highly successful graduate students in topology, and some of these have also had good students of their own.) The question was why Jones left. The suggestion was that he couldn't teach topology so he had to go elsewhere to do it because Moore was the teacher of topology at Texas. I'm not sure we got a very definitive answer on that.
Fitzpatrick: I think Moise feels that that was the case.
Fitzpatrick: He said that, for instance, Jones would teach other courses outside topology. In particular, Moise said he took a course in complex variables from Jones and didn't learn anything in it. Of course I sort of doubt that he didn't learn anything. We asked Moise if he corresponded with Moore after leaving Austin, and I think he said, 'Never' or maybe 'hardly at all', but he did say he visited Moore on fairly rare occasions when he would be going through Austin or in the vicinity of Austin.
Anderson: Or perhaps see him at a meeting.
Fitzpatrick: Yes. But he had an interesting story about the revised edition of Moore's Colloquium publication. Moore described to him about the bibliography in there. He said, "well I finished this book. I guess I ought to get a bibliography. How do you go about getting a bibliography for a book?
Well you're supposed to list papers by authors that deal with subjects similar to this, and I looked and found that I had a whole bunch of reprints in my office (This is Moore talking now, telling Moise) that various authors had sent me, so I just listed those as the bibliography." Moise was pretty amused at that.
Anderson: We got an interesting tidbit, recollection about Moore, from Mary Moise who was there in Moise's apartment when we were there at Bleeker St. in Greenwich Village. Mary said she recalled that Moore had kind of two special hobbies that have been referred to by other people. One was boxing. He liked to think of himself as a good tough boxer and well trained. Secondly, he liked to drive fast. He tried to beat his own record at going to San Antonio in so many minutes, going about as fast as his Cadillac would go. Mary's recollection was that there was a story that one Saturday…he used to go on Saturday afternoon I believe it was …
Fitzpatrick: have dinner in San Antonio
Anderson: have dinner in San Antonio and then drive back. There was one Saturday afternoon that Mary recalled having heard about why he couldn't go to San Antonio because he had a pussycat that wouldn't get out of the way of his car so he could get it out of the driveway. He was very fond of and concerned with his pussycat, almost more than driving to San Antonio. He didn't get out and move it or something; he just simply didn't go.
Fitzpatrick: Mary Moise also said that Mrs. Moore would give advice to wives of his students. In particular, she recalls learning from Mrs. Wilder (R. L. Wilder was a highly successful student of Moore) that Mrs. Moore told her that, as the wife of a mathematician, she ought not to have children because they would interfere with her husband's career. Mrs. Wilder told her that she was too late. They already had some, or one at least. At one point we asked Ed Moise about his relations with other Moore students, and he said he got along well with all of them save Bing; there was some strain in their relationship there. Mary Moise said that she thought that may have been because of their widely different political views. We didn't pursue that with …
Anderson: They both, of course, did fundamental work on three manifolds, and that was what they were both perhaps best known for in the long run. There may have been a combination of that kind of intellectual competition along with rather substantially differing political and religious views.
Fitzpatrick: We talked with Moise briefly about his own views during the McCarthy era and his support for mathematicians who had suffered because of that, and he emphasized that he was glad that he had done that, giving those younger mathematicians that kind of support.
Anderson: Moise, the name Moise is French for Moses. Moise came from a Jewish background. We asked whether he was aware of Moore's sentiments, or expressed sentiments, on anti-Semitism. I think the comment was made by Moise, as I understand it, that that kind of attitude did not apply to Jews whom he knew.
Fitzpatrick: That's right.
Anderson: We think that's true in a fair number of cases. While he was at Texas there was another well-respected graduate student who didn't work with Moore named Ted Harris who also was Jewish, as well as Martin Ettlinger, the son of H. J. Ettlinger, Moore's colleague
Fitzpatrick: They were both in classes with Moise in different stages.
Anderson: Yeah, they were both in classes with Moise in different stages, and Moise was never aware of any anti-Semitism permeating the atmosphere except perhaps in Moore's comments. But perhaps in those classes Moore didn't make the comments.
Fitzpatrick: Right, I think perhaps he didn't. When we were talking about Moise's views on other Moore students, the name of Eldon Dyer came up. Moise responded that Dyer did not like Moore, and he did like to learn, and that he was an undergraduate in applied mathematics and that Moore never forgave him for being in applied mathematics.
Anderson: I might give a little bit of Dyer's background. I think he graduated, got his degree in about '52. He was an undergraduate there my last year or so, and Moise would have known him somewhat there. Dyer himself died fairly early. He was one of the Moore students who most radically got into forms of algebraic topology as distinct from geometric or set theoretic topology, so he had an intellectual break with his tradition as well as perhaps some emotional disagreements. He was a very bright guy.
Anderson: We asked Moise about whether he thought that there was a kind of cooperative learning philosophy in Moore's classes. At the time I was there they were very small classes, just a few students on the graduate level. That was sort of guided cooperative learning because the people in the class would learn from other people in the class, guided by Moore under strict constraints as to what they could talk about outside of class. But in some sense, it was a forerunner of what is now known as cooperative learning for students, that students learn from other students more than they learn from the professor.
Fitzpatrick: But in that case the instructor was not presenting arguments, rather the students were presenting arguments to each other.
Anderson: Ed Moise also commented that he thought that Moore was rather unreasonable in his strict emphasis on competition. Moise did not know of Moore students who really stuck nearly as strictly to that, of his era at least, and it would also be true of my era, who stuck strictly to the "absolutely no talking outside of class" except maybe to
[turn tape over]
learn from a text or from lectures or learn about a body of knowledge.
Fitzpatrick: We asked Moise how he conducted his own classes, and he indicated that he tried to elicit from students questions or suggestions and maybe another student would build on that with a follow-up suggestion, and the class would proceed in that way with Moise acting as a moderator.
Anderson: One of the issues in the latter years of Moore's life, or at least service at The University of Texas, was the issue that he was on limited service, limited service sort of being half time service, for which I think he was paid something like half time. He used to teach about 21 hours a week under these conditions because the education of his students, the education toward becoming research mathematicians was his commitment to his students. We did ask Moise what his attitude was toward Moore's retirement, and the impression I got, and I think Ben also, was that Moise thought he should have retired before he did.
Fitzpatrick: He was fairly…Moise was definite on that point, 'well before he did' I think was the phrase he used.
Anderson: Yeah. This would have put him at variance with the recent Moore students, those from the 60's say, or late 50's, many of whom did not think he should have been.
Fitzpatrick: Moise is on record as believing that the strict Moore method in classes may be very good at first, to develop students' ability to think originally and independently, but that after that there should be more emphasis on their actually learning material, learning material to be used. I reminded him of the course that he taught the year he spent at Auburn, the baby real variables course which was strictly along the lines of Moore's own 624 class at Austin.
Anderson: Moise commented, and this is in some of Duren's, an article written by Duren and others who knew Moise at Tulane, that he (Moise) got interested in mathematics taking a course for nonmathematicians taught by somebody named George Cramer, and then he went and took courses with a person known as Dr. "Buck" Buchanan who helped guide him. He took his calculus from Bill Duren using Landau's book which was one of the more rigorous books of that time, and the more challenging. He expressed a belief, and I guess this is the general philosophical attitude, that the best education is the education children get from their parents. I think many of us believe that that's the way people start learning, should start learning.
Fitzpatrick: As was the case with many of Moore's students that we've talked to, Moise commented on Moore's patience in dealing with students. I have written down here 'Moore was ultimately patient in waiting for students to develop ideas.' Moise was more apt to try to elicit ideas.
Anderson: Which I think is true of most of us. It should be noted that Moore's classes, at least in the 40's when he had smaller numbers of students, instead of lasting three 50 minute periods, would last about three hour and a half periods during the week of just contributed time by Moore because he was interested in his students' learning. I've lost my train of thought.
Fitzpatrick: There are a couple of other things I have jotted down here that I'll read into the record. As Moore's graduate student in Austin, I guess one of us asked Moise when did he start reading, and he indicated that as a graduate student he never read, that he accepted Moore's conditions. He told us that he learned of the triangulation problem for three manifolds from Gail Young, and Moise quoted from Samuel Eilenberg about the Poincare' conjecture, but I don't remember just what he said. Maybe it was too hard and you shouldn't work on it. He also said that he was advised against working on the triangulation problem because he might just come away dry without any positive results. After he went into education, he said he went back to mathematics in the 1970's and he said, ' I had one good paper in the 1970's', and I think that was a very long paper.
Anderson: Yeah. I lost my train of thought when I was talking about Moise and the question of patience. I think that for all of Moore's students of the era when I was there, and I think Moise confirmed this, Moore really was tremendously patient with student learning. He would wait months or sometimes even years for students to come up with their own ideas and their own understandings of the basic subject matter. It was part of this "thinking" rather than "studying". I know that there is an interview with Ed Burgess. Ed would be an example of a fellow student who began when I did in 1941, who of course, knew Moise and others. When Burgess was interviewed I believe he sort of made the point about Moore had stuck with him over a period of ten years with several years out during the war, and eventually he got his degree with Moore and went on to develop some very good students in topology. Moore waited for him to develop. He started off without much background, and over a ten-year period, Ed Burgess certainly did develop into a good responsible and effective mathematician and teacher.
Fitzpatrick: On the whole, Moise thought that Moore's views on cooperative learning were unreasonable, the word Moise used. We talked a little bit about Moore's encouraging students, but Moise pointed out that he could also discourage a student. Back in those days at The University of Texas, there was a grade of G assigned which was lower than a failing grade of F. Moore assigned a grade of G in the second half of his topology course, and that meant essentially that that student could not register for the course again, so that was essentially telling him to get out, to go somewhere else. He did say that he and Martin Ettlinger learned from each other in class. He said that he heard two lectures from Moore, one was the well ordering theorem. Moore gave a complete proof of the well ordering theorem. I never heard of that in later days; he didn't prove it in any of the classes in the 60's. I think he
Anderson: I probably heard that argument back in the mid-forties.
Fitzpatrick: He told the students in later years just to accept that as an axiom, and in the meantime see whether you can get a proof of it. He said the other was an explosion point set, that is a connected set with a point such that if it is removed what's left is hereditarily disconnected. Then I got confused. I think Moise started out saying that was the other lecture of Moore's, but then he corrected himself and said that he, Moise, had shown Moore the set in class. Moise also said (this is a pretty direct quote), 'my ignorance was my own idea.' He didn't object. That goes along with his earlier statement that he liked to think, but he didn't like to learn.
Anderson: or study
Fitzpatrick: or study. He (Moise) also said that he thought that very few of his papers could be read by Moore.
Anderson: In his early conversations with us, he made one other statement that should be taken in context, not out of context. When he was talking about how he and Moore thought alike in terms of valuing thinking rather than studying, he, I think, said that Moore had the reputation of being the least learned man to be president of the AMS.
Fitzpatrick: I think that's right. At least I think Moise said that.
Anderson: I think Moise said that, and I think he's referring to overall mathematical knowledge in a sense rather than doing good mathematics. That isn't what that refers to.
Fitzpatrick: We asked Moise a little bit about Lee Lorch, who was an early mathematician who was a prime mover in promoting integration and acceptance of women into mathematics, and Moise told a story in an Arkansas newspaper that was very much opposed to Lorch coming to visit The University of Arkansas at Little Rock because the newspaper said, 'Everywhere this man goes, integration results.' We asked Moise a little bit about his literary criticism, his most recent career, and he said it hasn't been widely accepted by the literary community. He's had six short notes published, and those in only two journals, and his longer papers have not yet been accepted for publication.
Anderson: It's certainly clear that he's now not in a condition to likely produce other serious intellectual works. He has difficulty just writing down a word with a pen. We asked him what is it you're trying to say, and he could write down a few things, but just a word here and a word there, and he had difficulty remembering names and terms of things.
Fitzpatrick: Like the word complex variables, he had trouble remembering that. It was good for us that Mary Moise was there because she could help interpret what he was wanting to say to us. I just might mention on a personal note that he would get very frustrated with himself at his inability to express himself to us.
Anderson: On the whole, we thought that the interview with him was very worthwhile, and we were glad we did it. We're sorry we didn't get to talk to him in the same vein several years ago when he was able to speak more lucidly. He was always a man who was essentially eloquent and knowledgeable, and it's in some sense sad to see him in this state, but it's also realistic. He's, I guess, pushing 80 now.
Fitzpatrick: Yes. The board of education, SMSG decided that they would go away from Moise's geometry book, and I think he said due to number theory. But instead there's some reference to them using Blumenthal's geometry book and Ed Begle knew what he was doing in the sense that he got them to use Blumenthal's book because he thought it would be much less successful than Moise's. I'm not sure that I have that right, but that's what I have written down on paper. [laughter]
Anderson: I'm not sure of that either. Let me give some background about books that Moise wrote. I think one of the early books he wrote
[tape has period of silence]
Fitzpatrick: Dick Anderson was about to talk about Moise's books.
Anderson: Yes. He wrote this traditional but modified version of geometry with the language cleaned up, sharpened, and focused, much more intellectually comprehensible than traditional geometry books. It sold a good bit over the years. I don't know whether it's still in production. Some years after he wrote it I was approached by a publisher to write a comparable book and did, but it didn't sell as well as his. It didn't have the same kind of publicity and was used basically and sort of for honors type classes rather than standard classes. He also wrote Elementary Geometry From an Advanced Viewpoint which was a text for the training of high school teachers in geometry, or prospective high school teachers.
Fitzpatrick: Very successful.
Anderson: A very successful book. One that I personally taught out of.
Fitzpatrick: I did too. It may still be used. I don't know.
Anderson: It could well be. It had the kind of background in geometry that people who are going to be prospective teachers need to know. It was a well-received book. He later wrote a book on calculus as I understand it.
Fitzpatrick: It was sort of a traditional calculus but done reasonably correctly.
Fitzpatrick: It was widely used, but for a fairly short time period.
Anderson: I might add that, of course, I've known Ed (Moise) since the early days, and I consider myself a good close friend of his over the years. When he went in 1959 to Colorado to work on his geometry book for classroom use, the SMSG was having the high school meeting there, I was invited to go to the middle school SMSG meeting in Michigan. My wife and two youngest children and I stayed in Moise's house while he was out in Colorado and we enjoyed that. All along we have been quite close with both Ed and with Mary.
Fitzpatrick: You might mention that it was at Colorado when Erdos visited and raised the pseudo-arc problem to him as dissertation??
Anderson: No, that was at the end of the war though.
Fitzpatrick: Oh, then he was in Colorado again.
Anderson: Yes, this was an SMSG Colorado trip, not … I think at the end of the war he heard about the pseudo arc problem from Erdos. He characterized the pseudo-arc as his dissertation, one of the best dissertations I think
Fitzpatrick: if not The Best
Anderson: best, that any of Moore's students had, the ones that I know about at least. There may be other ones that should be accorded comparable status, but it was a tour de force, and he did it essentially on his own,
Fitzpatrick: bare hands
Anderson: bare hands, right. He was a very powerful guy when he got involved with a serious mathematical problem.
Fitzpatrick: I wanted to follow up a little bit on your discussion of books. He wrote a text for use as a Moore-type course. It was a short book called Problems, Courses in Analysis and Topology. It was to be used at the junior-senior level, and he said in his introduction to it that he thought it was something that ought to be done. Such a course ought to be taken, but he'd kept the book short because he didn't want to overdo it, and he thought that the student, after having developed his/her ability, needed to learn material, and that's why he didn't have more material in the book. Later he wrote a treatise, sort of the culmination of his work in Geometric Topology in Dimensions Two and Three in which he gives another proof of the triangulation theorem which is due to his student at Harvard. What was his name? Shalen or …
[ Fitzpatrick's memory was incorrect on this point. The proof of the triangulation theorem in the book was Moise's, not Shalen's. We are grateful to Professor Moise for calling this to our attention in his letter to Christopher Bourell of The Center for American History dated September 3, 1998.]
Anderson: Oh yes, I wrote that down.
Fitzpatrick: He had told me earlier that that was really a civilized proof of the triangulation of three manifolds problem and that he included that in his book.
Fitzpatrick: He talked about having only three Ph.D. students, two at Michigan and one at Harvard.
Anderson: So he was not known for the students that he had. He also did not try using the Moore method in extensive ways, and it's not at all clear that the Moore method would have worked when there are other accesses to courses, stimulating ones with major figures. Of course, I don't know.
Fitzpatrick: He told me that the way Shalen, how
Anderson: Shalen. He has written down S-h-a-l-e-n.
Fitzpatrick: The way they came in contact was that Shalen was interested in working on three manifolds and he went to some people in the department of mathematics there at Harvard, and they said, well the only guy here that knows anything about that is the (James B.) Conant, Professor of Mathematics Education. So Shalen went and looked Moise up and they started working together. He talked about his other students, Munkries who is now at the University of Illinois, no at MIT, and Ross Finney who is at Illinois at Chicago.
Anderson: I think maybe now retired.
Fitzpatrick: Yeah, maybe now retired.
Anderson: Shalen I think is at The University of Illinois, Chicago Circle.
Fitzpatrick: I think you're right. Finney is retired. Moise talked a little bit about his stay at the Institute and that he was invited by Dean Montgomery to stay on another year, I guess as his assistant, and then went back several years later for another visit there.
Anderson: Yes. I think Moise indicated he was there from '49 to '51 the second year as Montgomery's assistant. Later in '56 –'57 were the times when we think he was there. I happened to be there in '51-'52 partly through contacts with Moise and hearing about it, and I was there also in '55 –'56, so we didn't overlap at the Institute but we did at lots of meetings.
Fitzpatrick: We asked Moise whether he worked closely with Ed Begle on the SMSG, and he responded that he did not, and that he didn't know later people who worked in math education.
Anderson: For the record I did do some checking up on math or math educators who were students of Begle, and so on, descendants of Begle. Moise was not aware of this. Over the last fifteen or twenty years, Moise has been somewhat out of touch with the math community, being involved in literary criticism and with his own health problems, so he hasn't kept up with much of what is current in the math reform movement. Certainly his background and attitudes are highly consistent with the attitudes of the current reform movement in mathematics.
Fitzpatrick: I want to make one further comment about his relation with Bing, and I don't want it to give too strong a negative impression. He said that he and Bing respected each other for their work.
Anderson: Yes, I'm sure they did.
Fitzpatrick: Then Mary Moise added, 'and they forgave each other for their politics.'
Fitzpatrick: This is all that Dick Anderson and I can think of at the moment. If other thoughts occur to us later, we'll add them either to the tape or to a written addendum to the tape. We're going to close this one off now, and on a separate tape we'll go over our interview with Gail Young which wasn't as long. He seemed to tire a bit quicker than Ed Moise did. Well, we got him in the afternoon because either Gail's directions were bad or Dick was a bad navigator because it took us forever to get there. That's just a bit of humor there.
Addendum by Ben Fitzpatrick:
Someone has remarked that "Moise refused to be captured by R. L. Moore." As far as I can tell, Moise was never captured by anybody, except possibly by George Cramer, a professor at Tulane. Here's the story. As a freshman, Moise was required to take a mathematics course and found himself in one taught by Cramer. None of the students wanted to be in there, and Cramer knew it. He mechanically went through the material in a spoon-feeding fashion. Moise thought he had the ability, like a horse, to sleep standing up. Cramer always finished his lecture a minute or two before the end of the period, and he would say, "Here's a problem you might want to think about: ....)." Some student would invariably ask if that was a homework assignment or would it be covered on a test. "Oh, no, I just thought you might find it of interest." Well, after a while, Moise did find one of interest, solved it, and showed his solution to Cramer outside of class. Cramer then gave him another problem which he also solved, and before long Moise was hooked. He asked Cramer how he could study mathematics seriously, and Cramer told him to drop his course and get in a better one. Moise never took another course from Cramer, but he credits him for his becoming a mathematician.
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