Topology Atlas Document # topc-06 | Production Editor: R. Flagg

## AN INTERVIEW WITH JOHN ISBELL

### K.D. Magill, Jr.

Interview from Volume 1, #2 of TopCom

I'm not certain when I first met John Isbell. I do remember seeing him at the summer meeting of the AMS in 1966 at Cornell University but I can't even recall if we spoke. I do recall that he and Dov Tamari were having a serious conversation at the time. Dov was chairman of the mathematics department of SUNY at Buffalo and was probably trying to recruit John but was unsuccessful. The "old" University of Buffalo, a private university with a very small mathematics department had, not too long before, been designated as one of the four university centers of the SUNY system and Dov had been hired, appointed chairman, and was given the mandate of building up the department. He did an extraordinary job in this regard during the three years of his chairmanship, bringing in some extremely able people. Unfortunately, however, interdepartmental problems surfaced, with the consequence that some of the most able of these people left after the third year of Dov's chairmanship.

I was chosen to succeed Dov as chairman and was told that my major task was to continue to build on the foundation laid by Dov. In other words, a large part of my job was to continue to recruit outstanding talent. This brings me to what I remember as the second time I ran into John. That was in the fall of 1968 at the Indian Institute of Technology in Kanpur, India where we both were attending a topology conference. I remember promising John that I wouldn't ruin his conference by harassing him about accepting an appointment at Buffalo, but I also mentioned that I wouldn't be doing my job as chairman if I didn't at least bring the topic up. John said something to the effect that he wasn't terribly interested but he wasn't entirely uninterested either. I wasn't too optimistic but upon my return to Buffalo, I arranged for John to give a Colloquium talk. At that time, John was negotiating with several other universities, all of which were higher on his priority list than SUNY at Buffalo. But things worked out extremely well for us. To borrow a phrase from the Al Pacino character, Michael Corleone, in the motion picture The Godfather, I simply made John "an offer he couldn't refuse". John accepted a position and I am convinced that this was one of the turning points in the development of the mathematics department here at SUNY at Buffalo. We have since attracted other very talented people that very likely wouldn't have considered the place if John hadn't already been here.

KDM: What information can you give me about your ancestors? When did they come to the USA and where did they first settle?

ISBELL: Well. Your asking about my ancestors reminds me of the young man who liked pancakes... he had two and a half trunks full. My father collected ancestors, and he had several notebooks full. He pretended to follow some line back to the wife of Rollo the Norman, the founder of Normandy. Of course to Rollo too, but Rollo's wife ... in my father's genealogy, at least ... was a princess, an English princess named Gisela. So her ancestors are all there in the Anglo-Saxon Chronicle, right back to Sceof, son of Noah. The Bible never heard of Sceof, but it does have Noah, and it gives his ancestors right back to the beginning. So yes, I had them.

KDM: That's good, but when did they come to the USA and where did they first settle?

ISBELL: You don't mean all of them; I expect you mean the first American Isbell ancestor. That was my father's great disappointment. He tracked them back, through Alabama and Virginia, to 1659 in Caroline County, Virginia, and there the trail ends. The county courthouse burned in 1659, and when the smoke clears, there's old Throckmorton Isbell or whatever, paying taxes, suing his neighbors, and no clue to where he came from or when.

KDM: What were their occupations? In particular, what were the occupations of your parents and grandparents?

ISBELL: Father, army officer, mother, housewife. She taught school at first, up in the Virginia hills, but in 1917 she struck for the bright lights of Baltimore, and I think she had a pretty good time until they married in 1923. She was working as a typist. His father was in lumber. First traveling around buying it on the hoof, and then working at the central office in Nashville. Mom's father would be the only intellectual in sight, he was a printer, and he published a weekly paper when he could, in West Virginia and Virginia.

KDM: Any of them still living?

ISBELL: Yes, my mother is still living at home, with my older sister looking after her. Mom's 97. Frances is only 72, and she's in better shape than I am.

KDM: We weren't supposed to get to siblings until later in the interview. Let me ask, when were you born ... and where?

ISBELL: 1930, in Portland, Oregon. Dad was a captain stationed at Vancouver Barracks, Washington, at the time.

KDM: Back to the siblings. How many are there and what are they doing now?

ISBELL: Two, one of each. My brother is 71; retired from the Postal Service nine years ago after a blood clot in his aorta nearly killed him. He hasn't walked since, but I expect he's pretty happy. He, his wife, and both his daughters are now in the same small town where his wife grew up, Clarksville, Tennessee. One girl has two kids and a husband, a Professor of Spanish. My sister never married; she followed my father's line of work, Air Force Intelligence in her case. Besides shepherding our mother she's, not running the farm, but managing the property; they hire a farmer to do the farming. And she's a leading figure in the local branch of the Texas Historical Society.

KDM: Which of these people had the most influence on you?

ISBELL: That would have to be my father. My mother was a support, of course; her absence might have done God only knows what to me, but she wasn't absent, and it was my father who expected me to show something. He pulled me out of public school after the ninth grade, when I started to goof off, and sent me away to military school. That was ...

KDM: OK but let's talk about elementary school first. Where did you go to elementary school?

ISBELL: Where? That's Reno, grades 1 to 4; Minneapolis, 4 and 5; Gainesville, Georgia, grade 6. They keep moving officers around, you know. "Where are you from?" "Man, I'm not from, I'm an Army Brat. I'm here."

KDM: Oh. Well, then, high school was mostly in one place, was it?

ISBELL: What we called high school, I had all in one place, Staunton Military Academy in Virginia. Junior high school in Arlington.

KDM: What were your favorite subjects?

ISBELL: That has to be math. The only subject I took Saturday classes in. There was an enthusiastic young math teacher who organized a class of two of us, eleventh graders, to study analytic geometry. Then he overreached and tried to take us on to group theory. But he was a true Huntingtonian, like E.W. Huntington, the axiom man. He didn't see any need to tell us what groups were for, and he lost us after I think one lesson in group theory.

KDM: You keep answering the following question which, in this case, is what teachers influenced you the most?

ISBELL: Oh, well, I'm not sure Mr. Foster influenced me the most. His subject did. One reason I wasn't ready for group theory was that I wanted more analytic geometry than he and his book offered. Foster, and I think the authors, pitched it as showing the equivalence of geometry and algebra. Now I had pretty definite ideas about algebra, and geometry seemed a LOT bigger... any curve you can draw, not to mention disconnected graphs which of course you already get with xy = 1. How could they be equivalent? I did NOT have definite ideas about what a construction was. One of the Bernoullis said... of course I had no idea of this at the time... that the limit of a sequence should be thought of as the last or $\infty^{th}$ term. A sequence of three terms has a third term, he said; a sequence of ten terms has a tenth term, and a sequence of $\infty$ terms has an $\infty^{th}$ term. The task of the mathematician is to find it. Okay, so take an arbitrary curve; draw one, say your signature. A half-civilized algebraist, like Mr. Foster (Achilles Foster; he later got a Ph.D. and a professorship in Newark) would say you can't write an equation for it, and in that respect geometry is not reducible to algebra. But I figured you could write an equation for it, and I proved it. I cheated, of course. In fact, what I actually told all the kids who would listen was, I can write an equation to forge your signature. I would approximate the signature with a union of line segments. Ask them to imagine magnifying and getting a really close approximation, and they agreed that a union of line segments would make a good forgery of their signature. Then show that d(A,P)+d(P,B) = d(A,B) is an algebraic equation; with radicals, since the distance is the square root of the sum of the squares, but radicals are perfectly legitimate, you use them to write the quadratic formula. Finally point out that f(x,y)g(x,y) = 0 has for graph the set of all points (x,y) where f OR g is 0... the union... and you have it. Descartes freed from every blemish; algebra = geometry. No, the teacher who influenced me the most would probably be old Marshall M. Brice, the head of English. We groused about how Brice had no soul when he asked us on a test how many kisses the knight-at-arms took to close the eyes of La Belle Dame sans Merci... counting kisses seemed the opposite of poetry. But then I thought some more about it. I didn't get as far as Keats took his brother, I think it was; anyway there is a letter in which he mentions that the number... four... seemed about right, and at least treats the right and left eye equally. I did, however, begin to get the idea that if it's worth doing it's worth doing right. And Brice evidently took pleasure in making me look stupid when I came up with a remark intended to make me look smart. But God knows that's fair. And he did it very well. I was reading some Marlowe that year, my senior year, and Brice tried to get me to read Kyd. I'm not sure if any of Kyd's plays were even available, anyway I didn't even look, but I did take it to heart and started on Kyd when I had a college library. Kyd is to Marlowe something like Fourier to Laplace. Except that Shakespeare learned from Marlowe, while neither Newton nor Einstein learned from Laplace. But the point is, Kyd plays better then he reads, which is putting first things first. Just as Fourier's ideas are better than his definitions.

KDM: When did you first become interested in mathematics?

ISBELL: Interested? I think in the winter of 1936-37. In school, the numbers went 1,2, oh you know how they go; but when the temperature dropped to 0 it didn't stop dropping. The numbers kept right on going down. And that is much more vivid than looking at a lot of ants, or pebbles, and thinking a thousand, a million, and on and on. Just step out the door and there in your face is a number you had no idea of last week. It's not that I took up mathematical games, but the ontology of mathematics; that's not something you're going to forget. It must have been the same half-year or so that I got into fractions. Not in school, but in life.

KDM: I would imagine that you were an exceptional student. Did any of your fellow students impress you in any manner?

ISBELL: I think not in an interesting manner, for whoever might read this thing.

KDM: When did you graduate from high school?

ISBELL: 1947.

KDM: Where did you attend college or university? What were your major and minor subjects?

ISBELL: That's kind of a tangle. Five colleges, up to the B.S. I was longer at Chicago than any of the others, because after doing my fourth year there I started summer school, registering for one course with Irving Kaplansky. I minored in physics and majored in math.

KDM: Did any of your professors have much of an influence on you?

ISBELL: The one who influenced me most, I didn't take a course from. That was Saunders Mac Lane. I was reading their papers, and I got more from Mac Lane's papers than anyone else's at Chicago. I didn't see much of him during the academic year, but he engaged me in a conversation when he first saw me wandering around Eckhart Hall and then, we at least nodded when we passed, and then when Chicago rejected my application for an assistantship and I was sweating out my Texas and Oklahoma applications, Mac Lane wanted to know what I was going to do. Well, I wanted to know what I was going to do, too. I had spent three years in crummy colleges down there (one of those was Washington in St. Louis, but it didn't show me anything except an interesting German professor... he thought Coriolanus, Shakespeare's Coriolanus, was the perfect play; I guess Coriolanus is a sort of civilized Siegfried), and I didn't want to go back there, but I needed an assistantship. There was more. This was Joe McCarthy's second act... on a Shakespearean plan of five acts. Act III would be when Eisenhower held his nose and rode McCarthy's train to the White House. Well, Northern and California universities were firing leftists; Oklahoma was firing Quakers. To hold a faculty position in a state school there you had to sign an oath that you would shoot commies. Ainsley Diamond had been a noncombatant officer in the Air Force in World War II, but he wouldn't sign to shoot them. It didn't say 'shoot', it said 'bear arms'. I didn't mind that for myself, but when Oklahoma A & M fired Diamond, Nachman Aronszajn quit too, and they moved to the University of Kansas. Mac Lane urged me to stay in Chicago. I could certainly get a job to support myself, and I could study even if I couldn't pay tuition. I took an assistantship at Oklahoma A & M instead; but when I blew up after six months in Oklahoma I came back to Chicago to try to work out what to do next.

KDM: I'm surprised Chicago turned you down.

ISBELL: Well, I had a B average. Counting the D Chern gave me. But they don't like D's in math. And getting a D with Chern was not a smart move. I was fascinated with set theory and game theory and I goofed off in differential geometry.

KDM: What did you do after Oklahoma?

ISBELL: I went from Chicago to Lawrence, Kansas, and got myself considered as a candidate for an assistantship for '52-53. But it turned out that the Oklahoma A & M chairman, Wayne Johnson, had been urging A.W. Tucker at Princeton to do something about me. And somehow or other Tucker decided I should have a job at George Washington, where he was a consultant on an ONR project, and he took me over. A respectable job in Washington, for me in 1952, was like a non-teaching job in Baltimore for my mother in 1917; I was off like a shot. And Tucker decided, in due course, that I would do.

KDM: What areas outside of mathematics interested you?

ISBELL: You mean intellectual areas? No heavy interest outside of math.

KDM: Were you involved in any extracurricular activities?

ISBELL: As an undergraduate, none. Activities, yeah, but no organized extracurricular activities. In Nashville, my junior year, I played a lot of pinball.

KDM: When and where did you begin graduate school?

ISBELL: Well, my program of math courses for my undergraduate major didn't include the courses I took in Spring Quarter, so I guess I began graduate study at Chicago in March 1951. But I became officially a part-time graduate student only in that summer, and a regular graduate student at Oklahoma A & M in the fall.

KDM: Who were the faculty members there that impressed you the most?

ISBELL: That would be O.H. Hamilton, a 1938 R.L. Moore student. Under Hamilton's direction, I started to write what was supposed to be a master's thesis. I couldn't stick that year out, but before I left Stillwater I sat in a hotel for I think three days and finished the thesis, and Hamilton said I couldn't get the assistantship back but if I wanted to do something about getting enough credits he could okay it as a master's thesis. That was encouraging, I was doing something right; but it was even more encouraging seven months later when J.H. Roberts accepted it for the Duke Journal.

KDM: Who, among your fellow students, impressed you the most?

ISBELL: Well the best graduate students at A $amp; M had just left to go to Kansas with Aronszajn. I got to know them that year, with Al Jennings having married a Stillwater girl, and then my trying to follow the crowd to Kansas. I think you could say Al Jennings. He seemed to me clearly a pro. He was not world-class like Mac Lane and André Weil; but like Mac Lane, he seemed to be basically satisfied with the world. It was an attitude I hadn't seen much of. Wayne Johnson had it, but Wayne didn't strike me as a pro. Hamilton was a pro, but he didn't seem satisfied, more resigned. KDM: I seem to remember that your doctoral dissertation was in game theory. Who was your thesis director? ISBELL: Tucker. I don't think he expected it when I went to Princeton, and I certainly didn't, but I was sick and tired of being a student and I saw how to finish a game theory dissertation in two months. KDM: How old were you when you received the Ph.D. degree? ISBELL: 23. KDM: You told me who supervised your first paper. What was the title, where was it published, and when? ISBELL: "Homogeneous spaces", Duke J., 1953. KDM: So that was topology? ISBELL: Oh, yes. My first four papers, I think, were in topology. The second was a joint paper with Mel Henriksen, partially repairing an error in Ed Hewitt's very influential paper on "Rings of real-valued continuous functions, I". That second paper was published in the Proceedings in 1953. We wrote it at Kansas in June '52. The third was my sequel to Henriksen-Isbell; I saw how to get the complete result that Hewitt had claimed: all residue class fields of rings C(X) are real-closed. I did that in December '53, after finishing my dissertation. Then I think the fourth was my Tôhoku paper on "Zero-dimensional spaces", written in the summer of '54. That was a nice paper, but it appeared at the same time as a closely related and clearly better paper by Hugh Dowker, something like "Local dimension of normal spaces". KDM: So did your collaboration with Mel Henriksen go right on from 1952? ISBELL: Well, nothing like continuously. Obviously when we worked on matters of interest to both of us we exchanged preprints if not earlier previews. I remember sitting on a hillside at Fort Bliss, after I was drafted in October '54, reading Gillman-Henriksen "Concerning rings of continuous functions" while waiting for orders to attack the Blues or the Purple People-Eaters or whatever they were called. But we were together in Madison in the summer of '55 and didn't collaborate. Our second and third joint papers were written only when we were both at the Institute for Advanced Study in 1956-57 and they put us in the same office. KDM: You were drafted in October '54 and you were in Madison in the summer of '55? ISBELL: On furlough. I was invited for the four-week Summer Institute, but I only had two weeks' furlough time earned. I think maybe I had less: two weeks a year, and they were giving me an advance, letting me have two weeks after nine months. KDM: Did the army keep using you to attack Purple People-Eaters? ISBELL: Oh, no, that was just basic training. Then they sent me to Aberdeen Proving Ground and I wrote papers. When the Army permitted. We had a little celebration the day the Labs had advertised a lecture by Al Jennings on his dissertation and people came from as far as Penn, in Philadelphia, and from the University of Maryland, and they went to the room where the talk was to be and some asshole had to get up and say "I'm afraid Dr. Jennings has KP today. The lecture is canceled". KDM: I seem to remember Don Johnson telling me that you and he and Mel had published a joint paper and you and he hadn't met at the time. ISBELL: Yeah. I think that's much less unusual now than it used to be. The way that happened, Mel and Don had a forty or fifty-page joint paper which came out in Acta, and they had started another one that was just a stub when Don left Purdue and went to his first job at Penn State. I came in to Purdue for the year, and got copies of both, and I saw what to do with the stub. It didn't make forty pages, but it made a paper. [MH: The Acta paper was Don Johnson's doctoral thesis, he was the sole author, and it was about 50 pages in length. Don and I had written two papers on archimedean lattice-ordered algebras that appeared eventually in Fundamenta, and the three of us wrote the third one for Fundamenta to which John refers.] KDM: When did you become interested in Category Theory? Evidently, by the time you completed your book entitled "Uniform Spaces". ISBELL: Summer 1951. That is, after the Spring Quarter was over or practically over. I had gotten as far in Mac Lane's papers as, NOT the big category paper of 1945 with Eilenberg, but the new 1950 paper "Duality for groups". I didn't know how to do research in category theory for years after that. It was very hard, before Kan introduced adjoint functors. Homological algebra, and to some extent abelian categories, were well enough licked into shape that some questions were clearly worth working on; but papers in general category theory before Kan were heavy on the axioms and light on the theorems. KDM: You seem to have a very fruitful collaboration with both Bill Lawvere and Steve Schanuel. Would you to comment on this collaboration and on these two people? ISBELL: The first comment I have is that what I have with Bill isn't a collaboration. We have never even started a joint paper. We have talked about ideas, certainly about ideas in several of my papers, and I acknowledged Bill's help in those papers, and I think it went the other way a few times, but we don't work together. I think the best recruiting move I ever made was going on leave to Italy in 1973 to try to sell Fatima on Buffalo after Bill and Fatima turned down our 1971 offer. Talking with Bill, I often feel like a fly buzzing around a cow. (It seems to me I can liken Bill to a cow, if I'm just a fly myself.) On any easy question, I'll probably see the answer first. But his thoughts seem to move on a level where I don't function, I can barely see down there. Steve, now, I can work with Steve, and we have done five or six joint papers. The reason there haven't been fifteen is that I don't know enough. I am particularly proud of our joint paper on number theory. Steve knows at least ten times as much number theory as I, and one would think we would never start a collaboration in that area. One would be right; we didn't. I wrote a sort of semi-paper and was pleased enough with it to send a copy to Paul Bateman and to show it to Steve and Tom Cusick. Paul wrote back greatly improving my results. But the exchange of letters took more than a week. Meanwhile, Tom had shown me that I had extended a result of Dirichlet... a ridiculous little extension, but an extension. That gave a way of looking at the problem, so suddenly it was fifty times as interesting. I could do a tiny bit more with my methods, and, wham! Steve found the right method. It was in a paper of Walfisz, and it finished the job; Dirichlet had less than half solved the problem... probably not losing any sleep over it... and Isbell and Schanuel finished it. That's in Proc. AMS 60 (1976). 65-67, if any of your readers want the theorem. It's a very nice theorem, but there's a little story about it that must be told. At the next annual meeting of the AMS, the first evening I go into a restaurant with a couple of other guys, and there is Paul Erdös coming in with a couple of other guys. (Maybe gals, I don't recall). So I say "Paul! let$j = o(n)$, etc. etc." I get through the hypothesis, and I pause for breath. And he tells me the conclusion. So I say, "Oh, my God. Is that your theorem?" "No," he says. "It's a nice theorem. I never heard about it; but if there is a theorem, and that is the hypothesis, then this must be the conclusion." Oh, and Paul Bateman. His letter greatly improving my results was crossed by a preprint of our paper with much better results than his. KDM: You have published an enormous number of papers on many different topics. How many papers have you published by now? ISBELL: Math Reviews on-line counts 146 under my name. Six or so non-papers; corrections, a paper in Alexander Soifer's Geombinatorics, and the like. But I have about that many non-reviewed publications, at least three of them in the Monthly. And then I wrote three of John Rainwater's dozen or so papers, all of M.G. Stanley... that's four... and all of H.C. Enos, that's two. If you want an enormous number of papers, look up Erdös or Shelah. KDM: You have an extraordinarily broad knowledge of mathematics in general. Often, when I begin to do research on a particular topic and I don't know if something has been done, I ask you and if you know of no reference, then I know I have to go home and prove it. This exceptional knowledge is certainly a strong point. What do you regard as your other strong points? ISBELL: Ugh. Answering a question like that is a no-win shot. One can't help remembering the story of the enthusiastic disciple of Peano, telling Henri Poincaré that Peano's symbolic calculus or whatever it was "gives the mathematician wings". "Alas, poor Peano! Ten years with wings; and not to have flown!" Well, besides a fairly decent memory and a fair share of low cunning, I may have gained more than I lost by having an inability to close. I return a day after mailing off a submitted paper, or four months after, or twenty years after publication, to look at a solved problem again and see if there is any more in it. It costs time, but one-thirtieth of the time it pays off, and I may have gained more than I lost by it. KDM: How many doctoral students have you had? Who are they and what were their dissertation topics? What are they doing now? ISBELL: If we had been doing this three years ago, only 39 years after my doctorate, I would have asked you to omit the question; but I had a student to be proud of in 1994. The first was Richard Yoh, Ph.D., 1973. I would have to look up his dissertation title. It was something around adjoint functors and algebraic theories, and as I recall it boiled down to about a six-page paper in a decent journal. Yoh got a job at Florida, and started something I thought more interesting, on semigroups$S$and$S$-sets. As I recall, he published one paper on that and submitted another, which he couldn't get published. Anyway he came up for tenure at Florida and was fired. He was co-manager, as I understood it, of a car dealership in Gainesville, and at least a year after he left the university he was still doing that, maybe full-time. Then there was Miroslav Klun, Ph.D., 1974. Steve Schanuel chaired Klun's committee, because I was on leave in Poland at the time; but every major topic in the dissertation was well started before Steve took over. Klun was a very touchy man. He kept getting into quarrels with other graduate students, and with faculty members. As far as I know, only with three faculty members, but these were three independent cases, at least two more than one could reasonably expect. I was the third. The last I heard, Klun was still not speaking to me; and he was teaching at Northeastern. I don't think he had tenure, and I don't think he ever published the bulk of his dissertation. It was on models of the affine part of group theory. Some of the dissertation was on inverse semigroups, and he published that in Semigroup Forum. The next student, oficially my second, was Madhav Tamhankar in 1976. Tamhankar's dissertation was a very nice paper in Algebra Universalis. Almost all of it was proving a theorem I had published in J. Algebra in 1967; but my proof didn't work. The beginning of the line was A.A. Albert's 1940 theorem that in an ordered division ring, every element algebraic over the center is in the center. Albert had a restriction, I'm pretty sure the whole thing had to be finite-dimensional over the center, but that was just because... try to remember how antediluvian 1940 was, they hardly knew Bourbaki!... Albert didn't call an extension an algebra over a field unless it was finite-dimensional. (Infinity was transcendental.) Anyway, Bernhard Neumann pointed out in Math. Reviews that Albert had proved what I said. Tamhankar's theorem is that in an ordered ring, a division subring algebraic over the center is in the center. You have to work much, much harder to prove that. Tamhankar had one-year jobs, or maybe less, for about three years in Canada and the U.S., and finally went back to India where he had a secure job teaching engineers. I think that after leaving North America he published no more research. Now, 1994: Till Plewe. Till is going to be heard from, in fact he has already started. His dissertation at least doubled knowledge on spatiality of locale products of spaces. Nice products of spaces are spatial, e.g. products of two factors one of which is locally compact (theorem of Dowker and Strauss) and countable products of complete metric spaces (my theorem). Beyond the dissertation, I have a writeup in Topology Atlas on the state of knowledge in descriptive locale theory, which says there are two and a half (good) theorems in this very new subject; one is mine and the other$1{\frac{1}{2}}\$ are Till's. There are two further important papers, one joint with Anders Kock. Till is on a postdoc at Imperial College, London (with Steve Vickers).

KDM: When and under what circumstances did you meet your wife?

ISBELL: Yeah. I think Joan was similar material to my mother and me; but maybe she was behind the door when they gave out stubbornness. She was a sorority girl; that was compulsory. She dropped out and married when she had a proposal from a man already earning a living, and she had kids. And kids. She put her foot down at five. This was possible, because it was 1953. Joan fought her way back to college, and when we met in 1960 she had a new divorce and was one course short of a B.A. So her real life centered on campus. We were actually introduced by Don Silberger, who got a Ph.D. under Anne Morel in 1971 and is now a professor at New Paltz.

KDM: How many children do you have? What are their names and ages?

ISBELL: Margaret is 34, John Claiborne 33, Brecht 31. I have to tell you about Brecht's name. There we were with five kids, six kids, seven kids. There was no fear of Maggie getting lost, she being my first. Or Clay: my first son. But the new one was going to be just another kid. So like Walter Shandy's son, he needed a name of power. Unlike poor Tristram Shandy, Brecht got the name of power.

KDM: What are the professions of your children and their spouses?

ISBELL: Maggie has been working for the city of Bristol. Bristol, Avon, England; her husband Tony Thornborough is a journalist there. Neither of them has been very well paid, but they have two kids and Maggie is starting university in the Fall '96 at Bristol University. In education; she looks forward to working with kids instead of people who are already beaten. Now, Clay; he's the one who has a profession. Assistant professor of French at Indiana, Bloomington. His author is Germaine de Stael. Brecht graduated from MIT with a major in God knows what (political science with a side of English). He's been doing miscellaneous office work, as what used to be called a Kelly Girl. He wants to get into music publishing.

KDM: Do you have any grandchildren and if so, do you get the opportunity to visit with them on any regular basis?

ISBELL: As I said, Maggie has two kids; Zélie will be four this summer, and Alexander is two. I saw them in August '94 in Switzerland, August '95 all over the West (Chicago, Grand Canyon, Yellowstone), and this August we're taking a holiday in Wales.

KDM: What are your mathematical plans for the immediate future? In particular, what areas and problems have your attention at the moment?

ISBELL: Not a whole lot. I have two little papers to write up; one of them, I keep looking for a handle to turn it into a considerable paper. These are in descriptive locale theory and what could be called descriptive category theory. There is also an unsolved problem Ivan Rival has accepted for Order, and I would like to make him bring it out with a footnote saying 'The proposer has just solved this problem', but it doesn't look very likely.

Let me advertise Krull dimension of metric spaces. People keep saying Krull dimension doesn't work except for weird Zariski spaces, because all Hausdorff spaces have Krull dimension zero. But that is because everybody has been defining Krull dimension wrong, until 1979. In 1979 Ramón Galián gave a modified Krullian definition of dimension and showed that it agrees with all definitions of dimension for separable metric spaces. I gave an equivalent definition in 1985 and showed that for all metric spaces, it's greater than or equal to ind and less than or equal to dim. For all known examples, it's equal to ind. (Metric examples. For compact Hausdorff spaces this is in a knotty area where Pasynkov has done something. See the Sancho de Salases' paper (Juan and Maria Teresa) in Proc. AMS 105 (1989), 491-499; they don't cite Pasynkov, but they cite my 1985 paper, which does cite Pasynkov.) But I called my definition 'by Lebesgue or Krull, out of Menger-Urysohn'. The main problem was my being brainwashed; they tell you for thirty years that this silly definition copied from algebra is topological Krull dimension, and if you aren't careful you believe it. In fact, Galián had the definition right:

The Krull dimension of a topological space is defined as the minimum dimension of any lattice of open sets which is a basis for the space. The dimension of a lattice is what Krull said, the maximum length of a chain of prime ideals. (A chain with two points has length 1, one link.)

In 1986, Juan Navarro González sent me a copy of Galián's paper (incomplete, but all I have ever seen). So I asked him, "How do you prove our definitions are equivalent?" And he said, "Why, you proved it." And you know? He was right. What none of us has said in print is that of course this is how you transpose a definition of dimension from algebra to topology. Is the inductive dimension one more than the worst dimension of a boundary of a neighborhood? No, you take the best neighborhoods. Is the covering dimension the order of a bad covering? No, you take the best coverings you can get, get enough of. So for Krull dimension, you take the best lattice of open sets you can get enough of. (What the traditional definition actually uses is not prime ideals of the lattice of all open sets but prime principal ideals; that's different, but no better.)... The problem is to determine whether Krull dimension = inductive dimension for all metrizable spaces. People have been working on it without knowing it, because they've been trying to get into the gap between ind and dim and see what's there. Prabir Roy proved more than thirty years ago that there's a GAP there, and hardly any more is known now.

KDM: Do you have any plans for writing any more books?

ISBELL: Not bloody likely.