Topology Atlas Document # topd-47

Biography of John Rainwater

Robert R. Phelps

Department of Mathematics, University of Washington

From TopCom, Volume 7, #2
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The following paragraphs will describe the origins of John Rainwater, the impact of his work, the motivations for various parts of it and the prospects for his future.

Origins

John Rainwater came into existence at the University of Washington in 1952 when Nick Massey, a mathematics graduate student in Prof. Maynard Arsove's beginning real variables class, erroneously received a blank registration card. (In those years, each student filled out a card for every class, which first circulated among various tabulating clerks in the registrar's office before being sent to the professor.) He and a fellow graduate student, Sam Saunders, decided to use the card to enroll a fictional student, and since it was raining at the time, decided to call him "John Rainwater". They handed in John Rainwater's homework regularly, so it wasn't until after the first midterm exam that Prof. Arsove became aware of the deception. He took it well, even when he later opened an "exploding" fountain pen with John Rainwater's name engraved on it which had been left on the classroom table. After remarks by Arsove, such as "I guess I'll never see Rainwater except in a barrel," virtually all the students learned of the Rainwater prank. Several years later, when a group of mathematics graduate students and junior faculty solved some American Mathematical Monthly problems over coffee in the student union, it was only natural that they would submit them to the Monthly under J.R.'s name. As it does at present, the MAA doubtless suggested that someone who was submitting problem solutions should become a member of the Association. At that time, a prospective MAA member had to obtain the endorsement of two current members. An ideal endorser would have been Professor Carl Allendoerfer, who was not only Chairman of the Mathematics Department but also President of the MAA. Unfortunately, he was not the kind of person to participate in a joke involving the MAA. The solution was simple: A secretary was persuaded to put the endorsement form in with a pile of papers which required the busy Chairman's signature, and the deed was accomplished. (Allendoerfer was reported to have been more than a bit unhappy when he eventually learned of the matter.) John has continued to publish problem solutions; see the paragraph on Authorship and Motivation below.

The first of John Rainwater's ten published research papers were written in 1958 and 1959 by John Isbell, a young Assistant Professor. Isbell's response to queries concerning his motivation for using J.R. as a pseudonym has been simply to quote Friedrich Schiller "Der Mensch ist nur da ganz Mensch, wo er spielt." Unlike many of the Rainwater papers, there is no hint within these first two papers as to the actual authorship. (For present-day readers of this account, it should be pointed out that academic jobs were plentiful in the late 50's, so amassing a publication record was not as pressing as it is today.) A functional analysis seminar was started in the late 1960's, and it seemed appropriate to call it the "John Rainwater Seminar", in view of the work that J.R. had done in that field. As the functional analysts in the department over the years have changed fields, died or retired, the John Rainwater seminar has changed its emphasis from simply functional analysis to functional analysis plus Fourier analysis, then to these two fields plus dynamical systems. At present it is primarily a seminar in the latter area.

Impact

What about the impact of John Rainwater's research? This is something that it is always difficult to measure, but a rough idea can be obtained from the citations listed in the Institute for Scientific Information's "Web of Science". (The numbers which follow are those in the bibliography below.) His most cited paper, with 19 citations, the latest in 2000, was the first one, in topology. Number 6, his 1969 PAMS note on Day's norm, is his next most cited paper, with 17 citations, the latest in 1998. The algebra paper (number 14) has 14 citations, the latest in 2001. There are eight citations to both his second paper, the latest in 1989, and his third one, the one-page 1963 PAMS note, the latest in 2002. The latter has also been cited in books as "Rainwater's Theorem". Paper 15 on convex functions has six citations, the latest in 1995, while paper 10 on regular matrices has four citations, the latest in 1997. Paper 7, also about Day's norm, has three citations, the latest in 1993 and number 8 has two, the latest in 1998. There is even one citation to number 13, his unpublished 1967 Rainwater Seminar note on Lindenstrauss spaces. Papers 4 and 16 have received no citations to date. In summary, it appears that most of John Rainwater's published work has been reasonably well received.

Authorship and motivation

As mentioned earlier, John Isbell wrote the first two John Rainwater papers. I wrote the third one, and the motivation was simple: I needed the theorem for a paper I was writing, but it was a "folk theorem", observed more or less independently by five other mathematicians. It would have been a bit silly to have a half-page paper appear under the names of five authors, so I wrote to each of them, obtaining their approval to publish it under J.R.'s name (who acknowledged their "extremely useful conversations"). The fourth paper was written by Irving Glicksberg. I'm not certain of his motivation; this might be the only instance where the actual author thought that the paper was not good enough to appear under his own name. (The absence of any citations for it suggests that he was right.) Paper 5 is an unpublished note that was circulated to the experts. Paper 6 about Day's norm was again a case of a large number of people (six this time) having provided various parts of the proof, so a pseudonym was very much in order. Again, they are thanked for "helpful discussions". Paper 7, which deduced additional properties of Day's norm, was written by Edgar Asplund for a conference in Aarhus. Paper 8 on the abstract F. and M. Riesz theorem was written by Glicksberg. The result was proved by four people but it was only one and a half pages long, so the motivation is again obvious. The unpublished seminar note in number 9 was written by me for the Rainwater Seminar. Number 10 (Regular matrices ...) was written by John Isbell again (who, incidentally, has authored or co-authored six other pseudononymous papers under two other names). I proved the result in number 11 and subsequently learned that Day and Pelczynski were also aware of it. John Giles also proved it independently, and he was rather unhappy that the rest of us thought that it was not important enough to publish. Number 12 is an exposition I wrote for the Rainwater Seminar. Number 13 was proved by Peter D. Morris and me when he was visiting here; we thought it was too clearly an example of "proof by theorem" to be worth publishing. Paper 14 is a departure for John Rainwater. Not only is it in algebra, but he doesn't thank anyone for helpful conversations. He notes, however, that his work was supported by four different grants. (Culprits this time were Ken Brown, Ken Goodearl, Toby Stafford and Bob Warfield.) Number 15 was written by Isaac Namioka and me. We were able to generalize Elena Verona's theorem simply because we were familiar with some techniques she (as a new Ph.D.) had not yet learned and we would have been embarrassed to take personal credit for that. Number 16 was written by me and David Preiss; it has not yet shown up in in the Science Citation Index. Number 17 is a collection (surely incomplete) of problems or solutions which J.R. has published in the American Mathematical Monthly, the earliest in 1959 (sent by John Isbell), the latest in 1994 (sent by me). I have no idea who was responsible for problem 4908 (1963) from the University of British Columbia.

Future

Where does John Rainwater go from here? It would be a shame if he were to die. He is not as old or famous as N. Bourbaki (who may still be alive) but he is clearly older than Peter Orno, who only has three publications to his name, all in the 1970's. (At least one of his authors had an interest in pornography, hence P. Orno.) He is also older than M. G. Stanley (with four papers) and H. C. Enoses (with only two). It is to be hoped that someone will be able to help John Rainwater carry on, so that in the future people won't ask "Who killed J.R.?" The previous paragraph gives some guidance to potential Rainwater authors. Clearly, in the present employment climate, no junior faculty member would be willing to emulate John Isbell and publish a really good paper under a pseudonym. The other successful J.R. papers were those which simply had too many authors, all of whom were securely tenured faculty, so keep him in mind if you find yourself in such a situation. It would be nice to keep the tradition going.

Acknowledgements

A number of people have helped me to write this biography. My appreciative thanks go to Maynard Arsove, John Isbell and Sam Saunders for their information on J.R.'s origins and to the University of Washington Mathematics Librarian Martha Tucker for furnishing the citation material.

Bibliography

1. Spaces whose finest uniformity is metric, Pacific J. Math. 9 (1959), 567-570. MR 21:5180 Zbl 0088.38301
2. A note on projective resolutions, Proc. Amer. Math. Soc. 10 (1959), 734-735. MR 23:A618 Zbl 0105.16403
3. Weak convergence of bounded sequences, Proc. Amer. Math. Soc. 14 (1963), 999. MR 27:5111 Zbl 0117.08302
4. A remark on regular Banach algebras, Proc. Amer. Math. Soc. 18 (1967), 255-256. MR 34:8223 Zbl 0171.33802
5. On a renorming theorem of Klee, Unpublished note, 1968.
6. Local uniform convexity of Day's norm on c0(G), Proc. Amer. Math. Soc. 22 (1969), 335-339. MR 39:4647 Zbl 0185.37602
7. Day's norm on c0(G), Proc. of the Functional Analysis Week, Aarhus 8 (1969) 46-50. Matematisk Inst., Aarhus Univ., Aarhus. MR 40:7778 Zbl 0235.46048
8. A note on the preceding paper, Duke Math. J. 36 (1969), 779-800. MR 44:7299 Zbl 0201.45801
9. A characterization of certain dual unit balls, Rainwater Sem. Notes, 1970.
10. Regular matrices with nowhere dense support, Proc. Amer. Math. Soc. 29 (1971), 361. MR 43:5330 Zbl 0213.08301
11. A non-reflexive Banach space has non-smooth third conjugate space, Rainwater Sem. Notes, 1972.
12. A theorem of Ekeland and Lebourg on Frechet differentiability of convex functions on Banach Spaces, Rainwater Sem. Notes, 1976.
13. Lindenstrauss spaces which are Asplund spaces, Rainwater Sem. Notes, 1976-77.
14. Global dimension of fully bounded Noetherian rings, Comm. Algebra 15 (1987), no. 10, 2143-2456. MR 89b:16032 Zbl 0628.16010
15. Yet more on the differentiability of convex functions, Proc. Amer. Math. Soc. (1988), no. 3, 773-778. MR 89m:46081 Zbl 0661.49007
16. A class of null sets associated with convex functions on Banach spaces, Bull. Austral. Math. Soc. 42 (1990), no. 2, 315-322. MR 91j:46050 Zbl 0724.46017
17. Problems/Solutions of John Rainwater.
18. Collected Works of John Rainwater, Department of Mathematics, University of Washington.
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Date: October 21, 2002.