Diners were Dave Collingwood, Ramesh Gangolli, Jack Lee, Randy Leveque, Doug Lind and Ginger Warfield, faculty, and Julie Harris, Mark Johnson and Eric Scott , graduate students.

Its always nice to have a theory vindicated. Ever since popular demand on the part of the attending faculty members convinced us to increase the graduate student invitations to three, we have had the aim of having one from each level (archaeological layer?) of the graduate program. This time we finally managed it, and sure enough, it was great having three different perspectives.

Once the serious business of the evening had been taken care of (three orders of soup, two of pad thai...), we launched the discussion with a bit of history: the previous such dinner was directly responsible for the sequence of Friday afternoon research colloquia now going on. Ten faculty members have agreed to give summaries/descriptions of their research fields in a format aimed at graduate students. The talks are being very well attended and appreciated (as are the pizza socials which follow.) Even they give rise to some questions, though. Eric reported from the first year front that he and his classmates have a feeling that if they knew just a little more they could understand a lot higher percentage of the content. So maybe the sequence should be in the spring, assuming that it continues its existence as a One Quarter Deal. On the other hand, it is really most aimed at second year students, whose level of limbo-tude peaks right after they polish off prelims--now geared to be just before autumn quarter, so for them the current timing is best. On the other, other hand, there are many, many members of our faculty, and maybe what we need to do is extend the whole sequence over an entire year--not that hard to organize if one were to eliminate the pizza. A relevant comment in terms of that scheme was that Randy, who did one of the first talks, felt it would not be a particular burden to do another in a year or so ("I could do the first half of what I did and expand it a lot!")

I don't think we actually resolved that, and some later comments served to remove any clarity we might have achieved. But we did move on. Jack supplied the next direction by laying firmly upon the table the question: Does the department need to broaden its mission beyond training graduate students to do mathematical research? This hit a chord with Eric, who gave an immediate and unambiguous " Yes!" It turns out that he took quite a lot of chemistry as an undergraduate, and was struck by how much mathematics was involved--and by the fact that the chemistry department taught all of its own advanced mathematics, as did most of the natural sciences, leaving the math department high and dry. And since he feels strongly that a lot of what's important about mathematics is what it can do for these fields, the graduate program should reflect that. As he finished this statement, Mark,who had clearly been having increasing difficulty restraining himself, erupted into contradiction: "That's not what's beautiful about mathematics! The wonderful part is being able to take an idea and throw it in the air and not care where it comes down--to be able to take an idea and pursue it and not worry about what it will do for anyone!" Between the two of them, we had mathematics in microcosm, no?

At a later point, the topic recurred in slightly different context, and someone asked Randy to define Applied Mathematics. His answer seemed to me to speak nicely to both of those points of view: the beauty of Applied Math lies in its ability to abstract ideas from a variety of contexts and see what they have mathematically in common, so that one can then proceed with the mathematical aspects themselves. People tend to talk about abstract mathematics as if it were off in the ether somewhere--I liked hearing abstract turn up as a verb in that context.

Back to the program issue. Julie pointed out that in one direction our program definitely is broader than simple research preparation. Between Math 102, the PFF, teaching a summer course together with another TA (separate sections, jointly prepared) and her current experience teaching a section of 120 as part of a four-person team, she feels that she has had a lot of teaching preparation, which she values highly. This led to a discussion of the virtues of co-teaching or team-teaching, or variants thereof. If faculty members were to do some co-teaching with members of other departments, we would be far better acquainted with their needs and interests, and they with ours. There are heavy-duty administrative difficulties with that, though--not to mention some question how many of us are actually in a position to carry out such an activity.

About this point, limbo reappeared. I think it is the one invariant in these dinner conversations--and for good reason. It seems to be an invariant in graduate life. With our current scheme of things, it has been transferred (generally) to second year, which may have changed its flavor a little--but not much. Basically, there is no way around the moment when one emerges, blinking, from the tunnel of prelims-or-bust and looks around the wide open terrain available to the prelim passer. It is not uncommon for this stage to be accompanied by a certain nostalgia for the tunnel--at least there one knew what direction to travel. Mark feels he profitted greatly from having been picked up at this stage by the scruff of his mathematical neck and flung headfirst into mathematics that was well over his head. He is having the time of his life and has clearly not drowned. On the other hand, that does not seem advisable--or even an available option--for most students. So we're back to the road-maps-for-limbo issue. Jack's Icewater Seminar was pointed out as potentially pertinant (this caused a pause for etymology, with Ramesh giving a brief biography of the mythical researcher on our faculty list, with several publications to his credit, by name of John Rainwater--thence the Icewater title.) The snag to it is that although it is definitely designed to dunk people in deep intellectual waters, the people in question tend to be slightly more advanced ones--ones who have selected their field and are in search of a thesis topic. For the field-less, we got back to the idea of a variation on the Research Seminars. Ramesh suggested that a series of lectures with a fair historical component could give a good sense of the development of a field and of what style of mathematics it involves. When Mark questioned how much he would be interested in exploring a field other than the one in which he has landed, Ramesh countered with a scarifying tale of English graduate work as it existed a few decades ago. At that period, students fresh out of their bachelors programs were thrown straight into the English channel (figuratively!), and emerged, if at all, several years later with a damp thesis between their teeth (wet behind the ears, too--we did the water image pretty thoroughly!). Also with absolutely no inclination to escape from the furrow into which they had so painfully dug themselves (in the English Channel?--oh, well!) Result was a tendency to become narrower and narrower, proceeding, as one British mathematician said of himself, to know more and more about less and less. We agreed that the limit didn't look so hot in that case ("L'Hopital's Rule strikes again!" said Doug.) Mark expressed some second thoughts about his inclination to refuse to look at neighboring fields. But we didn't really formulate an ideal scenario in terms of talks or classes or portions of a class. Just the idea that serious contact with something deep but accessible in a number of fields would benefit second year students considerable.

I have gleeped over one of the recurrent topics--to wit, a possible Masters program. It arose as an alternative to the research juggernaut, but didn't arise very high. One reason is that incoming students know full well that their application and early demeanor categorically must not admit to the possibility that they have the faintest whiff of an interest in getting a Masters rather than a PhD, which makes it tricky to analyse the potential demand. A more serious one is that brought up by Ramesh: its not clear how much we benefit students if, to save them from finding themselves in the harsh realities of the job market for newly minted PhDs, we offer them the option of going into a program for which there is even less market. If we were engineers, we would have an eye on the latest hot trend in the field, hire on a couple of specialists and produce a flock of students prepared to take part in the hot trend. But we're not. We let (for instance) the current interest in wavelets slide quietly by rather than cashing in and developing some corresponding PR hype and with it a program for graduate studies. And unless we put our backs into developing a niche for our Masters students there isn't all that much to be said for creating more of them--or even for making our Masters a more serious degree. A serious degree which the outside world cannot distinguish from one available elsewhere for Wheeties boxtops is not a huge benefit to anybody.

I think I have shot my wad. I remember an eloquent statement of Jacks on the subject of how Math has been pursued over the centuries as Art, but supported by society as Science. At that point the conversation waxed philosophical, but all I remember is a bit about Platonism. I think it's because somebody brought up Witgenstein and I tend to go into shock when he turns up in a conversation. If anybody has anything to fill in (Witgensteinian or otherwise) I would be delighted to add it.