On maths conferences

by Willie Wong

Those of you who know (or know of) Doron Zeilberger will agree with me that he is a very opinionated man (see link to his page of opinions on the right). Recently he has two essays up about his experiences at the AMS fall sectional meeting in Penn State (around the same time I was in Florida), and at the Joint Mathematics Meetings (which I briefly described; come to think of it, I never wrote up my impressions of the talks in the other specialties. To make up for it I will allude to it a bit today). Some of Doron’s complaints were also noted in my post on the JMM, though my criticisms are not nearly as constructive.

I must admit that I am more or less guilty by Doron’s charge. But as he noted, not all of the fault lie in the fragmented mathematical specialties: some must fall with the organization in general of these conferences. At the Southeastern Meeting at Florida Atlantic University, the only “plenary” lecture I went to was the one given by Spyros Alexakis on his proof of the Deser-Schwimmer conjecture (I guess now it should be called the Alexakis Theorem). Not only was I interested in the subject, I also want to show support for a good friend. The talk was sparsely attended. On the one hand, I very much enjoyed the talk. On the other, I felt like I couldn’t blame people for not coming to the talk precisely because I enjoyed it. The talk was given at a level that was perfectly comfortable to me, someone who has dabbled for some years in geometry. It was at a level that was slightly above the Princeton Maths Departmental Colloquiums, and slightly below that of the Princeton Maths Geometric Analysis Seminars. It was not at a level for Joe “additive combinatorics” Schmoe. Frankly speaking, that was also why I didn’t bother going to the other plenary talks: if the abstract has more buzzwords that I don’t understand than I can count on my fingers, I don’t think I’d be able to get very much out of it. (To go on a slight bit of a tangent: the content aside, I thought Spyros did an admirable job on the presentation: a combination of overhead projector slides with large lettering, and clearly written formulae on the whiteboard, it was very enjoyable. He obviously spent some time thinking about how to give the talk.)

The scheduling of the plenary talks during “lunch break” of the special sessions certainly didn’t help, especially when the only close source of comestibles is the campus cafeteria.

Now, if I were just there as a listener/student at the Sectional Meetings, I probably would’ve bounced around the various special sessions taking in what I am interested (to the extent allowed by the not-completely-aligning schedules of the separate sessions). But as a speaker at one of the special sessions, who has some personal rapport with a lot of the other speakers, it becomes a difficult choice. If it were a really good friend, you can reasonable expect him not to feel snubbed if you want to hear something new, instead of something you’ve heard 3 or 4 times already (at a small risk of offending the session organizer). (Some of my friends pulled that on me to hear, I believe, Elliot Lieb or one of his co-authors.) If it were a complete stranger, you may feel a bit guilty but chances are he won’t notice your absence (at least, you can tell yourself that; with only 15 people to a room, any absence is very noticeable). When it is an acquaintance, on the other hand … So speakers are more-or-less locked down to the special sessions they are part of. In the case of a fully scheduled special session (such as the general-relativity-and-related-problems one in Florida), the participants have almost no hope of listening to anything else. (I almost made it to Cedric Villani’s talk, if it weren’t for coming down with swine flu on the morning of the last day.)

At the JMM, I went to a bit more of the other subjects. The GR session that I was running was only for the first day, so I had some time to browse the student posters and listen to other special sessions. I was particularly enthralled by the special session on Origami. It was quite exciting to hear about something I have absolutely no knowledge of presented in a way that I could easily understand by some personal heroes of my wife’s. And I was not the only one: the small special session room was packed to the brim (especially during Robert Lang’s and Erik Demaine’s talks). There were probably close to the same number of people in the room as were there at the last plenary talk of the entire conference (given by Igor Rodnianski on general relativity). Somehow, though, this wild popularity of the origami talks should be taken as the exception, but not the norm: origami, after all, is something that is different, that is pretty and exciting, and that sounds easy to understand. For the non-research-mathematicians (high school teachers, college students, etc.) there at the conference, it was easily the most understandable of all talks (coming in a close second is Glen Van Brummelen’s presentation on trigonometry). I also went to some talks about history of mathematics, and enjoyed a few presentations on the Antikythera mechanism: sitting there in the audience listening to the really excited speaker describing in droll technical jargon how they reached this-and-that conclusion based on here-and-there fragments of the mechanism, gives me a bit of cheap thrill like that associated to classic whodunnits. They were piecing together a puzzle, much in the same way Feynman tried to decipher the Mayan glyphs.

Slightly less pleasant was my participation in the “mathematics and technology” (whatever it was actually called) special session. The participants were mostly computer geeks with even less social grace than I, and the talks were focused on how to present mathematics in the new Web 2.0/Semantic Web paradigm. I definitely felt (maybe unintentional from the point of view of the speakers) some sort of undertone during that session, where every presentation is computer-based (of course) and none of them are with “standard” software (by which I mean PowerPoint, Keynote, or LaTeX-Beamer PDF slides). Many of them are with these funny XML/HTML/MathML hybrid that the presenter developed and that only works on a specific version of a particular web-browser with possibly a special plug-in installed. It felt a bit like a pissing contest. They all seemed to assume, as an axiom, that semantic web is the future, and that mathematicians demand it (either that, or they design their mark-up language to be as familiar to mathematicians as possible so that publishers can foist it upon us authors and layoff their typesetting staff). So after one of the presentations I couldn’t stand it and asked why mathematicians should care about it. All I got was a condescending answer that basically boils down to, “Have you been living in a cave? Web 2.0 is all the rage! Semantic Web is obviously better! Nyeh na na na nah!” And when I asked a follow-up about why users will want to switch away from LaTeX, the answer I get was something like, “Well, LaTeX obvious is not a language that fits our requirement because of such-and-such technical issues that makes it not separate content and presentation. D’uh!” So I got up and left.

I also went to several plenary talks at JMM. Like I said, I very much enjoyed Van Brummelen’s talk. Brian White’s talk on flows in geometry was also wonderful. It was aimed roughly at the right level (though a bit on the high side; which made me [selfishly] happier). I was a bit sad that he didn’t get to tell us about all he had prepared (there was allegedly some geometric flow inspired by or applicable to general relativity). But for a more general audience, it was definitely better that he omitted what he did omit. Carolyn Gordon’s talk I also liked a bit. I don’t completely agree with Doron’s assessment that it was terrible, but the pacing was a bit off. The topic she discussed was “can you hear the shape of a manifold”: Given a Riemannian manifold with boundary, we can ask about its spectrum–the eigenvalues of the Laplacian. Physically, this corresponds to stretching and fixing a drum head, and ask about the harmonics of the “bongs” it emits. The question then is: does the aural harmonics of a drum head (spectrum of the Laplace-Beltrami operator) determine the shape and tension of the drum (the intrinsic geometry of the Riemannian manifold). The talk started out on the right foot: she started motivating the discussion much like what I just described here. And then abruptly the motivation ends and the maths begins. The transition was certainly awkward, leaving the more general audience member hanging. I have a feeling that she tried to cater to too broad a group of audience (from college student to research mathematicians) and ended up satisfying none.

Igor’s talk was very nice. (So was Sergiu’s introduction.) But then again, I am biased. (It was a shame that only about 150 people or so stayed it; it may have something to do with the fact that it was on Saturday [the last day] when the weather was beautiful outside. It may also [I shudder to think] have to do with the fact that the topic was general relativity…)

I also went to two horrible talks. The first was not the fault of the speaker: it was fault of mine. (Horrible in this instance was for my personal experience.) This was Fernando Ferreira’s talk on … well, something. I saw that it was an invited address and it has something to do with classical analysis. What I didn’t see was that it was a session by the ASL and therefore will be on foundational issues, of which I am painfully ignorant. For me it was an hour wasted with words flying over my head that of which only a set of measure zero I understood. I’m sure it was a wonderful talk for the specialists. For me, well, I just sheepishly and quickly left the room after the talk ended. The other one I will not name. It was an invited address that should have a lot of potential judging by the title and the abstract. I don’t mind poorly motivated talks so much as long as I can still see some interesting mathematics. But this talk was hardly motivated at all, and 30 minutes into the talk he was still giving really elementary definitions. Note: if you are speaking to an audience for whom the basic definitions are not elementary and well-known, then giving those definitions and stating a theorem is definitely the wrong way to go about it. Do you honestly think that the audience can pick up on the intricacies of those definitions and understand what the theorem actually is stating? If you do not have any good motivating examples to talk about, then you might just as well make it a high level talk and apologize upfront. At least if you talk a little about the theorem and its proof, some portion of the audience will be satisfied. (I was sitting near the back, so after those 30 minutes of waiting for him to get to the point, I just got up and left.)

I mentioned that I also spent some time looking at the posters. Overall I was not very impressed with the level of undergraduate research or their presentation. Often too many words appear on the poster: a poster in the natural sciences should have tables and plots and other visual aid to present the data. A poster in maths should have equations, for crying out loud. I’m not going to stand there in front of a posterboard reading what is essentially a two-page paper expanded to 16 pages. The words should be reserved to give an introduction/motivation to why the problem is interesting, where it first came up, and where it can find application. The rest should be theorems and graphs. Of course, I was also not happy since there’s very little in way of analysis, and very much in way of combinatorics/number theory/graph theory. There are some differential equations problems, but most of them are numerical and the solution naive. And some of the questions studied by those students have absolutely no use whatsoever. While the answers may not be trivial, they are certainly trivia: no structure for generalization, no deeper meaning, just is. That, however, I cannot blame the students: taste in mathematics is acquired. An undergraduate just does not have the experience to see if a problem is interesting or not. No, the blame must lie squarely on the shoulders of their advisors.

Two interesting things I saw: one student made his poster and poster board, but forgot to put his own name, his school’s name, or the title of his project on the poster. So he has a little hastily scribbled piece of paper, folded in half, with those information on it, placed on the table in front of his poster board. Another student made the unfortunately choice of having the back-ground color of the title-bar dark green and the title/name/school information in navy blue. I got up as close as I could and still couldn’t decipher what her poster’s title was.