Perhaps, some day, you will attend one of my research seminars! I give these now and then, to let my colleagues here at UNSW, or at conferences, know the results of my latest exciting mathematical researches and breakthroughs. Over the years I have talked about group representations, Lie theory, hypergroups, special functions, number theory, combinatorics, and mathematical physics, but these days it is usually some aspect of geometry or rational trigonometry—whatever I have been working hard at for the last year or so.
Having given such talks dozens of times over the past few decades, I am now just starting to suspect, somewhat painfully, that most of them have probably been quite boring. Not to me of course!—I find them singularly interesting, especially when full of the adrenalin that talking for an hour in front of a room full (or half full, or one quarter full) of highly intelligent people gives you.
What made me suspicious? Nothing obvious, just a few subtle tell-tale signs, a hint here or there. People sleeping during the lecture. Audible snores. Some colleagues deeply engaged in test marking, others seeming to meditate quietly with their eyes closed, yet others studying the cloud formations out the window. The drooping eyelids followed by the dropping head, and then the automatic jerk as the body regains consciousness before hitting the desk. The awkward silence at question time, the nominal polite question from the seminar organizer or a friend in the audience.
So because one shouldn’t jump to conclusions quickly, I now make discreet observations of members of the audience at other pure mathematics seminars. And I am pleased to report that with some key exceptions, the phenomenon seems to be almost universal. Not only are my seminars boring, but in fact most pure mathematical seminars are boring—judging solely by the audience attention and reaction.
This is surely a conundrum, seeing as pure mathematics has to be one of the most fascinating areas of human endeavour! How can we explain it?
To answer this question, I have submitted myself to intense psychological self-examination in the interests of Science. The results are not pretty, and don’t cast me and my fellows in a glowing light. This is reality journalism, self-confession and science reporting, all rolled into one.
The need to impress When I give a lecture to my professional colleagues, I pretend I am interested in informing and entertaining them. In reality my motives are much more nefarious and self-centered: I want to convince them that I have not been twiddling my thumbs for the last year, that I deserve to get more research money, that I ought to be promoted, and that I am generally not the moron I appear to myself most of the time. To do this is no easy task, but I have a well-trodden path to follow.
The key is to make my talk as technical and difficult to understand as possible. If the listeners can’t absorb and follow my seminar, they won’t suspect it is mostly uninteresting, and ultimately rather trivial (the key result boils down to setting a derivative to zero, or solving a quadratic equation, or something equally mundane). I formulate the most general version of everything, give the most specialized and convoluted examples, and make sure that the theory gets dressed up as something much more subtle and difficult than it really is.
Keep expository stuff down to a minimum Since most of my colleagues aren’t familiar at all with the particular areas I investigate, they would probably benefit most by an entertaining, expository, and wide ranging overview of the area. They would like to see the gems in the subject, the really beautiful arguments, the most important and useful results, the surprising connections with adjacent disciplines. But giving them what they want would be like dousing water on my all-important reputation. Most of the really interesting things in my area have been established long ago, perhaps by Euler, Sophus Lie, Felix Klein or Hermann Weyl. How is explaining their lovely insights going to enhance my reputation, increase my prospects for promotion, or improve my chances of getting one of those obscenely rich Australian Research Council grants?
Rising up in the cult of complexity Modern pure mathematics gets a bit insular, and so it becomes really challenging to compare the relative importance of different people’s work. Is my theory of Modular cuspidal cohomology of the functorial duals of p-adic proto-sheafs on a transcendental delta ring more interesting than your theory of Simplicial foliations of the pseudo-twisted maximal operator on the spinor bundle of a perverse quantum monoid? Who’s to say?
What ultimately counts is what we can get our colleagues to believe about the depth and importance of our research fumblings, how many papers in prestigious (i.e. unreadable) journals we publish, and how big and influential our circle of citation/conference-buddies becomes. This is a zero-sum game, my friend, and the complexity and incomprehensibility of my seminars is a key tool to impress the Dickens out of you and my colleagues. Academic self-interest must prevail, and so I am happy to say that my next seminar will be…deep, profound and extremely important! In other words, boring.