Opinion 78: Music and Lyrics in Math Talks

By Doron Zeilberger

Written: March 8, 2007.

Human beings have bodies and souls. Computers have hardware and software, and math talks have lyrics and music. Most math talks have very hard-to-follow lyrics, and the average math talks' lyrics, in an average colloquium or seminar, is only followed by one or two people in the audience, usually the person who invited the speaker, and possibly his or her grad students.

But like a good song, and a good opera, you can still enjoy it if the music is good. The "music" in a math talk is the speaker's enthusiasm, body-language, and off-the-cuff heuristic explanations.

Sometimes you can recognize a familiar word, and relate it to something of your own experience, whether or not the meaning that you attribute to it is what the speaker meant, and this can also enhance your enjoyment.

I was lead to write this by John Duncan's last Friday's Rutgers Colloquium talk. The title promised to be about a connection between finite groups and infinite-dimensional Lie algebras. I knew what both meant, so I attributed a prior probability of %70 that I will understand at least some of Duncan's talk.

It started promising. First, John was using the blackboard, and not those obnoxious laptop or overhead projectors. Then he wrote on the blackboard, in fairly large letters: "Finite Groups" and "Infinite-Dimensional Lie Algebras", and drew two arrows, one in each direction. That part I still understood.

Then came the details. Maybe I am not as smart as my colleagues, but my conjecture is that very few people in the audience understood them. He also used all the three blackboards, the last one being far away from where I sat, and wrote in small handwriting, so it was not possible to make-out some of the words. But I don't think that it mattered, even with a larger "font", I would probably not have understood any details, and this way I had an excuse.

From time to time there was a familiar word, for example quaternions, and it was clear that he was using the Gelfand principle of presenting the simplest non-trivial example to illustrate his point. Here I got the gist in very general terms, but I was still clueless about the details.

The lyrics of John Duncant's talk were pretty incomprehensible. But the music was divine! It was so clear that John loves what he is doing, and loves mathematics in general, and these positive vibes made me feel so good! I went home much more satisfied than if I would have understood every word, but with a speaker who didn't have that contagious enthusiasm and that true-love-of-math aura.

Surely, it is nice to enjoy both music and lyrics, but if it is a choice between the two, I rather have good music and bad lyrics than vice versa. Unfortunately, so many talks have both bad lyrics and bad music. Such talks do indeed fit into my beloved academic father Harry Dym 's definition of Hell:

Hell is a boring incomprehensible math talk that goes overtime .

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