multijimbo

Some many (many) years ago now, when I was but a young and eager PhD student, in the bar at a conference, I asked a senior colleague for his definition of a classical mathematical result. I was curious because we often refer, when speaking and in writing, to classical results of X and Y. His answer was that a result was classical if it were part of the mathematical literature before one got to graduate school and started seriously studying the field.

[This senior colleague took some offense the next morning, when I referred to a classical result of his. He said, it was because it made him feel old. I didn’t say it at the time, but he was one of the Old Men of the field, from my point of view. In retrospect, I can understand his mild annoyance, but I still stand by what I said.]

This definition has always made sense to me, and for reasons that I’m sure someone has studied for the whole or part of their career (and so themselves establishing results that might well be classical). When we come into a field, we survey the landscape of what’s known at the time we make our entrance, and we (or at least I) don’t necessarily spend much time exploring the time sequence of when different results were established, unless of course that time sequence is itself important to our work.

I had a similar experience with music. I didn’t listen to music much when I was growing up; I was more of a reader, devouring lots of science fiction, particularly short stories, but that’s a detour for another day.

I was young, single digits young, when the Beatles broke up in 1970, and I remember when John Lennon’s Double Fantasy came out in 1980, and since my engagement with music blossomed at some point between those two, the Beatles were a classical band but one whose break up happened at some indeterminate point in the infinite expanse of the past.

I try to bear this in mind when I’m teaching, to be sure to provide some temporal context to the results I present to the class. When teaching Graph Theory, this leads to a broad expanse of time, from Euler and the bridges of Koenigsberg in 1736, to results that might have appeared only in the few months before we see it in class, still preprint and not yet formally published.

One reason that this came up recently was something I read, or listened to; I’ve been reading a lot of articles and listening to a lot of podcasts about current politics, and with apologies but I didn’t make note of where I first or most recently heard this.

I can remember when the Berlin wall fell, where I was and who I was with. I remember, a bit less clearly, the fall of the Soviet Union and the independence of the former Soviet republics. So my political understanding stretches from the nuclear bomb drills in elementary, middle and high school, through these significant events of the late 1980s and early 1990s, and all that has happened since.

But people significantly younger than me, those whose political awareness has blossomed during the past decade, have a very different understanding of politics than I do. They are working from a very different baseline.

And we’ll see over the coming years how difficult it is to modify or reestablish such baselines. It will be interesting. Despite a much more well developed sense of the music in my lifetime and before, born of lots of listening (with so much more to do, it must be said), but I still have this instinctive reaction to the Beatles and their breakup, and where it sits in my personal time line.

~ by Jim Anderson on 6 April 2025.

Posted in bizarre and random things, education and university life, mathematics