Recently I gave a talk to some prospective students and others at a university open day. It’s the talk I’ve given before, many times in fact, and it’s a talk I enjoy giving. In this talk, I take the audience on a journey from the Pythagorean Theorem, possibly the oldest mathematical fact that we as humans have, to Beal’s conjecture, an unsolved problem to which I don’t expect to see a solution in my lifetime.

The talk went well, I think. People came up to me and asked questions afterwards, always a good sign, and they laughed at the few jokes I scattered through the talk (and not at non-joke times), also good signs.

Reflecting after the talk, though, and thinking about ways of improving the talk for the next time I deliver it (since we are always in a cycle of continuous improvement), I found myself wondering whether the time had come to develop a different talk.

And I started thinking about why I was thinking this. The audiences for this talk are essentially disjoint from one another, except perhaps by some coincidental happenstance, and so for the audiences the talk is new each time.

The reason I was thinking this is that I am beginning to get a bit bored of this talk. Looking back, I can see that this is not an uncommon pattern: give a talk some number of times, and it can become difficult for the speaker to generate the same enthusiasm the n-th time they give the talk as they had the first or second time. And a large part of carrying an audience is precisely that enthusiasm.

And this is a much broader issue. This issue has the potential of leaking into teaching, particularly if someone teaches the same class for several (or many) years in succession. Unless they take active steps in refreshing their material, perhaps finding new illustrative examples, then they might find their enthusiasm waning and their energy falling, and ultimately their students drifting off.

Part of this I think comes back to this issue of the distance between experienced practitioner and beginner, an old theme. But it’s more than that. This issue of distance is one that requires work but can be overcome.

But the issue of enthusiasm is a different sort of issue, and one that might well be harder to directly tackle. I think there’s great value, as a teacher, in engaging with a certain collection of material on an extended basis over the course of several years, because that does provide me with the opportunity to shape how newcomers will first encounter that particular part of mathematics, or aikido, or whatever it is I find myself teaching.

But I’m beginning to see that this issue of my enthusiasm is a bit more insidious of an issue, because the students I’m sure are very perceptive to my levels of enthusiasm and engagement. If I wane, they wane. If I engage, they engage. And so this is something for me to bear in mind when I go into the classroom or the dojo, and teach.

In some arenas, there is a seemingly straightforward solution to this, which is to rotate teachers among the classes taught, so that no one teaches the same class for more than a few years in a row.

But I have issues with this. Sometimes, as with me and aikido, this sort of rotation is not possible and so the issue is one I have to confront directly. It also can prevent this deeper engagement with the material that needs some years to develop, particularly when what I’m teaching is not directly related to my area of greatest familiarity. And ultimately, I think it’s better to address these issues rather than put into place strategies that might or might not mitigate its effects.