Learning to learn

It has happened a few times over the past couple of years that someone will come up to me with some piece of mathematics that they're having trouble with and ask me if I can help them with it. I'll have a look over it and say something along the lines of "I'm not familiar with this specifically, but I think I should be able to pick it up pretty easily". The usual response to this involves some degree of indignation.

Of course I understand why. Nobody likes to feel stupid or belittled, and this is certainly not my intention, but I can see how someone might feel that way. If I were in that position it would probably be my first response as well. But with that said, I don't think it's an entirely reasonable one.

I'm not trying to show off how clever I am. They were the ones to come to me asking for my help (and if I can I try my best to). Presumably they came to me because they expected I had some degree of expertise, but I get the impression the sort of expertise they were expecting was that of having been taught the subject previously. Sometimes this is the case of course, but mathematics is such a broad topic that you will rarely have seen everything at a sub-postgraduate level no matter how educated you are.

The point of having gone to university and graduated with a degree (even a bachelor's) specialising in mathematics or a mathematics-heavy field like physics is not to simply learn as much of a field as you can and leave it there. The point is to equip yourself with the tools to teach yourself new things, and I hope to some extent I have managed to do that. I've taught myself things I never saw at university and so I know my limitations. Some concepts and techniques I'm reasonably familiar with and others I'm not; some things take more time and more effort to learn than others. It just happens that through study and experience I've managed to achieve the minimal level of competence to teach myself what they're having trouble with.

So my exasperation does not come from a place of ignorance. I have struggled with maths in the past, I know what it's like. The fact remains, however, that my degree would be worth very little if I hadn't picked up the ability to learn high school- or early undergraduate-level maths with relative ease. If someone's problem left me just as nonplussed as they were, then I should probably be seeking partial reimbursement from my university. I certainly hope they don't take it as a personal slight; I have no doubt that if they had studied what I had then they would have just as little trouble with their present difficult as I might (and, I would hazard, quite possibly even less so).