When I was at school, I had a decent run of being the best mathematician in the school. One of my good friends was the second-best. (Well, so I thought at the time; in fact if I remember rightly he turned out to do better at Cambridge than I did. Perhaps at school I just had the advantage of being a year ahead.) He was a more naturally sporty type than I was, and he once observed that it always made a refreshing change to spend time with me, because while to everybody else in the school he was primarily a mathematical genius, from my point of view he was first and foremost a rugby player.

I too fall between two obvious categories, in various contexts. For example, I'm a hybrid mathematician and programmer; so to my colleagues at work, I'm often the person they think of when they have problems of a mathematical nature, whereas my mathematician friends tend to think of me when they have computing-related problems. For another example, I dress in a way that makes me look somewhat like a goth at work but somewhat like a normal in a goth club.

I don't imagine this sort of thing is in any way unique to me; it seems obvious to me that very few people are going to fall at the extreme end of any spectrum you can name.

However, there are a few spectra of which I generally consider myself to be at or near one end, and on those spectra it's occasionally disconcerting to encounter someone even further towards the same end. One of those spectra is the one ranging from pure maths through applied maths to physics; I've always considered myself to be a pure mathematician through and through, with a general distaste for the sloppy and approximate world of applied maths and no time at all for the uncertainties of actual physics. I avoided all the applied courses I could during my degree, and never regretted it.

So it's been rather a surprise this morning to find myself being consulted on a physics-related maths topic, on the grounds that I was more of a physicist than the mathematician consulting me. I couldn't actually do the maths in question, but I was able to explain intuitively what it all (well, most of it) meant in physics terms, which was what I was actually asked for. Evidently I'm further away from the end of that spectrum than I'd previously thought.