I've just been watching a documentary film on BBC2 called 'Beautiful Young Minds' about students competing for places in the British team for the International Mathematics Olympiad. It was a good film, but it was also mildly frustrating how the film inevitably focused in on the people most sharply on the autistic spectrum and reinforced stereotypes unnecessarily. When I went to the training session at Cambridge when I was in the sixth-form, one of the best parts was the bright, fun company. It was wonderful finding other people interested in mathematics to talk to about it, but we talked about many just as interesting things and it was one of the first places where I felt I naturally fitted in. I don't remember it feeling competitive but then I don't think I was ever a real contender for a place on the team. I could often answer IMO questions but not consistently enough. I was mostly just relieved that I wasn't too many orders of magnitude less clever than everybody else there and that I could make genuine contributions to my team's attempts to solve problems.
The training session was incredibly intensive experience. The few breaks you had were spent trying to solve various ongoing problems we were given to look at. We were divided into teams of four, who we did things together with for the length of the training session. Most of the time was spent solving problems, discussing problems, showing our solutions to the others. I suspect, the main aim was to fire people up to go and do lots of work on their own later. It was at home, struggling, often for days, on old questions and other problems that you slowly made progress. It wasn't anything like the sort of learning that you did at university. It was more like learning to write better. There aren't epiphanies, and I think to a certain extent, you just have to do lots of it, and it's only looking back on what you did a year ago that you see the progress that you've made. Every problem that you looked at was new and any heuristics for solving problems had been inculcated long ago. The sort of learning that I was doing back then was not like the sort of learning that I ever remember seeing described in educational research.
I'd forgotten the huge number of hours I spent back when I was younger, just trying to solve problems, not trying to actually learn anything specific per se, partly for the sheer pleasure of solving problems and the satisfaction when you did finally figure one out, and partly because I knew somehow that I was imperceptibly getting gradually better at doing so. I don't remember being tempted to look up the answers ever and I suspect that I've lost that patience since. Those days and hours spent are one of those things that probably has had a long-lasting influence on me somehow, but that you forget because it's in the past. Watching the film brought back memories