I don't buy the "you can't teach yourself this on your own" thing. At least not in the sense that genius is a necessary requirement. The more time I spend on th

I don't buy the "you can't teach yourself this on your own" thing. At least not in the sense that genius is a necessary requirement. The more time I spend on this stuff, the better I seem to become. The pace at which I learn may be different than other people (which might be due to genetics but it could just as well be due to environmental factors such as having fewer distractions than other people or simply having had habits growing up which weren't necessarily mathematical but might have served to grow the components of the brain that made all this stuff easier) but I seem to be able to do it if I just dedicate enough time on it. In other words how good a person becomes at the task is essentially monotonically increasing (as long as you don't take a long break and forget it all), the difference between individuals is the slope. The curve doesn't seem to have any upper limit, though at times it seems to have a very slow rate of growth. But you'll only reach a desired level if you invest enough time on it. In school you have a fixed time-constraint, which is why, together with the mental model I described, some people fail (as well as not investing enough time on it of course). Talent or genius only affects how rapidly a person learns, but as long as you're motivated enough to keep going and your time-constraints are wide enough I don't see a rational reason you couldn't do it. But I also think the growth-rate could be bumped up for everyone if we talked more about the ins-and-outs of how to go about teaching this all to ourselves.