Blog post: randomc: Vaguely mathematical intuition

Intuition can be thought of as a measure of the ease and clarity with which awareness of an environment is maintained. So to have 'good' intuition means to be able to maintain accurate and clear awareness without struggle.

Say you play a racquet sport; then to have good intuition for the sport involves what? Aside from physical awareness of the court, good intuition is also predicated on sharp awareness of possible tactics and strategy. I play squash, and i used to play a guy in his fifties who would consistently thrash me even though i could easily outrun him and my shot accuracy was probably superior. The guy just knew the game better than i did. He out-thought me.

Years ago i competed with a couple of friends in learning the guitar. We all started from scratch at the same time, listened and tried to emulate the same kind of music, and shared what we learned as a kind of social ritual. After a couple of years, it became very clear that one of us, call him Dave, was just gifted. He understood the instrument in some way that we didn't. He played in a way that engaged - you actually enjoyed listening to him when he played. The odd thing was that technically he was probably a little behind in the group, when it came to the difficulty of the stuff we were working on. But we were teaching him tunes that we'd written in order to learn how they could be made to actually sound good.

Now I'm quite a competitive person, and so being thrashed by a fifty year old and having my own music played back to me with a cherry on top tends toward pissing my right off. I wanted to know what the edge these guys have over me is.

And it's this: they just feel the environment they are in. Of course, it's talent, it's a gift, but i don't think that that puts what they do out of reach. You just have to learn to think like they think.

Right then, crunch time. Mathematics is an environment.

Of course it is. Why is platonism so enduring in mathematics, why are mathematicians so inclined to perceive abstract mathematical objects as having an independent existence?

The idea of mathematical intuition is almost taboo. Mathematics is taught as operations, as a skill set.

In terms of economic output i suppose this is a precise definition of what mathematics is, but in terms of actually realising potential, policy should identify all students of mathematics who are capable of developing these skill sets.

At present, the norm in academia seems to be a kind of macho ; 'i learned through an ultra-operation focused curriculum therefore so shall you'. But I've hung around enough mathematicians and scientists to know that they don't really think like that, whatever they or their macho posturing may tell you.
Read and comment on the full post