[jvvw]

I assumed that everybody did this when trying to solve a maths problem they are stuck on (thinking university type level maths rather than school maths) and when I was teaching I would always get people to go back to the definitions.

I wasn't amazing at maths research (did a PhD and post-doc and then gave up) but my experience was that it was partly thinking hard about things and grappling with what was going on and trying to break it down somehow, but also scanning everything you know related to the problem, trying to find other problems that resemble it in some way that you can steal ideas from etc.