This is a really cool point. There's a relevant quote about how mathematicians use this technique:

Every supposed genius has a bag of tricks—a list of obscure technical methods that hardly anyone knows about, that they have mastered. Every time they hear about a problem, they go through the list mentally, to see if one of the tricks might work. They hardly ever do, but once every year or two, you get a match, and then you look brilliant, like you’ve had some staggering insight. But actually all you did was notice that percolation theory is applicable, or something.

It's from here