This happens to me both sleeping and awake. When I’m stuck on a problem and decide to walk away from it for a while, I subconsciously spin off a thread in my mind and move on to something else. The number of times I’ve had a eureka moment 3-5 hours later (not realizing I was even percolating on it) has to be in the hundreds.

Happens probably twice a week when I sleep on the problem as well.

To parlay this back to the current LLM craze, if we just export all our problems to some fuzzy non deterministic solver without ever trying to understand the problem, our collective brains will atrophy severely.

I use the LLM my work pays for, sparingly, because I refuse to let that atrophy occur.