During your waking day, when you think about a problem you start tackling it with a specific strategy and accumulate thoughts (assumptions) regarding those strategies. Even if you discard them over the course of your day, you are still biased/focused towards that train of thought.

A good night's sleep which takes your mind out of conscious thought then resets/defocuses your mind again and you are more receptible to new ways of tackling the problem.

(All of the above is just vague anecdotal evidence, and I have no idea if there is any scientific basis for any of it.)

The Psychology of Invention in the Mathematical Field by Jacques Hadamard, himself a mathematician is not scientific but a good source of anecdotes and systematic attempts at introspection.

I find that 'stepping away' from the details after immersion for a few days and allowing the pieces to re-align themselves does seem to pay benefits, even with the mundane and practical problems I need to solve. I agree with the grandparent post that alcohol is not the only de-focusing agent around.

Related: I was reading somewhere yesterday (reddit?) about hypnogogia and how creative types used the gap between sleep and wakefullness to tap the minds creative/artistic thought.

Basically a light version of using drugs for creative stimulation: instead of creating the altered state, tapping the altered states that are already present at certain times.

Not necessarily the sleep itself, but I've had many good ideas while trying to fall asleep, when I wasn't actively focusing on anything.

The default mode network is thought to be involved in creative thinking, and it's most active when you're not actively focused on a task: https://en.wikipedia.org/wiki/Default_mode_network