I believe I have experienced this multiple times, but I remember one event in particular when I couldn't solve a book exercise for several hours, I slept in frustration. When I woke up I knew the answer immediately as if it was obvious.
https://link.springer.com/article/10.3758/s13421-012-0256-7
https://www.sciencedirect.com/topics/computer-science/spread...
Human brain runs a defrag process (quite literally) when the body sleeps. Not only this removes the cruft from the day but also rearranges and makes links for the knowledge gathered through the day.
This is so. much. true. Curiously, it's very well known and yet ignored most of the time, for some reason.
For simpler problems, a night sleep can be enough. Just tell your brain to work on it before you go to sleep and the solution will be ready for you by breakfast, like magic.
Or sometimes, a work in the park.
"Give your brain some space" should be taught in every school and yet many times we tell kids the opposite.
> Rajpopat said, "I had a eureka moment in Cambridge. After 9 months trying to crack this problem, I was almost ready to quit, I was getting nowhere. So I closed the books for a month and just enjoyed the summer, swimming, cycling, cooking, praying and meditating. Then, begrudgingly I went back to work, and within minutes, as I turned the pages, these patterns starting emerging, and it all started to make sense. There was a lot more work to do but I'd found the biggest part of the puzzle."
> "Over the next few weeks I was so excited, I couldn't sleep and would spend hours in the library, including in the middle of the night to check what I'd found and solve related problems. That work took another two and half years."
I (and probably every programmer (or mathematician, physicist, carpenter, or problem solver) on the planet) have felt this effect first-hand. Incredible how well the brain can collate and sift through information if you just give it the space to do so.
A related effect, when I was a time where all I did was look at a screen all day, looking up new information, I couldn't solve problems nearly as fast. Looks like I wasn't allowing the incubation period in my mind to start and continue unabated.