"2013-2018: I revisited this conjecture every time when I learn a new tool, without any success though. But at least thinking about it helps me quickly fall asleep many nights."
I believe Feynmann said the best people always had the top unsolved problems in the top of their minds and whenever a new technique or result arrived, they would drop everything and try out the new attack on the old problem.
I'm kind of surprised it helped him fall asleep. Whenever my brain starts to think about technical problems in the middle of the night I know I have a few hours of wakeful puzzling ahead of me
I had a friend at university who studied mathematics with me (I studied both maths and computer science, but he was a genuine mathematician, and a pretty good one, much better than me), and he told me that he often takes problems "to bed". After that he would often wake up with at least a half solution in his head. Sometimes a full solution.
Ramanujan was like that too. He believed that a goddess sends him solutions in his sleep. Not sure if the goddess is real, but the formulas certainly were real.
I find reading technical work makes my brain fall asleep very quickly. I am sure if I read Knuth's books at night I would be asleep within fifteen minutes.
I am not sure thinking about technical work would help sleep, because thinking could be orthogonal to reading.
Oh, I'm with you regarding technical reading being a good way to fall asleep! But reading someone else's train of thought is a different way to engage the brain than trying to figure out a mathematical proof on your own - that's a lot more like what pondering over programming problems would be like for us I think
This speaks to very interesting difference in biological constitution. Like the two comments below, I find my mind working harder asleep than awake. More than once I went to bed with a problem and wake up either with a solution, or with a much better perspective on the problem.
I believe Feynmann said the best people always had the top unsolved problems in the top of their minds and whenever a new technique or result arrived, they would drop everything and try out the new attack on the old problem.