I had this problem near the end of my PhD (physics). Because of a sad conjecture of circumstances I ended up having a problem to resolve quickly. The more I wa

I had this problem near the end of my PhD (physics). Because of a sad conjecture of circumstances I ended up having a problem to resolve quickly. The more I was thinking about it, the harder it looked. I then went to some people who were also physicists (not necessarily in my specialty) to discuss it, and see how it goes. It was confirmed that the problem was indeed hard. So I did the only think which made sense in that context: I simplified it. And was crossing fingers to still have a more or less working model, with known limitations. Which ended up not being that easy, but was ok-ish - and solvable. I then want for dinner with a friend, and by main course she casually suggested a completely different approach. It flipped my depressed world around. So to summarize the advices: see if the problem is really hard, then discuss with clever people to see if they feel the same, then simplify. Or take a few steps back and consider looking at it though a completely different perspective. Good luck!