In a letter do his former PhD student Feynman gives this amazing advice:
“The worthwhile problems are the ones you can really solve or help solve, the ones you can really contribute something to. A problem is grand in science if it lies before us unsolved and we see some way for us to make some headway into it. I would advise you to take even simpler, or as you say, humbler, problems until you find some you can really solve easily, no matter how trivial.”
Wait. It's not this the same Feynman that talked about having a list of the most important problems to work on?
This seems to be contradictory. Should we focus on the small things we can do or try to work on the most important problems in our field?
This is why you should use ideas as tools not truths.
You can use both ideas to your advantage by:
1. Work on the problems you can do something about and interest you. No matter how small they are.
2. Keep a list of big problems. When you find a way to attack the problem, try it. Most of the time it will not work because it's a hard problem. Go back to your small problems until you find some way to attack the big ones again.
Ambition is not the enemy. It can be an amazing friend if it comes together with humility. You should do the possible while you try to do the impossible.