Richard Feynman supposedly said something like

You have to keep a dozen of your favorite problems constantly present in your mind, although by and large they will lay in a dormant state. Every time you hear or read a new trick or a new result, test it against each of your twelve problems to see whether it helps. Every once in a while there will be a hit, and people will say, “How did he do it? He must be a genius!

I wonder what other low-hanging fruit there is in trying the right tricks on the right problems?