If I have done the public any service, it is due to my patient thought.

Useful work is more often the product of staying with a question than of being unusually clever about it. Patience is the rare part. Most people leave a hard problem after the first few passes, when the obvious answers are exhausted and the interesting ones have not yet surfaced. Whatever you give sustained, unhurried attention to will eventually give something back.

Pick one question you keep half-thinking about and give it a proper hour with nothing else open. Return to it tomorrow rather than declaring it finished. Progress that slow is easy to mistake for none.