This is a beautiful letter from Richard Feynman to a former student on what constitutes “important problems”. I’ve always felt that important problems are those that advance your own knowledge, and ideally, the knowledge of others. But there’s an even simpler definition: any problem that brings joy in its solving is worth your time.
You say you are a nameless man. You are not to your wife and to your child. You will not long remain so to your immediate colleagues if you can answer their simple questions when they come into your office. You are not nameless to me. Do not remain nameless to yourself – it is too sad a way to be. Know your place in the world and evaluate yourself fairly, not in terms of your naïve ideals of your own youth, nor in terms of what you erroneously imagine your teacher’s ideals are.