The joy of doing any scientific research is in the quest for new ideas and deeper understanding. Finding something new yourself is exhilarating. Second to that, but still very important, is the pleasure of explaining it to someone else who cares.
In the pursuit of the unknown, you are never sure what you need to know. You can never know too much. Yet when approaching a new problem, you always know both too much (about the wrong things) and too little (about the question at hand). A big step towards the solution is figuring out exactly what it is that you really need to know.
-- Kenneth R. Davidson
What I cannot create I do not understand.
-- Richard Feymann
A good stock of examples, as large as possible, is indispensable for a thorough understanding of any concept, and when I want to learn something new, I make it my first job to build one.
What does it take to be [a mathematician]? I think I know the answer: you have to be born right, you must continually strive to become perfect, you must love mathematics more than anything else, you must work at it hard and without stop, and you must never give up.
– Paul Halmos
If you want to master something you must really care about it, and if you want to excel in a certain field you must be obsessed with it.