Descartes Before the Horse
"I do not so much ask clever questions as I do ask so many questions that some are bound to be clever. I prefer this over the former."
"It is a deeper subject than I appreciated and, I begin to suspect, deeper than anyone yet appreciates. To see it whole is certainly a daunting, for the moment even impossible, task." (Robert Langlands, writing about the theory of automorphic forms.)
"Think, dig up what is unknown as if you are tired of answers and cannot rest without questions. Then attack these questions as if you cannot rest without answers."
"I want to be giving a lecture, finishing up an important proof on the blackboard, when someone in the audience shouts out, 'What about the general case?' I'll turn to the audience and smile, 'I'll leave that to the next generation,' and then I'll keel over." (Paul Erdős.)
"Better known for other work." (Lara Pudwell, after referencing a result due to Ted Kaczynski.)
"Understanding what a theorem means is a prerequisite to understanding its proof." (Contemporary Abstract Algebra, pp. 82, Theorem 4.3.)
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