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A long time ago an older and well-known number theorist made some disparaging remarks about Paul Erdős’s work. You admire Erdős’s contributions to mathematics as much as I do, and I felt annoyed when the older mathematician flatly and definitively stated that all of Erdős’s work could be “reduced” to a few tricks which Erdős repeatedly relied on in his proofs.
Tags » David Hilbert
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In dealing with mathematical problems, specialization plays, as I believe, a still more important part than generalization. Perhaps in most cases where we unsuccessfully seek the answer to a question, the cause of the failure lies in the fact that problems simpler and easier than the one in hand have been either incompletely solved, or not solved at all.