The most interesting point in the Gribbins' excellent biography of Feynman is the value of "irresponsibly" ignoring existing research and working everything out for yourself from first principles.
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At least in my own case, understanding mathematics doesn't come from reading or even listening. It comes from rethinking what I see or hear. I must redo the mathematics in the context of my particular background. ~ Stephen Smale
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It is always the case, with mathematics, that a little direct experience of thinking things over on your own can provide a much deeper understanding than merely reading about them. ~ Sir Roger Penrose
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