In the most independent-minded people, the desire not to be told what to think is a positive force. It's not mere skepticism, but an active delight in ideas that subvert the conventional wisdom, the more counterintuitive the better.

The three components of independent-mindedness work in concert: fastidiousness about truth and resistance to being told what to think leave space in your brain, and curiosity finds new ideas to fill it.

In fact, most of these comrades who I gauged to be more brilliant than I have gone on to become distinguished mathematicians. Still, from the perspective of 30 or 35 years, I can state that their imprint upon the mathematics of our time has not been very profound. They’ve all done things, often beautiful things, in a context that was already set ou

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