How To Understand Things

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The smartest person I’ve ever known had a habit that, as a teenager, I found striking...

I. The smartest person I’ve ever known had a habit that, as a teenager, I found striking. After he’d prove a theorem, or solve a problem, he’d go back and continue thinking about the problem and try to figure out different proofs of the same thing. Sometimes he’d spend hours on a problem he’d already solved. I had the opposite tendency: as soon as I’d reached the end of the proof, I’d stop since I’d “gotten the answer”. Afterwards, he’d come out with three or four proofs of the same thing, plus some explanation of why each proof is connected somehow. In this way, he got a much deeper…

How To Understand Things

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