It took me a while to really admit to myself that just reading a book is not learning but entertainment.
This should be tattooed onto every book. Related: My math education completely changed when I realized theorems should be treated as problems - "prove this" - and the printed proof should be treated as hints to be consulted in a pinch.
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I wish someone would have communicated this to me years ago.
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Ramanujans first access to modern math was a Corr’s book collection of results - just lists of lists of results without proofs. He asked wow is that so and wrote proofs to convince. In that process he created new results and proofs as if a ‘sow secretes urine’ as mozart put it..
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.. or cow mother secretes milk as ramanujan might have put it. Bottom line: the only way to learn is to rediscover things yourself.
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I wish I'd realized this earlier. It was always clear that some of the best books are done, not read (my favorite example is Little Schemer) but less clear that any book can be done, with the right mindset.
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