4th: math is a "highly reactive" species of idea, so you get more returns starting earlier. like, you learn about multiplication and division, and meditate on intuitions about flows; then when you play with a hose and put your thumb over the output --> fast spurt --> recognition.
the good kind is where you explain all the data better / unify all the skills more elegantly. real math is about doing that iteratively, each time re-including your new understanding into the pool of data to be explained / understood.
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maybe at the most basic it's just: learn to stick with looking at something that you have no idea how to go about understanding, until your brain invents new understandamathings. difficult but trainable skill, better feedback in math.
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though, the better feedback in math is also easily goodhartable. (i personally do not understand number theory or the appeal of number theory, and always have a slight sneaking suspicion that a lot of it is sort of just noticing that simple questions can be super hard to answer
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