A new & peculiar essay, on a (very!) unusual approach I've been using to deepen my understanding of mathematics: http://cognitivemedium.com/srs-mathematics
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It's based on a whole tonne of heuristics (many described in the essay) for really pulling the proof of a theorem apart, atomizing it into a million simple observations, a sort of proof network.
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The end result (ideally) is a state of what I think of as "being inside a piece of mathematics", a sense of being able to work directly with the objects & change my understanding of them in a way that doesn't directly use conventional symbolic or verbal or visual representationspic.twitter.com/Jmyo3bi6hA
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(Accidentally uploaded without a spellcheck, now fixed!)
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This kind of reminds me of how I’ve heard
@JohnMayer describe playing scales/ songs.Thanks. Twitter will use this to make your timeline better. UndoUndo
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I remember sitting in a cafe looking at matrix correlation / cross correlation *forever*. Endlessly writing it in different ways. Wondering why something wasn't intuitive. Definitely felt like I was getting a deeper understanding, which led to breakthrough ideas for my ms thesis.
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If I read this correctly it is similar to my own programming and data modelling experiences, when the domain is new and half-imagined.
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This notion of being inside a piece of mathematics reminds me a lot of this wonderful MathOverflow thread:https://mathoverflow.net/questions/38639/thinking-and-explaining …
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How people think about math, and how that relationship changes as they become more expert, is super fascinating to me
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