Hard to describe because it's often _not_ especially visual (more spatial / kinesthetic, a kind of felt sense). And I rarely think much seriously about mathematics these days.
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Thanks! “Slightly colored but not really visual” is really interesting, and I think I know what you mean.
It’s probably been decades longer since I’ve thought seriously about mathematics than since you have! I’m running off of distant memories of experience here
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It's just an evoked sense. For instance, when working on this paper (arxiv.org/pdf/quant-ph/0 ) I thought pretty hard for a while about some of the central objects. Enough that much of the core work was done on long walks.
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All hard core thinking is done on long walks [why?]
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For people who seem to have a kinesthetic aspect to their thinking, I wonder if they are actually literally thinking more.
I sometimes wonder if working while stationary, in a chair, is a way of artificially reducing the quality of your thinking.
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There are also types of thinking, including mathematical thinking, where being absolutely motionless on your back (or in an armchair) with your eyes closed is absolutely necessary (I find, and I’m not the only one)
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oh i have also found i needed to be on my back but only very occasionally
there is also this from terence tao:
mathoverflow.net/a/38882/290
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Yes, there are exactly five things that ever been written about how to do mathematics, and that is one of them!
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it is a shockingly small sample of writing huh
this plus some stuff bill thurston wrote plus... proofs and refutations? how to prove it? i'm at 4
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Uh… I kind of thought there was one more, but I may have been thinking of stuff Rota said in person
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rota probably wrote some of it down in discrete thoughts and indiscrete thoughts? although i haven't read either in ages. genuinely sad he died before i had a chance to meet him at MIT, i loved his writing
I’m embarrassed to say I have not actually read Indiscrete Thoughts, and didn’t even know Discrete Thoughts existed! Thank you, added to my queue :)
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have fun! would love to see a thread of quotes and highlights
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