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I remember reading something like this from Einstein as a 14- or 15 year old, & thinking "wow, maybe math isn't for me". By 24... it seemed totally obvious that of course this is how things work when you're seriously into something.
The strange thing is: this isn't really discussed publicly very often. Yet when I've talked to people who do creative work, especially with mathematics, a considerable fraction seem to have similarly unusual experiences, though the sensory modality may be different.
You studied under Rota? That's amazing! I came across a bunch of his writing as a freshman in college during the phase where I was heavily into combinatorics and really loved it.
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