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The mathematician does not study pure mathematics because it is useful; he studies it because he delights in it and he delights in it because it is beautiful.
Well, the first rule is that you can’t really know anything if you just remember isolated facts and try and bang ’em back. If the facts don’t hang together on a latticework of theory, you don’t have them in a usable form.
Perhaps unhappiness can stem from having only one perspective to play with.