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Pictures aid understanding. But in the vast majority of sophisticated mathematics (that I've seen), pictures would be unable to accurately represent the real assertions.

For instance, if I want to talk about 26-dimensional discontinuous space (the space of the basic alphabet), there is no visualization that can help you grasp the totality of the matter.

I believe there are a few interpretations of what math actually is (formal reasoning, interpretation, etc), philosophy of math 'junk'. I'll leave that to a more-beered time. :-)




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