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The reality is that having a great mentor is a privilege, not a given. I don't think anyone is arguing that having a genius and brilliant teacher wouldn't help, rather that it is possible to reach an "advanced" (grad/undergrad level) understanding of mathematics without the luxury of having someone who is far more knowledgeable to turn to for help.

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Precisely. GP here. I didn't argue against having a great mentor. If you go to a great university you clearly have an advantage. I think it's perfectly doable to teach yourself mathematics if you study intense enough eith correct tools.

I think a big part of "mathematical maturity" is knowing how important it is to have someone else look over your proofs.

Of course you can learn a ton on your own by reading and working exercises and doing research, but there is no substitute for collaboration.

Mathematics is inherently a social activity, even if the bulk of it can (counter-intuitively) be done in relative solitude.

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