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Sadly Calc iii is not “real” math, just an applied version of what newton created 300 years ago. Real math starts at analysis and abstract algebra. It is extremely inefficient to learn this kind of math completely by yourself since there is a specific ‘math intuition’ that is hard to gain without a great teacher.

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That seems a little harsh as a reply to the previous comment - calc 3 is math, but sure, upper division or graduate math also requires the ability to prove things, which is why people who did will in calc-3 might not necessarily do well in more advanced courses until they learn the additional skills. But it's not like the ability to apply theorems and calculate accurately is orthogonal to the ability to do proofs - the attention to detail and ability to keep track of the steps is certainly similar, I would argue.

You dont need to be a graduate in math to prove things. Check out the IMO and tell me it isn't real math, and it's only highschool level.

I'd guess Khan Academy was among the first to provide such teaching. Is it "self-taught", I don't know (I think it qualifies, though). It can be done.

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