Ideal Undergraduate Sequence Main question:
I looked above and what I'm interpreting out of it is that one should be able to do proofs after studying some intro to proofs class, calculus multivariable+vector calculus, and differential equations linear algebra.
Is it possible that one won't be able to do proofs after finishing doing calc 3/vector calc and differential equations?
I really want to be a pure mathematician and not some high school teacher in the future. I suck at other subjects. math's all I got left, i.e. I can't write, I can't code, manual labor or mcdonald's job sounds possible future. I'm taking calculus 3 and differential equations right now and I'm wondering whether there's no hope in me becoming a mathematician if I fail to be able to do proofs like the ones in algebra or analysis like weistrass M-test and something banach after finishing calculus 3 and differential equations.
I cannot prove theorems at this point independently and can't study some class like real analysis or number theory right now.
Optional questions: (ignore if you're busy) Is what the link above says that if you can't do proofs after calc 3 and differential equations, you'll never be a mathematician?
Does finishing taking calculus 3/vector calculus and differential equations transform your mind to being able to do proofs? I mean why did we suggest (in the hyperlink above) that people should take multivariable calculus and differential equations before a serious proof class? Are calc 3/ differential equations special?
Are math teachers in high school the people who took calculus 3 and differential equations but just didn't have the intelligence or weren't transformed from such an experience to be able study proof writing?