upvote
This is tricky, because, in fact, hard math having an intelligence floor is one of the nastier realities of the human condition. Anyone who is even quite intelligent but has really pursued the rigorous stuff, unless they are in fact a prodigy, eventually realizes they have an abstraction ceiling (and this term is a common one thrown around in people studying mathematics, because intelligence denial is so obviously false when you do hit your abstraction ceiling).

Most people are correct that they lack the intelligence / mind for a lot of hard math (even epsilon-delta proofs are enough to eliminate the majority of the population, no matter how good a teacher you are, and these are just basic undergrad calc).

And yeah, sure, people have different kinds of intelligence and such, but there is still a g-factor, and people of low intelligence almost universally can't do hard math, whereas most people who can do e.g. advanced undergrad math can generally do almost all other advanced undergrad fields reasonably well. The world isn't fair here.

reply
> Anyone who is even quite intelligent but has really pursued the rigorous stuff, unless they are in fact a prodigy, eventually realizes they have an abstraction ceiling

Eh. I'm a math PhD who fled academia because it was too much for me. But I have never encountered this term "abstraction ceiling" nor did I succumb to it. I simply ran out of motivation to pursue higher math, especially when following through on learning and research became more and more labor.

> even epsilon-delta proofs are enough to eliminate the majority of the population, no matter how good a teacher you are

Disagree. It's a notoriously hard subject to teach, and with all the demands placed on e-d in so little time in your average curriculum, it doesn't require appeals to IQ to explain its infamy. With enough motivation and practice, the quantifier alternation is comprehensible to any sound mind. What your average mind (and student) lacks is exposure to formalism, abstraction, and how these things tie in with what they are familiar with, which is symbolic manipulation. With the exception of geometric proofs (another educational bugbear), they have little context for what formalism is or why it matters.

reply
I would even go as far as saying that mental conditioning and training is also required, on top of mental capabilities.
reply