[JoeyBananas]

My claim is that mathematics as practiced by mathematicians is not as rigorous as they think it is, and infact they're not even aware of the advances in rigorous mathematics that they're not using. Even though those advances are super important.

[Tainnor]

What important discoveries have you made using your supposedly "more rigorous" mathematics?

[JoeyBananas]

Loaded question

[Tainnor]

Well, you've been claiming that these advances are "super important" and that set theory is not rigorous, but you have provided no evidence for either claim.

[JoeyBananas]

I never said "set theory is not rigorous." Euclid wrote Elements without knowing anything about set theory. Math was done for thousands of years without modern set theory or any modern notion of logical foundations. Set theory is more rigorous than what came before it.

It's not as rigorous as type theory (yes, this is an umbrella term) because type theory can be verified by a computer. Homotopy type theory is an example of the type of math that set theory can't handle

There are so many layers of ignorance to unpack here and I don't care to be your unpaid tutor

[Tainnor]

> because type theory can be verified by a computer

proofs in FOL can be checked by a computer without any need for type theory - just look at metamath.