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What important discoveries have you made using your supposedly "more rigorous" mathematics?
Loaded question
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Loaded question
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.
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
> One can roughly divide mathematical education into three stages: Similarly with programming. 1. Write programs that you think are cool 2. Learn about data structures and algorithms and complexity and software organization. 3. Write programs that you think are cool. But since you know more, you can write more cool programs. If things are working as they should, the end stage of mathematics and programming should be…
1. Hack programmatic-functionality in a first language
2. Master the intricacies of a first language, understanding all programmatic concepts through the lens of that languages specific implementation-details. Pedantically argue with those familiar with different language implementations, due to a kind of implementation-plurality/ essential-form blindness
3. Learn additional languages, and 'see past' specific implementation details and pitfalls of each; develop a less biased understanding of the essence of any task at hand
Earlier quoted context omitted.
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.
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 exam…
proofs in FOL can be checked by a computer without any need for type theory - just look at metamath.