[codeflo]

> apparently

When someone takes the time to explain undergrad-level concepts in a comment, responding with "are you an expert?" is a level of skepticism that's bordering on hostile. The person you're responding to is correct, it's rare that the theorem statement itself is particularly hard to formalize. Whatever you read likely refers to the difficulty of formalizing a proof.

[freehorse]

To be fair, the comment did not explain any concept that I can see, or why this statement is simple. It gave the statement and said it was simple to formalise. It does seem simple enough to me (basic arithmetic statement with a few variables and a bunch of quantifiers) but if somebody has no expertise/intuition, I think it is a fair question, without any hostile intent assumed.

[IsTom]

> it's rare that the theorem statement itself is particularly hard to formalize

That's very dependent on the problem area. For example there's a gap between high school explanation of central limit theorem and actual formalization of it. And when dealing with turing machines sometimes you'll say that something grows e.g. Omega(n), but what happens is that there's some subsequence of inputs for which it does. Generally for complexity theory plain-language explanations can be very vague, because of how insensitive the theory is to small changes and you need to operate on a higher level of abstraction to have a chance to explain a proof in reasonable time.

[zozbot234]

Yes, if the theorem statement itself is "hard to formalize" even given our current tools, formal foundations etc. for this task, this suggests that the underlying math itself is still half-baked in some sense, and could be improved to better capture the concepts we're interested in. Much of analysis-heavy math is in that boat at present, compared to algebra.

[kelipso]

Lol it’s weird seeing high school redditors saying gatekeeping and are you an expert in the same thread as university professors, all talking about the same topic. But I guess that’s HN for you.

[phyzome]

I think it was a fine question to ask in the context of a discussion of epistemology.