Now we know that either P=NP is proveable from the axioms of set theory, or its converse is

This isn't to be said casually; it would be a huge result if you could prove it, and very different from the case of neither being provable. Most things that are true about the natural numbers are not provable in any given set of axioms.

I mention this because I read that and woke up and said "What? Really?" and then read the following parenthetical and was disappointed. I suggest editing the text. If we don't know anything in particular about the relation of P=NP to set theory, it shouldn't be said.