> After casually reading his notes, I think that he is saying this. The > axioms of modern set theory are too burdensome for actual > mathematicians, who in practice take a somewhat Platonic view of their > subject. But he is unsatisfied with the pragmatic Platonist approach > that we take, particular in the manner in which mathematics is taught at > pre-college levels.
How do you get from there to his claim that you can't prove the fundamental theorem of arithmetic?
He thinks we need to roll up our sleeves and > rethink foundations so that we get something that really is usuable, so > that we can finally truly rid ourselves of Platonism, superstition, > instinct, gut reaction, religion, etc, etc.
It seems to me what he's saying is simply incoherent. He likes Lie groups, so it's OK to talk about them, so long as you cross your fingers and say you are really talking about constructable numbers. But integers, which are about as constructable as it gets, he is willing to blow off, apparently merely out of disinterest in number theory as opposed to Lie groups.
> But on the whole, even if his tone was not exactly politic, I liked a > lot of what he said. But I don't think it is going to change the world.
"Let's make things way harder to prove for no reason, and do it in an incoherent way" is a tough sell.