>>12050797>Also what sort of novel logical structure are physicists using were they claim their theory predicts certain shit even though they can't actually prove it? What the fuck does it mean to convince a physicist vs convincing a mathematician?Well standard renormalisation group methods are typically what we might reach for to convince ourselves physically that the mass gap is satisfactorily solved within QFT. If you're a string theorist, you would probably also show that it's implied through the AdS/CFT correspondence.
It's just that we don't bother with axiomatic QFT, because we need to be ready to throw away any one of these "axioms" at a moment's notice, so there's really no point. And because we have no axioms, there's no possibility of mathematical "proof". Having said that, it does accurately represent reality, so we content ourselves with that.
As for the rest, with Newton, infinitesimals, etc. No I don't think this is equivalent, and I don't really care very much to be honest. Classical mechanics is a completely different being since we can observe the macroscopic world and so axiomatising that part of physics isn't really that hard. With QFT, there's nothing. There's even fringe debate over whether locality is necessary. So of course there are no foundations we can intuit, since we aren't capable of divining the fundamental axioms of the universe.
Secondly, as for "some new maths" to describe non-perturbational methods - I was referring to how many nonlinear models can be treated exactly as of the mid-20th century, and how many were shown to have natural connections to algebraic geometry, etc. and can be exactly constructed in that way. But none of that requires much mathematical rigour, and the solution of the Yang-Mills problem isn't likely to introduce many techniques we don't know already, and is more likely to just put them on a firmer foundation for the mathematicians who worry about such things. Almost no physics is really changed by this.
