RE: Mathematician Claims Proof of Connection between Prime Numbers
September 26, 2012 at 3:18 am
(This post was last modified: September 26, 2012 at 5:01 am by Categories+Sheaves.)
From another forum where I was kicking this around,
I mean, you can have different models for theories (e.g. Skolem's paradox involves the existence of countable models of ZFC). The founding gesture of category theory is to assume we're working in some fixed 'universe', (a proper class of stuff) and discuss the morphisms in, say, the category of groups (plus functors between categories and all that). Mochizuki--for some reason--is able to get some mileage out of discussing functoresque mappings (he calls them 'muations') between different universes/models; hence the name "inter-universal teichmuller theory". Weird and radically new stuff. I do hope everything checks out... (iirc it was around this time last year that Ed Nelson claimed to have a proof that the Peano Axioms were inconsistent, and that got shot down within a week).
fishfry Wrote:By the way this guy Mochizuki went to Princeton at age 16 and got his Ph.D under one of the world's most eminent number theorists at age 22. He's the real deal.There's a (closed) MathOverflow topic about him, and some respectable math blogs discussing it (Terence Tao jumped in their comments section, so they have to know what they're talking about).
I mean, you can have different models for theories (e.g. Skolem's paradox involves the existence of countable models of ZFC). The founding gesture of category theory is to assume we're working in some fixed 'universe', (a proper class of stuff) and discuss the morphisms in, say, the category of groups (plus functors between categories and all that). Mochizuki--for some reason--is able to get some mileage out of discussing functoresque mappings (he calls them 'muations') between different universes/models; hence the name "inter-universal teichmuller theory". Weird and radically new stuff. I do hope everything checks out... (iirc it was around this time last year that Ed Nelson claimed to have a proof that the Peano Axioms were inconsistent, and that got shot down within a week).
