> Wow, I was already impressed with the new comment feature on erdosproblems.com and how it's already been used to solve some of the problems. Excited to see if AI can make a meaningful contribution here.
Since then, there has been some discussion of GPTPro finding a bunch of references, thus enabling many of the problem statuses to be changed from "open" to "solved". But it seems that LLMs couldn't find the right reference for this problem.
But there was a different meaningful contribution from AI here instead.
> you're assuming a lot. Including a notion of mathematical existence which bears little relation to any concept that most lay people have of what mathematical existence might mean.
John Horton Conway:
> It's a funny thing that happens with mathematicians. What's the ontology of mathematical things? How do they exist? In what sense do they exist? There's no doubt that they do exist but you can't poke and prod them except by thinking about them. It's quite astonishing and I still don't understand it, having been a mathematician all my life. How can things be there without actually being there? There's no doubt that 2 is there or 3 or the square root of omega. They're very real things. I still don't know the sense in which mathematical objects exist, but they do. Of course, it's hard to say in what sense a cat is out there, too, but we know it is, very definitely. Cats have a stubborn reality but maybe numbers are stubborner still. You can't push a cat in a direction it doesn't want to go. You can't do it with a number either.
> So if my theorem is correct, and Quake gutted id Software, was it worth it? Well I'd say yes absolutely.
https://x.com/SandyofCthulhu/status/2069592330152362034