soVeryTired

Does Iain M Banks count as pop culture?

*her work

Far more than 500 person-years have already gone into Navier-Stokes.

AI comment

Or maybe the PhD impersonator discovered a soundness bug in a component of Lean and was able to exploit it.

With no humans able to understand the proofs the impersonator has produced, there's no way of knowing.

Not sure I agree - they dropped hundreds of papers, most of which were so badly written that they were incomprehensible. If it wasn’t for the lean certificates on 30% of them, the mathematical community would have told them to go and whistle.

I think the consensus here is that most of the papers are effectively correct. But it would take years of study just to understand most of the problem statement - so we have to wait for the mathematical community to digest the borderline-nonsense that OpenAI spewed out.

But up until now, the mathematics community has valued the "prove" part much more highly than the "deliver an insight" part. Mostly because with a little work they went hand in hand.

And going from zero proofs to one proof (even a sloppy one) is a big deal regardless of whether it was written by AI or a human.

Probably true for the dedicated problem solvers (of which Tao is one IMO). But I doubt there's ever been a better time to be a theory builder (more like Peter Scholze, or Grothendieck).

Some up with an idea and leave the system to check it 15 different ways, and see whether you can simplify an existing body of theory. It'd be like having an army of lightning-fast grad students.

What's an example of your belief system conflicting with a motivated example? I'd love to understand that a bit more.

Wintermute and neuromancer!

Was it a marketing win though? My takeaway is: if you're doing groundbreaking work with openAI's models and they find out, at best they'll outspend you and scoop you. At worst they'll steal your chat history.

Yeah - I think he’s worried that we have a tool that’s almost an oracle that can just get straight to the heart of a given problem.

The problems aren’t always that interesting in their own right. But the quest to solve them is often what drives the invention of new techniques.

We ultimately got the Langlands program and a large amount of algebraic number theory out of attempts to solve fermat’s last theorem. A “clever” approach using techniques from the 1800s wouldn’t have been anywhere near as fruitful for mathematics as a discipline.

Out of interest, would you call BERT an LLM? It’s pre trained but not particularly large.

It’s neither large nor language-based. ARC-AGI-1 is grid-based and nonverbal.

Use of a transformer is not necessary or sufficient to qualify as an LLM.

Undetectable by a human reader. Come on, give the post a charitable reading.