Cal Newport

I want to provide some context about what is and is not actually happening in this particular example.

Now, I want to start here by reading some comments from the mathematician Thomas Bloom, who is a world's expert on Erdos's open problems.

Now, OpenAI released a companion commentary paper

that collected comments from eminent mathematicians on this result, and Thomas Bloom was one of the mathematicians they asked for his comment.

So I want to read to you from Thomas Bloom's comments about this new result published in the commentary paper that OpenAI put out.

So Bloom starts by saying, I mean, this quote, he says a lot of things, but the quote I'm going to read here starts with Thomas Bloom saying,

If the result of this paper was a proof of the unit distance problem, that would be truly incredible.

So just to step back here, what he was saying is that if the LLM had found a way to prove that Erdos' conjecture was correct, that's a much harder thing than proving a counterexample, that really would have been incredible.

He goes on to say, While I was still very surprised to hear of this result, this was dampened slightly when I learned it was a construction of a counterexample, and still further when I learned that the nature of the construction being...

with the benefit of hindsight, a natural, albeit highly non-trivial generalization of the original lattice-based construction of Eratosius.

All right, so again, let me translate the mass speak here.

He's like, okay,

When I first heard this problem was solved, I was like, oh, my God, that's incredible.

And then when he learned it, well, it wasn't solved.

There was a counterexample to the existing proposed solution.

His enthusiasm was dampened.

And then when he saw that the actual counterexample construction wasn't some new original leap of mathematics.

It actually was just taking the original construction that Erdos had proposed that he thought matched his answer and then just –

I don't know how to say that.

I'm going to say this wrong.