Cal Newport

Lots of different, like a vast knowledge of many different existing results and techniques that can be trained on it.

Many more than most mathematicians can keep in their head.

So it's willing to like systematically explore answers, mix and match different approaches and see what works.

You can also, a lot of these systems will use a formal proof verifier so it can try a bunch of stuff and see what works.

So it's been really big for mathematics.

So this result, what Thomas Bloom is saying is this result is not some brand new capability that we didn't know that AI had.

He's saying it's in the trajectory of those existing type of results we've been doing for the last years.

It falls in that sweet spot where AI-enabled math tools really work well.

Now, I want to be fair.

There's two things about OpenAI's result that do separate it from this sort of existing recent explosion in AI, augmented computers-aided math work.

Number one, this was done, at least they claim, just purely with an LLM prompt, right?

The tools that mathematicians are using tend to be using modular architectures with many different types of models hooked together.

You'll have an LLM

You'll have a formal proof verifier, usually using a formal verification language like Lean, which LLMs can speak very well.

You'll have some sort of complicated control logic.

You'll have specialized training of the LLMs on very specific types of math techniques that are relevant to the fields you're looking at.

This was not that.

There was no elaborate scaffolding.

It was actually just a prompt to a reasoning machine that just talked for like 150 pages, and in there they found an answer.

So that is different about this result.