Last week, OpenAI published a press release titled,

An OpenA. model has disproved a central conjecture in discrete geometry.

They were talking specifically about the planar unit distance problem,

which was first posed by Paul Erdos in 1946.

Now, this is actually a pretty simple problem to state.

It basically says,

what is the maximum number of pairs of points in a set of endpoints in a flat plane that can be exactly one unit of distance apart?

Now, back in the 1940s, Erdos proposed an answer to this question.

He couldn't prove it, but he thought he knew what the answer was.

Last week,

OpenAI essentially announced that they had used an LLM to prove that Erdos's proposed answer was, in fact, incorrect. The OpenAI press release was accompanied by a video that featured dramatic

music and a group of researchers writing earnestly on a comically small

blackboard as they explained why this was a big deal. Here, let's play a clip of that video.

This is the first mathematical breakthrough due to an AI. It's been described as the most well-known problem in combinatorial geometry.

So for a whole subfield of mathematics, it's like maybe the best known problem there is.

The mainstream press soon picked up on this story with enthusiasm.

Here's the new scientist headline.

Mathematicians stunned by AI's biggest breakthrough in

mathematics. People on X predictably went even more wild. Peter Diamindis tweeted the following.

An open AI model just proved an 80-year-old math conjecture from Paul Erdos, one of the most prolific

mathematicians in history. We're going to

solve everything. All right. So what's actually going on here? Did AI just reach genius level?

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