An 80 Year Old Math Problem Was Just Solved By The Usual Suspect

OpenAI says an internal general-purpose reasoning model has disproved a famous math problem. No, it's not ChatGPT, they haven't released this model publicly.

What's the Problem?

In 1946, Paul Erdős (mathematician) asked the question that started this problem: if you place points on a flat plane, what is the maximum number of pairs that can be exactly 1 unit apart? Think of it like arranging points so that as many connections as possible share the same fixed distance. The unit distance can be any fixed value (1cm, 5 inches, etc.).

A square grid gives you a lot, but Erdős felt you could do better. So he put a cash prize on it. $500 if you could prove him wrong. That's around $8,500 in today's money.

OpenAI Comes In

Not exactly for the $500, but for eternal bragging rights. And redemption.

You see, OpenAI had pulled a stunt like this before. But it turned out that the model was using existing answers in its training data. That incident led to a public apology and an executive leaving the company.

Thankfully, this model said no peeping. It showed that there exists an infinite number of point sets where you can construct more unit-distance pairs than the square grid allows. The model didn't just search for an existing solution. It produced a totally new construction with tools from algebraic number theory. According to Google, that's a branch of math that's unrelated to counting dots on a page.

What's The Fuss About?

This time, OpenAI brought in outside mathematicians to verify the work. They co-signed a paper endorsing the result, so their necks are on the line. This is one of the first publicly verified cases of an AI system independently solving a famous open math problem without human hand-holding.

OpenAI says this is a sign that AI is moving from "helpful calculator" to "research partner". The same abilities could eventually help with problems in biology, physics, science as a whole.

The model hasn't been released to the public.