https://x.com/OpenAI/status/2057176201782075690
Today, we share a breakthrough on the planar unit distance problem, a famous open question first posed by Paul Erdős in 1946.
For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids.
An OpenAI model has now disproved that belief, discovering an entirely new family of constructions that performs better.
This marks the first time AI has autonomously solved a prominent open problem central to a field of mathematics.
Was that a problem?
So how come the AI instance didn’t propose the problem and then the solution?
The headline is false, and the description of what the AI did, if read carefully, bears this out. The AI did not “solve” the problem, it merely found a better class of solutions, better than the existing human-generated solutions.
The problem is not definitively solved until a human or AI can demonstrate that their new class of solutions is indeed The Best Possible. In other words a “Proof” in the mathematical sense.
Having a solution to a problem (which humans already had), and then finding a better solution to that problem (which the AI did), does not preclude finding yet another solution that’s even better.
So the headline is clickbait. That said, it’s an interesting article and kudos to OpenAI for finding the new solution.
The real question is not “did it find the ‘solution’, rather, did it find “one of the solutions”.