Very proud that an OpenAI model disproved Erdős’s longstanding unit distance conjecture, with an elegant and intricate proof that brings sophisticated ideas from algebraic number theory to bear on geometry.
For whatever reason, mathematics has been the field most amenable to research breakthroughs with AI. I consider it lucky that it was mathematics after all - a field where experts have been willing to engage deeply with us, and with proofs generated by our models. I'm grateful for that, and don't take it for granted. Math is an artistic endeavor, and perhaps for artists, it is precisely their appreciation for art that saves them from the possibly grotesque feeling of a machine producing it.
Our goal is not to replace humans. We aim to chart a path forward where humans continue to have a significant role to play, even as we build exceptionally powerful AI. I am excited to use math as a domain to explore these paths, and
@SebastienBubeck,
@merettm, and I are excited to engage with the broader mathematical community to chart them together. Please reach out if you are interested!
I'm optimistic this will help us navigate how AI impacts society in domains like coding and general co-working.
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.