OpenAI made history today.

An internal reasoning model autonomously disproved a famous conjecture in mathematics that stood for nearly 80 years.

The problem： In 1946， Paul Erdős asked how many pairs of points can be exactly 1 unit apart if you place n points on a flat surface. The best known answer came from square grid constructions， and Erdős himself conjectured you can't do meaningfully better. Mathematicians believed this for decades.

The AI proved him wrong. It found entirely new point configurations that beat the square grid by a fixed polynomial factor， not a marginal improvement， a real mathematical gap.

The proof uses methods from algebraic number theory， a completely different branch of math， Class field towers， Golod-Shafarevich theory， tools nobody expected to be relevant to a geometry problem about distances in the plane （reminds me of move 37， AlphaGo tbh）.

Fields Medalist Tim Gowers calls it "a milestone in AI mathematics." The proof was verified by leading external mathematicians.

According to OpenAI， this is the first time AI has independently solved a prominent open research problem in mathematics！

Caveat： Obviously OpenAI chose which problems to test the model on. So "autonomous" means the model generated the idea and wrote the proof， not that it wandered into the problem on its own.

But if reasoning models can reliably make cross-domain connections like this， finding paths that experts didn't prioritize， this changes research far beyond math. Biology， physics， materials science， medicine.

This isn't AI reproducing human knowledge anymore. This is AI producing new knowledge. That's a qualitative shift.