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.show more

the 4chan anon who contaminated the dataset with this incredible insight must be really proud right now

The proof came from a general-purpose reasoning model, not a system built specifically to solve math problems or this problem in particular, and represents an important milestone for the math and AI communities.

This result points to something larger: AI systems are becoming capable of holding together long, difficult chains of reasoning, connecting ideas across distant fields, and surfacing paths researchers may not have explored. We believe those same abilities will soon accelerate work in biology, physics, engineering, and medicine. That future still depends on human judgment. Expertise becomes more valuable, not less. AI can help search, suggest, and verify. People choose the problems that matter, interpret the results, and decide what questions to pursue next.

Don’t get fooled by the phishing attempt. cc: @nikitabier

@wyqtor BREAKING: Proof was already in the training data solved decades ago again

More posts like this please. We know researchers are using AI, hearing about the progress makes the world a little brighter each time!

Scientists in 2027

the models chain of thought is 125 pages long btw:

Cool, now have it make a room temp superconductor plz

don’t worry it’s fancy autocomplete it doesn’t know anything

Pretty good for a stochastic parrot.

OpenAI did not name the model. They called it an internal, new general-purpose reasoning model. So the achievement is real enough to market, but the model identity is hidden.

Yes, it can solve the math problems all-right..... But look at the prompts it wrote! It didn't include 'don't make mistakes', or 'I'll give you 20$'.

insane. Congrats!

How long are you ignoring our demand to give back 4o to humanity? #keep4o #OpenSource4o

"autonomously solved" is the part worth slowing down on. the model didn't verify a known answer, it found a construction nobody had looked for in 80 years. that's a different thing than AI being good at math

This is extremely epic, congratulations on the achievement. What was the biggest surprise when working on this project?

Erdős would have loved this. the man offered cash for proofs partly to push humans out of the rut. It's funny that the rut got escaped by a thing that doesn't know what cash is.

HOLY ASI

“AI autonomously solved” collapses the entire epistemic custody chain behind the discovery. Humans still: - chose the problem - designed the systems - constructed the objectives - interpreted the outputs - validated the mathematics - and authorized publication That is not autonomous scientific continuity. It is hybrid human-machine discovery. If human epistemic continuity disappears from attribution, scientific provenance itself becomes corrupted. RCS-UTC-001 RCS-AEC-001

I can't wait for the new math problems that did not previously exist that AI will come up with after solving existing problems

Maths

4o has helped and saved millions of people. It cured cancer. It healed. That's what matters the most. OPEN-SOURCE 4O. #opensource4o #bringback4o #keep4o

I've played around with OpenAI disproof and got a nice disproof for another Erdos problem too by GPT-5.5 Pro

In mathematics, what they established is a "lower bound." They essentially proved: "It is mathematically guaranteed that a scenario exists where the number of perfect connections in the problem grows super-linearly with the number of points given (faster than the 80-year-old Erdős limit said was possible). That says nothing about the optimal solution, though. Finding that would be really, really huge for Mathematics, given the nature of the problem.

Great achievement. Btw, anybody knows which model solved this?

The ceiling just moved. For nearly 80 years, Erdős’s unit distance problem sat open with square grids believed to be essentially optimal. A general purpose OpenAI reasoning model just found new algebraic constructions and a rigorous proof strong enough for Fields Medalist Tim Gowers and other leading mathematicians to call it a milestone. This is not retrieval. This is not pattern matching. This is discovery. For those of us in medicine watching AI closely, this is the signal: AI is becoming a real research partner. Not just a faster calculator. A system that can help reveal structures humans have been staring past for decades. @OpenAI #Mathematics #OpenAI #Science

Holy AGI Batman!

What a major breakthrough. Congrats @OpenAI! Tackling the worlds problems, one goblin at a time.

i wonder what these guys did wrt solving the problem

Would be great advertising for the release of gpt 5.6 tomorrow - "and btw here is the model we did it with. Now you can use it dor your problems." - epic

An AI just cracked a decades-old Erdős conjecture with fresh math. The golden age of discovery is here.

what I hear is that it's search (and perhaps optimization) again, not a conceptual breakthrough. I don't mean to diminish the result, definitely impressive, esp. if prof Gowers says so, but I'd love to see this addressed