Top AI Product

On May 20, OpenAI announced that an internal reasoning model independently disproved a major unsolved conjecture in discrete geometry — the planar unit distance problem, first posed by Paul Erdős in 1946.

## The problem

The question: how many pairs of dots can sit exactly one unit apart in the plane? For nearly 80 years, mathematicians believed square grids were essentially the optimal arrangement. OpenAI’s model found an entirely new family of constructions that beats the grid — and proved it mathematically.

## What’s actually notable

The proof came from a general-purpose reasoning model — not a system trained specifically for mathematics, not scaffolded to search proof strategies, not targeted at this problem in particular. A model built for broad reasoning produced a novel mathematical result that several respected mathematicians independently verified. OpenAI published their companion remarks alongside the announcement.

## Why it matters

There’s a difference between “AI solves competition math” (pattern-matching known techniques) and “AI produces a genuinely new construction no human found in 80 years.” This is the latter. If general reasoning models can independently extend the frontier of open mathematics, the claim that LLMs only interpolate from training data gets materially harder to sustain. The “AI accelerating research” thesis just got its strongest single data point.