AI solved an 80-year-old major math problem

For 80 years, mathematicians tried to crack a math problem that an OpenAI model recently solved in roughly the amount of time it takes to binge-watch your favorite season of a TV show.

It marks the first time a prominent open problem that’s central to a field of mathematics has been solved autonomously by AI.

Let’s break it down

The challenge was the "unit distance problem," first posed in 1946 by legendary mathematician Paul Erdős. We’ll spare you the head-spinning details and skip straight to the “Give it to me in plain English” part:

• If you put n dots on a sheet of paper, how many pairs of dots can be exactly one unit apart?

Erdős believed he knew the best possible arrangement. And for nearly 80 years, nobody could prove him wrong—until OpenAI came along with a new solution.

Well, kind of…Instead of confirming Erdős's hunch, the model found something even more surprising: a counterexample showing how his conjecture was wrong. The AI model’s answer was checked by a group of actual mathematicians, who then wrote a 19-page companion paper explaining that yes, the robot is right.

Why didn't humans solve it first?

There are multiple theories, according to experts.

1. The solution is highly counterintuitive, as most people sought to prove Erdős’ conjecture rather than disprove it.
2. Modern math rewards specialization, while AI can pull concepts from across its entire knowledge base—in this case, the unrelated fields of algebraic number theory and discrete geometry.
3. AI has the time, attention, and persistence to stick with certain methods that other researchers might abandon, which proved particularly useful for this problem.

Bottom line: The answer to Erdős’ conjecture took OpenAI’s model less than 32 hours and $1,000 in tokens, per some back-of-the-envelope math by a former researcher.