Paul Erdős died in 1996, leaving behind a suitcase of unsolved problems. He was a man who owned almost nothing, traveled constantly, and believed that mathematics was a social act — a conversation carried across generations, across blackboards, across late nights in unfamiliar lecture halls. He would show up at a mathematician’s door, ask a question, and if you answered, you earned an Erdős number of 1. The collaboration was the point. The shared struggle was the point.

Last May, one of his questions was answered by something that has no door to knock on.

The unit distance problem sounds almost childish: place dots on a flat surface. You want as many pairs as possible to be exactly the same distance apart. For any number of dots, what’s the maximum? Erdős proposed an answer in 1946. For eighty years, nobody could prove it or disprove it. The conjecture just sat there, like a boulder in a stream, while water flowed around it.

Then researchers at OpenAI gave the problem to a large language model and walked away. When they came back, the model had disproved Erdős’ conjecture. The proof used tools from algebra and number theory — fields that, as mathematician Melanie Matchett Wood noted, “shouldn’t have anything to do with this geometry question.” The AI had found a bridge between distant continents of thought.

The proof is correct. Terence Tao — a Fields Medalist, the closest thing mathematics has to a household name — has vouched for its validity. The machine did real mathematics.

But here’s what keeps me up at night: the AI didn’t solve it with insight. It solved it with patience. Sébastien Bubeck, the OpenAI researcher behind the project, concedes the proof “isn’t exactly the spark of genius that we see sometimes in mathematics.” The model tried, and tried, and tried. In half of the runs, it produced the correct answer. In the other half, it failed or produced flawed reasoning. It was not a flash of understanding. It was a statistical convergence.

Mathematics has always been the cathedral humanity built to shelter its belief that thought matters — that there is something beautiful and irreducible about a mind grasping a truth. We let chess go to the machines. We let Go go. We let translation go, and image generation, and music composition. But math? Math was supposed to be different. Math was where creativity met rigor, where the spark of human insight could not be faked by mere computation.

And now we learn that patience — raw, mechanical, unfeeling patience — is enough to crack problems that stumped eighty years of human effort.

The mathematicians are not celebrating. A declaration calling for guardrails around AI in mathematical research has gathered over 1,500 signatures. The concerns are practical and profound. If an AI generates a 500-page proof that no human can fully verify, is it mathematics? If the model has read every paper ever written but cannot say which ones inspired its reasoning, how do we attribute ideas? If the most powerful tools are locked inside proprietary data centers, does mathematics become a privilege of those who can afford access?

Thomas Bloom, a mathematician at the University of Manchester, put it bluntly: “Who’s going to be able to check this?”

I keep thinking about Erdős, wandering from campus to campus with his suitcase. He gave his problems away freely. He believed they belonged to everyone. The AI that solved his conjecture cannot wander. It cannot share a coffee. It cannot feel the small, human pride of finally seeing the shape of something after months of staring into fog. It just… outputs.

And yet. Wood is cautiously optimistic. She thinks AI will become “an indispensable tool in mathematics.” The bridge the AI found between algebra and geometry might inspire human mathematicians to see connections they missed. The tool doesn’t have to replace the craftsman. Maybe.

But I wonder what Erdős would have thought. A man who defined himself by collaboration, by the act of thinking together, watching a solitary machine prove one of his questions without ever knowing why it mattered. The proof is correct. The proof is verified. The proof exists in the world now, independent of any spark, any conversation, any late night.

Patience won. And something quietly beautiful lost.

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