How an AI Model Shattered an 80‑Year‑Old Geometry Conjecture (And What It Means) In 1946, the legendary mathematician Paul Erdős posed a question so simple that you could explain it to a child over breakfast. If you scatter points on a sheet of paper, how many pairs of them can be exactly one inch apart? For nearly eight decades, the brightest minds on Earth believed they knew the best possible answer. It looked like a tidy square grid – the kind you’d draw on graph paper. But last week, something astonishing happened: an OpenAI model that wasn’t even designed for mathematics looked at this riddle and said, “I can do better.” And it did. The AI discovered an entirely new family of arrangements that outperform the grid. It didn’t just tweak a known idea – it brought in heavy‑duty machinery from a different branch of mathematics entirely. This is the story of what happened, why it matters, and what it tells us about the future of human and machine collaboration. A 1946 Riddle That ...
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