An 80-year-old challenge in geometry has been cracked by mathematicians working for the tech firm Open AI using a single prompt from an AI chatbot.
The company has not revealed all the precise details and steps of how it did this, nor the name of the AI system that achieved the result, which it has published on its website. However, the finding has been verified independently by mathematicians not connected to the firm.
OpenAI announced on 20 May that its chatbot software had disproved Paul Erdős (1913–1996) on what is called the unit-distance problem. In 1946, Erdős worked out what he suggested was the best arrangement of points on a plane so that as many pairs as possible are at a given distance from each other – and he put down a challenge: no one could do better.
Now, OpenAI says that its system has done precisely that. It did so by using techniques in algebraic number theory, which enabled it to choose points with coordinates that were the solutions of particular equations. And the finding has astonished mathematicians.
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