AI just solved an 80-year-old Erdos problem,' and mathematicians are amazed

A geometry conjecture was solved after decades of unsuccessful effort by human mathematicians using a straightforward query to a chatbot. OpenAI announced the result and experts described the method as clever and elegant. The outcome is presented as a milestone because it would merit publication in a top mathematics journal and major media attention even if done by humans. Timothy Gowers stated that no previous AI-generated proof met those standards. Daniel Litt said the result is the most interesting one produced autonomously by AI so far. The unit distance problem is used as context: placing nine dots to maximize pairs one inch apart, with the question generalized to any number of dots. Paul Erdős made a conjecture in 1946 that the optimal strategy resembles a grid with smaller spacing to create many one-inch pairs across grid points.

"After 80 years of fruitless struggle by human mathematicians, a major geometry conjecture has at last been solved via a straightforward query to a chatbot. The company OpenAI, maker of ChatGPT, announced the result yesterday, together with comments from a number of experts, who declared the artificial intelligence's method clever and elegant. The achievement follows months of loudly reported but less impressive AI-powered advances in mathematics and marks a true milestone."

"Unlike all those previous feats, this result would merit publication in a top math journal, as well as major media attention, even if it were performed by humans alone. No previous AI-generated proof has come close to meeting those high standards, wrote Timothy Gowers, a mathematician at the University of Cambridge, in commentary solicited by OpenAI. On supporting science journalism If you're enjoying this article, consider supporting our award-winning journalism by subscribing."

"This is the unique interesting result produced autonomously by AI so far, says Daniel Litt, a mathematician at the University of Toronto, who was consulted by OpenAI to verify the proof but is not involved with the company. The unit distance problem is simple to explain but formidable to solve a mathematician's favorite quality. Draw nine dots on a sheet of paper. The goal is to get as many pairs of dots as possible to be an inch apart."

"For any number of dots, even billions or trillions, the problem asks: What's the highest number of pairs you can get? In 1946 mathematician Paul Erdos made a guess at the best strategy. It was the grid approach but with a much smaller spacing between dots, so pairs could be established across several grid points."

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