AI Cracks 80-Year Math Puzzle Stumping Top Mathematicians

After eight decades, a machine just outsmarted one of history's most brilliant mathematicians at his own game.

Paul Erdős, a Hungarian genius who wrote over 1,500 papers in his lifetime, posed a deceptively simple question in 1946. If you scatter dots on a page and rearrange them, how many pairs can you position at exactly the same distance apart?

Erdős proposed that the best solution was a grid pattern. For 80 years, nearly every mathematician agreed.

Then OpenAI's latest model found something better.

"This is the unique, interesting result produced autonomously by AI so far," mathematician Daniel Litt from the University of Toronto told Scientific American. The discovery sent shockwaves through the mathematical community.

Erdős was so confident in his grid theory that he offered $300 in 1982 for anyone who could prove or disprove it. He later raised the bounty to $500.

The eccentric mathematician lived an unusual life. After losing his sisters to scarlet fever and his father to a World War I prison camp, young Erdős found comfort in numbers. "They were my friends," he recalled. "I could depend on them to always be there."

He spent his adult life traveling the world, showing up unannounced at colleagues' homes with his signature greeting: "My brain is open!" He'd fall asleep at dinner parties if the conversation strayed from mathematics.

Erdős loved posing problems for others to solve, offering cash prizes from $10 to $10,000. His influence was so vast that mathematicians still measure their "Erdős number" based on how many degrees of collaboration separate them from him.

The Ripple Effect

OpenAI's breakthrough did more than solve one puzzle. Within days of the announcement, Princeton mathematician Will Sawin used the same approach to find an even better solution.

Then Thomas Bloom, Will Sawin, and their colleagues cracked another open problem Erdős had posed in the 1970s called the sum-product conjecture. "Once you know that something might be possible, you're willing to try a bit harder to actually get it to work," Bloom told New Scientist.

The discovery marks a turning point. Just a year ago, the idea of AI independently solving such problems would have seemed laughable. Even a month before the announcement, OpenAI's own researchers didn't think it possible.

This wasn't OpenAI's first attempt at Erdős problems, but it was their first genuine success. Last year, they mistakenly claimed their model solved ten problems when it had actually just found existing solutions buried in academic papers.

This time, they brought in independent mathematicians to verify the work before announcing anything. The careful approach paid off.

What makes this moment special isn't just that a computer solved a hard problem. It's that AI discovered something humans hadn't thought to look for, opening doors we didn't know existed.