Mathematicians are trying to make sense of OpenAI’s Tuesday release of findings on more than 300 open problems made by an internal artificial intelligence model — a staggering quantity of mathematical progress that builds on AI developments that have stunned the research community.
The new results, which have previously eluded human beings, span many corners of mathematics, from algebra to geometry to differential equations. OpenAI released them with muted fanfare.
Last month, the company drew fierce backlash from mathematicians for the way it handled its solution to one of math’s “Millennium Prize” problems, each deemed so important they carry a $1 million prize. (The Washington Post has a content partnership with OpenAI).
OpenAI’s Tuesday release does not include a solution to any of the remaining Millennium Prize problems, which were designated by mathematicians at the turn of the century as deep questions that could motivate wide-ranging discoveries. But the company’s internal AI model did make a breakthrough on a modified version of the famous Riemann hypothesis, among many other discoveries.
“Among analytic number theorists, we would discuss, ‘isn’t it embarrassing that we still can’t get anything nearly of that strength,’” said Alex Kontorovich, a professor at Rutgers University, at an impromptu panel at a dinner for the National Museum of Mathematics. “And that’s what was solved tonight.”
OpenAI and other AI companies test internal models on math problems to benchmark their capabilities — a practice has begun to rankle some mathematicians, including an independent advisory board that the company consulted on how to share results.
“We do not endorse this practice, and we ask them to stop testing advanced mathematical problems on proprietary models,” the board wrote in September.
“We want this progress to push the frontier of human knowledge and enable further progress in mathematics,” OpenAI said in a statement.
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