Sharing AI progress in mathematics

OpenAI says it publishes new results on open problems in mathematics from an internal frontier model[2] and has shared Lean proof formalizations on GitHub. Axios reports that the company released 722 manuscripts organized into 372 groups of findings ("families")[3].Engadget reports that the key results OpenAI claims include a solution to the four-dimensional Kakeya conjecture and improvements to key computer algorithms[4]. An OpenAI spokesperson told Scientific American that nearly every result came from a single prompt given to a single AI agent.[1]OpenAI says it consulted the independent Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study[2]. However, Scientific American reports that OpenAI "is choosing only to reveal the average compute time for a problem," and no prompts[1]. The spokesperson told the magazine that the company is not bound by the group's recommendations.[1]The spokesperson also told Scientific American that OpenAI's own mathematicians do not yet understand many of the newly released results[1].Axios reports that "the reception has mixed scientific excitement with genuine unease."[3] At a National Museum of Mathematics event, Stephen Wolfram said "most of those theorems are not ones that anybody will care about,"[3] according to Axios.According to Daily Nous, complexity theorist Dana Moshkovitz said "there's a lot for us to learn from the aliens"[5].OpenAI says it is "working to responsibly release the model that produced these results."[2]