Rumoured OpenAI proof pushed MIT theorists to post a 95-page paper in three days

"The current version of the manuscript is complete mathematically, but it is not in the shape we wished to share in," the authors wrote on its first page ^[8]. According to Quanta Magazine, Minzer, Fei and Wang hurried the draft out so an OpenAI press release would not overshadow it. It went online on September 14 ^[7][17].

To say how much the rumour sped things up, you need a baseline. Quanta's baseline is that writing up findings like these would typically take months or longer ^[6]. That describes the usual process, so the gain for this particular paper is an estimate. The rumours arrived soon after OpenAI announced a proof about the behaviour of fluids, and they said the unique games result might go public any day ^[4]. The announcement came 25 days after the first text ^[19]. By then the human paper had been public for 22 days ^[18].

Minzer and his students had already proved their result and were writing it up when the rumours began ^[5]. The rumour changed the release date and the polish. Quanta describes the team as "prioritizing completeness over clarity" ^[7]. I think the episode supports a narrow claim: an expected AI announcement set the publication schedule for one group working on a neighbouring problem, a group led by a leading expert on the conjecture ^[3]. To show that AI sets research priorities, you would need evidence of groups changing which problems they work on. One team posting finished work early is a sample of one.

A proof of the conjecture would imply that current methods for many seemingly unrelated problems cannot be improved, and it would bring researchers a big step closer to a unified theory of computational difficulty, according to Quanta ^[12]. Complexity theorists want to know why approximate solutions are sometimes easy to find and sometimes hard ^[15]. "A lot of work has been devoted to trying to figure out where is the boundary," said Ryan O'Donnell, a theoretical computer scientist at Carnegie Mellon University ^[13][14].

Quanta's account does not say whether mathematicians outside the company have checked OpenAI's proof. Researchers met the wave of AI proofs with what Quanta calls a mixture of alarm and curiosity ^[9].

Their reaction to the human paper was less ambivalent ^[9]. "He's put out many great papers on this topic," O'Donnell said. "This is another truly great one." ^[10]