Unique games conjecture

He points to what he calls creative-seeming math breakthroughs, without naming them.

Last week, we reported on OpenAI's 722 AI-written math manuscripts and on Scott Aronson's claim of a proof of the unique games conjecture.

OpenAI later withdrew three of those papers.

His other evidence is a new benchmark called TasteVal from P0 Research.

One of them is a problem that my wife, uh, had been working on for the entire time that I've known her.

It's called the Unique Games Conjecture, and there were many, many experts working on this for 25 years.

[upbeat music]

Why was it the biggest-

These were, these were, these were pro- these were problems that, that had not been solved, that in many, many cases there were whole communities of researchers who were trying to solve.

One of them is a problem that my wife, uh, had been working on for the entire time that I've known her.

It's called the Unique Games Conjecture, right? And there were many, many experts working on this for 25 years.

Okay? You know, we now, we now have a proof from, from the, uh, uh, uh, OpenAI model.

And as one reader of the papers put it, "Any one of these would normally be a career." Scott Aaronson calls it the Mathocalypse.

One of the results is a proof of the unique games conjecture, which his wife, the complexity theorist Dana Moshkovitz, worked toward her whole career, and their nine-year-old son told her, "Mommy, I heard you got cooked." Her verdict on the proof? Some alien craziness.

Will DePue had two frontier models rank the big discoveries of the last three years, and eighty-one percent of that list came out in this one drop.

OpenAI's Mark Chen calls it a decade of mathematical progress in a week.

Whether you're thrilled, depressed, angry, or whatever else about it, yesterday was surely one of the biggest days in mathematical history.

And yes, among the three hundred and seventy-two huge results released yesterday by OpenAI on the recommendation of its advisory group of Timothy Gowers, Edward Witten, and other distinguished mathematicians, was a proof of Subhash Khot's Unique Games Conjecture, UGC, a statement that my wife has worked toward proving for the entire time I've known her.

Then there is the other kind of new problem, where those in denial, who three years ago took comfort in talking about how LLMs could not do math, have to find a new way to explain why anything an AI can do is not real or not meaningful.

Shtetl-optimized.

[upbeat music] On Tuesday, OpenAI published hundreds of math results from an internal model that it has not released.

Yesterday, we said OpenAI's materials did not confirm a proof of the unique games conjecture, one of the big open problems in complexity theory.

Quanta Magazine and the mathematician Gil Kalai now report that the release does announce one.

The complexity theorist Scott Aaronson called Tuesday, "Surely one of the biggest days in mathematical history." At the same time, three mathematicians from King's College London and Cambridge posted a paper that questions the computer checks behind such results.