On the morning of September 11, 2026, Dor Minzer (opens a new tab) received a text message from a friend asking whether he was close to settling one of the most famous open questions in theoretical computer science. Minzer, a professor at the Massachusetts Institute of Technology and a leading expert on the “unique games” conjecture, initially thought it was a joke. Then more messages started coming in, and the rumors began to cohere. The artificial intelligence company OpenAI, fresh from announcing a bombshell proof about the behavior of fluids that sent ripples through the math world, had allegedly discovered a proof of the unique games conjecture. They might make the result public any day. If Minzer had any results of his own to share, the messages suggested, now would be the time to do so.
The unique games conjecture is an iconic question in computational complexity theory, the study of the inherent difficulty of mathematical problems. Roughly speaking, it states that a problem about satisfying multiple constraints at the same time can be extremely hard, even if you’re willing to settle for a poor approximation of the best possible solution. A proof of the conjecture would also automatically imply that current methods for solving many seemingly unrelated problems can’t be improved. Researchers would be a big step closer to a unified theory of computational difficulty.
To read more, click here.