The Mathocalypse

Yesterday was a landmark day in mathematical history as OpenAI announced 372 groundbreaking results, including a proof of Subhash Khot's Unique Games Conjecture. The UGC has implications for a number of optimization problems, suggesting they are indeed NP-hard, even when seeking solutions slightly better than those obtainable via semidefinite programming relaxation.

While a Lean certificate confirms the proof, many mathematicians are struggling to understand it, as it appears to have been written by an AI. My 9-year-old son was not wrong when he said that a robot had solved the math problem his mother had worked on for her entire career. The proof invents an entirely new and bizarre code with a noise test, and the race to comprehend it has only just begun.

Despite the AI's role in the discovery, there are still mitigating factors for Khot, such as the vindication of the UGC's truth and the potential for a more harmonious mathematical world with AI assistance. Other notable achievements include solving the 3SUM problem in O(n1.9992) time and the All-Pairs Shortest Paths problem in O(n2.9995) time, which refute long-standing conjectures.

However, the AI model used to produce these results is not unique and could be accessible to paying ChatGPT customers in the future.