AI Closes 20-Year-Old Open Problem in 30 Minutes; Verification Takes 5 Days

Dimitris Papailiopoulos, a Microsoft Research scientist, used GPT-5.6 and Claude Fable 5 to close a question open since 2001: whether the MIMO detection problem can be solved by a fast polynomial algorithm wherever it is statistically possible. The models independently claimed that no gap exists and provided proofs for different algorithms. Papailiopoulos chose Claude Fable's algorithm—a coarse linear estimate with rounding followed by greedy bit flips—and asked GPT to fix its proof, which was 'mostly wrong but salvageable.' He then spent five days iterating with both models to simplify the argument into a verifiable form, rejecting any steps he couldn't follow despite allowing worse constants. The final proof is elementary, building on known techniques from the 2010s. However, the result is not yet peer-reviewed, and the idealized channel model means it won't improve real routers. Papailiopoulos also suggests the models distill collective human intuition, and that many abandoned problems await similar solutions.