When rumors circulated that an AI had found a proof of the unique games conjecture, Dor Minzer and his students Yumou Fei and Shuo Wang rushed to finish and post a long-awaited paper they had been refining for years. They published a 95-page draft quickly and candidly - complete mathematically but not polished - partly to avoid being overshadowed by an imminent AI announcement. OpenAI later publicized a large batch of machine-generated proofs, including one for unique games, provoking a mix of alarm and curiosity across complexity theory; peers still hailed Minzer’s result as “truly great.”
The work tackles constraint-satisfaction problems on graphs - the framework of the unique games conjecture - and focuses on Khot’s 2-to-1 variant, which addresses cases where the best solution satisfies every constraint yet approximations remain hard. Minzer, Fei and Wang proved a closely related, slightly weaker 4-to-1 version by building a bridge from the graph-coloring formulation to error-correcting-code constructions. After years of partial advances (including a 2018 milestone) and several failed attempts, they combined a new code with previous pieces to achieve the result in April 2026. That 4-to-1 theorem already yields many of the conjecture’s important consequences, notably new hardness results for classic graph-coloring problems.
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