A counterexample to Naimark's problem in ZFC
We construct in ZFC a unital infinite-dimensional simple complex C ∗ -algebra with a faithful tracial state whose nonzero irreducible representations are all unitarily equivalent. This gives a negative answer to Naimark's problem without additional set-theoretic assumptions.
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Answer to: Which of the results released by OpenAI went against the conventional mathematical wisdom?mathoverflow.netNik WeaverOct 8, 2026
Maybe one of the less earth-shaking results, but close to my heart: "297. A ZFC counterexample to Naimark's problem ". It's been known since 2004 that the existence of a counterexample is consistent with ZFC, and I think it's probably fair to say that the conventional wisdom was that a positive…