Mathematician Rejects OpenAI's Conjecture Breakthrough Within 24 Hours: 'AI Proved Every Sentence, but It's No Longer About the Original Conjecture'

OpenAI claimed that its next-generation AI model solved ten world-class mathematical problems, including disproving the Connes rigidity conjecture. The next day, a human mathematician responded with a paper arguing that the AI's counterexample is invalid. The author, J. L. Nielsen from the Topology Physics Center at the University of Kansas, traced OpenAI's 37,000 lines of Lean 4 code from start to finish, mapping each object back to its mathematical prototype, and identified two independent failure paths. The Connes rigidity conjecture states that if two groups have the same associated algebraic structure and satisfy two additional conditions (ICC and Kazhdan's property (T)), then the groups must be isomorphic. OpenAI's model constructed two non-isomorphic groups that generate the same algebra, with proofs that both groups satisfy ICC and property (T). Nielsen pointed out that one of the AI-constructed groups actually did not satisfy the additional conditions, being neither ICC nor having property (T). She listed three possible reasons: the code's representation of property (T) did not faithfully correspond to Kazhdan's original definition; the proof only held for part of the group but was applied to the whole; or the group in the code is not what the explanatory document describes. Nielsen also performed a line-by-line check of the code, listing each mathematical object's name and line number in a cross-reference table. She found that the lemmas used to prove ICC applied to objects after a dual transformation, not to the original group with its central elements, so they did not directly cover the critical elements. She wrote her two rebuttals as Lean code and compiled them under Lean 4.32.2. The paper's final section discusses the broader context: the Lean kernel ensures formal correctness, but not whether the statement actually proves the intended conclusion. Quoting Terence Tao, verifying a proof checks the formal statement itself, not its alignment with intent, so human review cannot be replaced. Past audits of five common Lean benchmarks found 4,833 issues, including counterexamples, empty theorems, and unreliable axioms, all machine-verified, with humans later constructing counterexamples to show the proven statements were false. Nielsen wrote that OpenAI's formalization may have correctly established every conclusion it claims, but what it did not establish—and what the Lean kernel cannot check—is whether these conclusions relate to the original conjecture's wording. The Connes rigidity conjecture remains open.