Freitag, Mutchnik credit ChatGPT 5.6 with logic counterexample
TL;DR
- James Freitag and Scott Mutchnik posted a 21-page arXiv preprint on August 31, 2026 claiming a counterexample to the stable forking conjecture.
- The conjecture was formulated by Hart, Kim and Pillay in 1996 and had stood as an open problem in model theory since.
- The authors say they prompted ChatGPT 5.6 to construct the counterexample but wrote all proofs themselves without AI assistance.
The abstract is two sentences. "Using ChatGPT 5.6, we find a counterexample to the stable forking conjecture. This answers a long-standing open question of Hart, Kim and Pillay (1996)."
James Freitag and Scott Mutchnik posted the 21-page preprint to arXiv on August 31, 2026, filed under mathematical logic and quantum algebra. The conjecture they target dates from 1996 and asks, roughly, whether forking independence in simple theories is pinned down by stable formulas alone.
Their counterexample is "the theory of an infinite-dimensional vector space over the division ring of fractions of the quantum graph algebra of the random graph." Swap a commutative field for a noncommutative division ring, and the forking relation goes unstable while the theory stays simple.
The authors are precise about the AI's role. "We prompted ChatGPT to construct a counterexample to the stable forking conjecture with a detailed series of prompts which took into account the many restrictions," they write. They add that "the proofs of the relevant facts...have been written entirely by the authors, and no AI tool was used in the actual writing of this manuscript."
The preprint has not yet been peer reviewed.
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In July, I asked a couple model theorist friends of mine what they considered the major open problems of logic. They both mentioned the stable forking conjecture. This has now been resolved using ChatGPT. arxiv.org/abs/…
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Originally reported by arxiv.org
Read the original article →Original headline: A counterexample to the stable forking conjecture