Researcher Dmirty Rybin used ChatGPT 5.6 Pro to find a counterexample to the Dinitz–Garg–Goemans conjecture, a graph theory statement that had remained open for roughly thirty years, according to New Scientist. Rybin instructed the model simply: “find a counterexample that proves the Dinitz–Garg–Goemans conjecture is not true.” The AI returned partial results initially, and after Rybin prompted it to continue three times, the system produced a complete counterexample following about five and a half hours of computation.
What the Dinitz–Garg–Goemans conjecture asserts
The Dinitz–Garg–Goemans conjecture is a graph-theoretic claim about routing and costs in networks. Informally, it states that when transporting goods through a network, splitting shipments into smaller parts and sending them via alternate routes cannot lead to a lower total cost, because there will always exist an equivalent unsplittable (single-path) routing. Until now, the conjecture remained an observation without a general proof, and no counterexample had been found.
According to Rybin’s report, the construction produced by ChatGPT shows a case in which splitting shipments into fractional parts and routing them separately yields a cheaper solution than any single unsplittable route, thereby falsifying the conjecture.
Significance and caveats
Rybin emphasized that this result does not mean AI will replace mathematicians. He noted that disproving long-standing combinatorial or graph-theoretic conjectures has become something of a trend among AI researchers: a single counterexample is enough to invalidate a conjecture, and AI systems are well-suited to search for such counterexamples because they combine large computational resources with extensive coverage of the literature, partially offsetting a lack of human-style creative insight.
It is also notable that the task was carried out with relatively simple prompts on the most advanced publicly available ChatGPT version.
Next steps
The report does not provide the detailed mathematical construction or publication details. Typically, the following steps are to present the counterexample and its verification in a peer-reviewed mathematical venue and to have independent researchers reproduce and validate the findings.
