ChatGPT 5.6 Pro Disproves 30-Year-Old Graph Theory Conjecture in 5.5 Hours

1 articles · Updated · New Scientist · Jul 23

Four prompts totaling fewer than 60 words led ChatGPT 5.6 Pro to a structured counterexample that falsified the 30-year-old Dinitz-Garg-Goemans conjecture, according to a post on X by Autokernel co-founder Dmitry Rybin.
The conjecture held that a split-shipment network flow problem could always be converted into an unsplittable one without raising total cost; the counterexample shows that claim fails.
Rybin said he had spent weeks thinking about the problem before the model solved it in 5.5 hours, while mathematicians said graph theory is especially prone to conjectures breaking once a few vertices are added.
The result adds to a burst of AI-driven math claims this year, including a May breakthrough on a decades-old Erdős conjecture and fresh reports of counterexamples to other long-standing problems.
Researchers said current models appear strong at finding counterexamples and other lower-complexity results, but still fall short of building the deeper theory needed for the hardest open conjectures.