A basic AI prompt has disproved the Dinitz-Garg-Goemans conjecture, a 30-year-old problem in graph theory. Dmitry Rybin used ChatGPT 5.6 Pro to find a counterexample after entering fewer than 60 words across four prompts. The process took 5.5 hours.
Rybin, co-founder at AI start-up Autokernel, posted the counterexample on X. He instructed the AI to “do a breakthrough and find a structured counterexample” and followed up with three prompts urging it to continue searching.
The conjecture concerns whether certain shipping scenarios in graph theory can be converted without increasing costs. Rybin said on X that he had spent many weeks thinking about the problem.
Chris Bowman-Scargill at the University of York noted that graph theory conjectures often fail when complexity increases. Abhishek Saha at Queen Mary University of London said current AI models suit such problems but have limits on deeper conjectures.
Alexander Yong at the University of Illinois Urbana-Champaign said AI will help discard dead ends and prove many conjectures through its ability to test ideas rapidly.
