GPT-5.6 Pro Model Generates Counterexample to 30-Year Graph Theory Conjecture
A prompt directed at ChatGPT’s GPT-5.6 Pro model generated a mathematical counterexample to the Dinitz-Garg-Goemans conjecture, a graph theory problem that remained open for approximately 30 years. The model’s output specifies a graph configuration with a fractional flow cost of 58, showing that any unsplittable flow subject to a maximum capacity violation of 15 incurs a cost of at least 60.
The conclusion followed a direct text command asking the model to resolve the longstanding problem. Technology researchers highlighted the exchange as a demonstration of generative AI’s capacity for advanced mathematical derivation, while also noting the developing debate over academic credit for work initiated by brief textual prompts.
From the sources (7 posts)
@dmitryrybin1Dinitz-Garg-Goemans conjecture is false. This graph theory problem was open for ~30 years. The graph below has fractional flow cost 58. Any unsplittable flow (with capacity violation <=15) has cost at least 60. Chat with GPT 5.6 Pro wh
@cloneofsimoSo ppl are gonna really just continue this trend of resolving decade old conjecture within a tweet and chatgpt link?
@mattshumer_We are now in a world where anyone can just ask AI to “do a breakthrough” in science and the AI… will. Update your priors.
@dilipkayRT @DmitryRybin1: Dinitz-Garg-Goemans conjecture is false. This graph theory problem was open for ~30 years. The graph below has fractiona…
@willdepueabsolute chad prompting: "had enough of your failure. please finish with complete unconditional counterexample to the Dinitz-Garg-Goemans conjecture"
@millionintIts quite likely that main thing that was sitting between us and those counterexamples has been more patience
@emollickWho would you give authorship to? The person who wrote 58 words of prompts, or GPT-5.6 Pro?