{"slug": "chatgpt-proves-dinitz-garg-goemans-conjecture-is-false", "title": "ChatGPT proves Dinitz-Garg-Goemans conjecture is false", "summary": "A user claims to have disproven the Dinitz-Garg-Goemans conjecture, a graph theory problem open for ~30 years, using ChatGPT 5.6 Pro. The user states the graph below has fractional flow cost 58, while any unsplittable flow with capacity violation ≤15 has cost at least 60, providing a counterexample.", "body_md": "Dinitz-Garg-Goemans conjecture is false. This graph theory problem was open for ~30 years.\nThe graph below has fractional flow cost 58. Any unsplittable flow (with capacity violation <=15) has cost at least 60.\nChat with GPT 5.6 Pro where this was found:\n\n- I know counterexamples to old conjectures are becoming a meme at this point. But I really cared about this problem and spent many weeks thinking about it a while ago (in both directions, proof and disproof). I think almost all graph flows experts thought about this problem.\n- The conjecture was based on absolutely stunning result of Dinitz, Garg, and Goemans: any fractional flow can be routed to unsplittable flow by violating graph capacities by at most max(demand). The chat with gpt pro here is an absolute meme\n- Your 'many weeks thinking about it' was asking the model to try again 4x. 😂\n# Join the conversation", "url": "https://wpnews.pro/news/chatgpt-proves-dinitz-garg-goemans-conjecture-is-false", "canonical_source": "https://twitter.com/DmitryRybin1/status/2079906232069177643", "published_at": "2026-07-23 19:36:33+00:00", "updated_at": "2026-07-23 19:53:05.437194+00:00", "lang": "en", "topics": ["artificial-intelligence", "ai-research"], "entities": ["ChatGPT", "GPT 5.6 Pro", "Dinitz", "Garg", "Goemans"], "alternates": {"html": "https://wpnews.pro/news/chatgpt-proves-dinitz-garg-goemans-conjecture-is-false", "markdown": "https://wpnews.pro/news/chatgpt-proves-dinitz-garg-goemans-conjecture-is-false.md", "text": "https://wpnews.pro/news/chatgpt-proves-dinitz-garg-goemans-conjecture-is-false.txt", "jsonld": "https://wpnews.pro/news/chatgpt-proves-dinitz-garg-goemans-conjecture-is-false.jsonld"}}