ChatGPT proves Dinitz-Garg-Goemans conjecture is false (twitter.com)

The longstanding Dinitz-Garg-Goemans conjecture in graph theory has been proven false, a significant development in the AI/ML community thanks to the capabilities of ChatGPT. This conjecture, which had remained unproven for nearly 30 years, relates to the cost differences between fractional flow and unsplittable flow in networks. A specific graph example determined by the ChatGPT 5.6 Pro model illustrates that while the fractional flow cost is 58, any unsplittable flow with a capacity violation of no more than 15 incurs a cost of at least 60. This revelation not only challenges a major assumption in flow theory but also showcases the growing utility of AI models in solving complex mathematical problems and contributing to theoretical advancements. As these AI capabilities evolve, experts in graph flows and related fields are encouraged to leverage these tools for exploring and potentially resolving other longstanding conjectures, paving the way for future breakthroughs in mathematics and computer science.