A 30-year-old mathematical question known as the Dinitz-Garg-Goemans conjecture has been disproven by an AI model using simple prompts.
Key facts
- •Dmitry Rybin used four prompts totaling fewer than 60 words to prompt the AI to find a counterexample.
- •The Dinitz-Garg-Goemans conjecture had remained unsolved for 30 years before being disproven.
- •Chris Bowman-Scargill of the University of York noted that graph theory conjectures are frequently proven false due to the way structural behavior shifts in networks.
- •An AI model recently found a counterexample to the Jacobian conjecture, which had stood for nearly a century.
- •Alexander Yong of the University of Illinois Urbana-Champaign expects AI to soon prove conjectures by combining knowledge of literature with the ability to test many possibilities.
The Dinitz-Garg-Goemans conjecture, a long-standing problem in graph theory, has been proven false after an AI model identified a counterexample. Dmitry Rybin, co-founder of the AI startup Autokernel, used ChatGPT 5.6 Pro to solve the 30-year-old puzzle in approximately 5.5 hours. The process required only four prompts totaling fewer than 60 words.
By the numbers
The Nature of the Conjecture
Graph theory involves the study of networks composed of nodes or vertices. The Dinitz-Garg-Goemans conjecture functioned as a logistical challenge regarding the distribution of shipments from a warehouse to multiple locations. It posited that a scenario involving split deliveries could be converted into one where shipments remain unsplit without increasing the total shipping cost. By finding a counterexample, the AI has demonstrated that this premise is false.
AI's Role in Mathematical Research
The use of AI to solve mathematical conjectures has increased recently, with models successfully addressing problems related to Paul Erdős and the Jacobian conjecture. Experts note that AI is particularly effective at identifying 'low-hanging fruit' in fields like graph theory, where structural behavior can change significantly with the addition of just one or two vertices. While some mathematicians, such as Abhishek Saha of Queen Mary University of London, suggest current models lack the capacity to build the complex theory required for the deepest open conjectures, others believe AI will become a vital tool for researchers to navigate promising directions and discard dead ends.
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This article was independently rewritten by ManyPress editorial AI from reporting originally published by New Scientist.
