Grok 4.5 overturned a graph theory conjecture that had baffled the mathematics community for 30 years in 8 minutes; Musk liked and shared it.
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Breakthroughs in AI within the field of mathematics are accelerating. Grok 4.5, a model under xAI, overturned a graph theory conjecture that has puzzled mathematicians for around 30 years in just 8 minutes during an informal internal discussion, drawing wide attention from the tech and investment circles.
The event originated from a post by user Dmitry Rybin on the social platform X on the 23rd. He stated that the Dinitz-Garg-Goemans conjecture has been disproved—a graph theory problem unresolved for about 30 years. According to his account, the relevant discovery was made with the help of AI, and the post included specific graph theory counterexample data.
Subsequently, xAI founder Elon Musk liked and forwarded the post, commenting that "Grok 4.5 just solved a longstanding 30-year graph theory conjecture."
This incident quickly drew market attention to cutting-edge AI capabilities. The breakthrough by Grok 4.5 Medium was achieved through informal channels; notably, this was not a meticulously designed benchmark test, but was triggered accidentally during a routine discussion on the team’s Slack channel, further highlighting the real-world mathematical reasoning abilities of today’s top AI models.
Unexpected Breakthrough: Mathematical Discovery in a Slack Conversation
According to a post by Justin Sun on platform X, after Rybin's original post was shared in the internal Slack channel, Capy—an AI running on Grok 4.5 Medium—took the initiative to try solving the problem, and within 8 minutes found a novel counterexample, thereby overturning the conjecture.
The impromptu nature of this process made it particularly striking. The AI was not specifically assigned this problem in a controlled research environment, but instead stepped in "on its own" during a random team discussion, independently completing the reasoning and verification.
The Dinitz-Garg-Goemans conjecture lies in the field of graph theory, centering on the cost relationship between fractional flow and unsplittable flow. According to Rybin’s account, the found counterexample graph has a fractional flow cost of 58, while any unsplittable flow with capacity violation no greater than 15 would have a cost of at least 60—this gap directly refutes the validity of the conjecture.
This conjecture has remained unresolved for about 30 years since its proposal, and is regarded as a classic open problem in combinatorial optimization and network flows.
Notably, Rybin mentioned in his post that the above discovery was initially made through a conversation with GPT-5, and he included the relevant chat log link. Justin Sun later demonstrated that Grok 4.5 Medium also independently completed this refutation.
This means that on the same mathematical challenge, both OpenAI’s GPT-5 and xAI’s Grok 4.5 provided effective solutions in a short period, offering a direct view of the ongoing competition in mathematical reasoning ability among top AI models, and giving the market a new benchmark for evaluating the technical strengths of both companies.
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