Two frontier AI models recently produced counterexamples to long-standing mathematical conjectures, but the viral narrative collapsed under scrutiny. xAI's Grok 4.5 and OpenAI's GPT-5.6 Pro each generated solutions to different 30-year-old problems in network optimization and graph theory, yet neither result has passed peer review, and the internet compressed two distinct claims into one cleaner story than the facts support.

What Math Problems Did These AI Models Actually Solve?

The confusion starts with attribution. Dmitry Rybin, a Ph.D. graduate of the Chinese University of Hong Kong, Shenzhen, used GPT-5.6 Pro to construct a proposed counterexample to the Dinitz-Garg-Goemans cost conjecture, a network optimization problem from 1999. His claimed counterexample is remarkably small: a graph with just 7 vertices and three demands, where the fractional cost is 58 but every acceptable unsplittable solution costs at least 60. That gap of 2 is enough to break the conjecture if verified.

Meanwhile, a separate claim emerged from the Capy agent running on Grok 4.5 Medium. According to AGNT Labs, Capy found that the Hoffman-Singleton graph refutes Graffiti Conjecture 284, a graph theory problem from Siemion Fajtlowicz's Graffiti program. That graph has 50 vertices and 175 edges, making it far larger than Rybin's example. The two problems are not the same, yet Elon Musk's amplification of the Grok result and subsequent media coverage blurred the distinction.

The Dinitz-Garg-Goemans conjecture concerns routing demand through a network. In fractional flow, you can split a demand across multiple paths. In unsplittable flow, each demand must travel along one path. The 1999 result showed that fractional flows can be rounded to unsplittable ones while controlling congestion, but the cost question remained open: can you do that without increasing total cost? Rybin's proposed counterexample says no.

Why Does the Attribution Gap Matter So Much?

The distinction between these two claims is not pedantry; it reveals a fundamental product lesson for AI science startups. When Elon Musk's X post said Grok 4.5 had solved a graph theory conjecture open for roughly 30 years, it conflated the model, the agent, the toolchain, and the verification process into a single achievement. The original Capy post was more specific: Capy was running on Grok 4.5 Medium, and the target was Graffiti Conjecture 284. An agent using a model, tools, and a workflow is not the same thing as a raw model solving a problem from a blank prompt.

Neither result has cleared peer review, but both come with detailed verification scaffolding. Rybin's GPT-5.6 Pro claim includes proof certificates, a verification program, machine-readable counterexample data, and LaTeX source code. The Grok-linked claim similarly includes verification notes from AGNT Labs. If these artifacts are correct, the graphs should survive expert inspection. If one hidden path or capacity condition was missed, either claim could fall apart.

How Should AI Science Startups Report Mathematical Discoveries?

• Separate Model from Agent: Clearly distinguish whether a raw language model produced the result or whether an agent using the model plus tools and a workflow generated it. This distinction affects how the capability should be interpreted and credited.
• Include Verification Artifacts: Provide proof certificates, verification programs, machine-readable data, and source code that allow independent experts to check the claim. A finite counterexample can be verified by direct computation, making peer review faster than for traditional proofs.
• Avoid Narrative Compression: Do not merge separate claims into one headline just because both involve AI and mathematics. Rybin's 7-node flow example and Capy's 50-node graph refutation are distinct achievements with different implications for different fields.

The mathematical community is watching closely, but the cautious view remains the strongest one. Rybin's GPT-5.6 Pro result may be a real counterexample to the Dinitz-Garg-Goemans cost conjecture. Capy, running on Grok 4.5 Medium, may have found a real refutation of Graffiti Conjecture 284. Both claims are recent, and both need expert checking. If either result holds, it is a serious moment for AI-assisted mathematics. If both hold, it is bigger. But the field does not get there by rounding off the facts or conflating distinct achievements into a single viral narrative.

The real lesson is not that frontier AI models can solve old math problems. The real lesson is that attribution discipline is the product lesson. If your AI science startup cannot separate model, agent, toolchain, prompt history, and verification, you are not reporting discovery. You are telling a marketing story.