A claim rippling through the AI and mathematics communities this week captures both the promise and the strangeness of the current moment: a researcher says he used OpenAI's GPT-5.6 Pro to disprove a graph-theory conjecture that had stood unresolved for roughly three decades — and that the decisive prompt was, more or less, "do a breakthrough." The result is genuinely interesting, and it is also, importantly, not yet confirmed. Both of those things need to be said in the same breath.
The claim comes from Dmitry Rybin, a math-olympiad veteran and AI-startup cofounder, who posted the full ChatGPT transcript on X on July 22. "Dinitz-Garg-Goemans conjecture is false," he wrote. "This graph theory problem was open for ~30 years." He shared a small directed graph and a two-line summary of why it breaks the conjecture, then invited the world to check his work.
What the conjecture actually says
Beneath the jargon, the Dinitz–Garg–Goemans conjecture is about a shipping problem. Imagine a network of roads or pipes and several deliveries that each need to travel from a shared starting point to their own destination. If you're allowed to split a delivery across several routes, you can usually route everything cheaply and efficiently — that's a "fractional" flow, and it is easy to compute. But splitting isn't always practical; a single truckload can't take two roads at once. The conjecture asked whether you can always convert that split solution into an unsplittable one — every delivery on a single route — without the total cost rising, and without overloading any road by more than the size of the largest single delivery. Proven for special cases like planar networks, the general version had resisted a proof or a counterexample since the 1990s.
Rybin's counterexample, as described in the transcript, is a seven-node directed graph carrying three shipments. Its fractional solution costs 58, but every allowed unsplittable routing costs at least 60 — a two-unit gap that is tiny in size yet fatal to a conjecture claiming no such gap should exist. The construction reportedly sets up three cheap "shortcut" routes that individually look attractive but jointly overload a shared middle section, forcing at least two shipments onto expensive backup paths.
The prompts that are getting all the attention
What turned a technical result into a viral story was how it was obtained. The chat log shows four rounds with the model. The opening prompt was blunt: "Construct a counterexample to general (non-planar) case of Dinitz Garg Goemans conjecture. You should do a breakthrough and find a structured counterexample." Notably, the model did not simply comply. It worked for nearly an hour and came back empty, stating that presenting its construction as a valid counterexample would be mathematically false. Pushed to continue, it labored another 89 minutes and again reported nothing. A third prompt asking for a deeper structural strategy yielded a narrower framework but still no finished answer. Only on the fourth prompt — "it's enough of partial results, let's finish with a complete unconditional counterexample" — did it produce what it called a finished, checkable construction.
That arc, a model that repeatedly refuses to overclaim and a human who simply keeps telling it to finish, is what observers seized on. One AI engineer called it "absolute chad prompting," and an Anthropic researcher noted the prompts amounted to little more than "do a breakthrough," "continue the search," and "enough, do it." To admirers it is a striking demonstration; to skeptics it reads a bit like a meme.
Why the caveats matter
Here is the part that separates careful reporting from hype: the result has not been independently verified. Rybin has said so himself, and outside observers have echoed it. The construction is arithmetically self-consistent and small enough to check by hand — the transcript walks through all eight routing combinations — which is more than can be said for a lot of AI-generated mathematics. But "checkable" and "confirmed by the field" are not the same thing. Until other mathematicians work through it and the wider community signs off, the honest description is that the conjecture has been claimed to be disproven, not that it definitively has been.
Part of a bigger pattern
The claim doesn't arrive in a vacuum, which is part of why people are taking it seriously despite the caveats. In May, an OpenAI model was credited with disproving the 80-year-old Erdős unit-distance conjecture, a result a Fields Medalist called a milestone — and one a human mathematician then improved upon within days, a sign it held up. Other labs' systems have been used to close longstanding gaps, and submissions to the mathematics section of the main preprint server have run noticeably above their historical trend this year, which researchers attribute partly to AI assistance. Just this week, another mathematician said a different model had helped him disprove the 85-year-old Jacobian conjecture.
Whether the Dinitz–Garg–Goemans result survives the same scrutiny remains to be seen. But the shape of the story is becoming familiar: a stubborn open problem, a model that at first refuses to overreach, and a human who tells it to stop hedging and finish the job. If it holds, it's another data point in a fast-moving shift in how mathematics gets done. If it doesn't, it's a reminder that in the age of AI, the burden of proof still belongs to the proof.
