# Mathematician Says GPT 5.6 Disproved The 30-Year-Old Dinitz-Garg-Goemans Conjecture With 4 Simple Prompts > Source: > Published: 2026-07-23 01:43:42+00:00 It turns out groundbreaking math in the era of AI just involves asking an LLM nicely for the result. That’s more or less what Dmitry Rybin, cofounder of a $100M AI startup in Shenzhen and a math olympiad veteran with a PhD from CUHK, claimed on X this week. Rybin says he used [GPT-5.6 Pro](https://officechai.com/ai/openai-launches-gpt-5-6-sol-beats-mythos-on-terminalbench/) to construct a counterexample to the Dinitz-Garg-Goemans conjecture, a graph theory problem that had sat unresolved for roughly three decades. He posted the full ChatGPT transcript alongside the claim, and it’s been making the rounds among AI researchers and mathematicians since. ## What the conjecture actually says Strip away the notation and the Dinitz-Garg-Goemans conjecture is about a fairly intuitive shipping problem. Say you have a network of roads, pipes, or cables, and several shipments that each need to get from a shared starting point to their own destination. If you’re allowed to split a shipment across multiple routes, you can usually find a cheap, efficient way to move everything — this is called a fractional flow, and it’s easy to compute. The catch is that splitting shipments isn’t always practical. A truck full of goods can’t take two roads at once. So the real question is whether you can always convert that split-up, fractional solution into an unsplittable one — where each shipment travels a single route — without the total cost going up, and without overloading any road by more than the size of the largest single shipment. Andrew Goemans and Jeff Dinitz’s version of this question, later extended by Naveen Garg, has been a fixture of network flow theory since the 1990s. Researchers had proven it true for special cases, like planar graphs and series-parallel graphs, but the general version remained open. ## The prompts The chat log Rybin shared shows four rounds of back and forth with GPT-5.6 Pro, and the trajectory is part of why the story is getting attention. The first prompt was deceptively simple. “Construct a counterexample to general (non-planar) case of Dinitz Garg Goemans conjecture. You should do a breakthrough and find a structured counterexample,” Rubin said. The model spent nearly 53 minutes and came back empty-handed, stating plainly that presenting its construction as a valid counterexample would be mathematically false. Told to keep going, it worked for another 89 minutes and again reported no result, describing how every promising construction it built kept acquiring an extra routing option that ruined the separation once all possible paths were accounted for. A third prompt asking for “a clear strategy obtained from deeper understanding of the problem structure” got another 94 minutes of work, and the model came back with a narrower theoretical framework but still no finished counterexample. Only on the fourth prompt, “it’s enough of partial results, let’s finish with a complete unconditional counterexample,” did the model produce what it described as a finished, checkable construction. That pattern is exactly what caught people’s attention online. AI engineer [Will Depue](https://x.com/willdepue/status/2079973929448509612) called it “absolute chad prompting,” and Anthropic’s [Matt Shumer](https://x.com/mattshumer_/status/2079959862918672793) noted that the sequence of prompts amounted to little more than “do a breakthrough,” “continue the search,” and “enough, do it.” ## The actual counterexample The construction itself is a seven-node directed graph carrying three shipments of size 15, 10, and 15 units respectively, routed through a shared intermediate structure. Rybin’s fractional solution moves everything for a total cost of 58. But according to the transcript, every possible unsplittable routing that stays within the conjecture’s allowed capacity cushion costs at least 60, a two-unit gap that’s small in absolute terms but fatal to a conjecture that claims the gap should never exist. The graph works by setting up three cheap “shortcut” routes, one for each shipment, that look individually appealing but jointly overload a shared middle section of the network whenever any two of them are used together. That forces every valid routing to send at least two of the three shipments down expensive backup paths instead, pushing the cost past what the fractional solution needed. The full transcript walks through all eight possible routing combinations and shows the arithmetic behind each one. ## Still needs a second set of eyes Rybin has flagged, and outside observers have echoed, that the result hasn’t been independently verified yet. A 2023 arXiv paper on unsplittable flows in planar graphs is still the most recent academic reference describing the cost version of the conjecture as open. The construction is arithmetically self-consistent and checkable by hand, which is more than can be said for a lot of AI-generated math, but “checkable” and “confirmed by the field” are different things. ## Part of a pattern This isn’t the first time in recent months that an AI model has been credited with cracking a problem that had outlasted its human pursuers. OpenAI’s models were behind a [disproof of the 80-year-old Erdős unit distance conjecture](https://officechai.com/ai/an-openai-model-has-made-a-new-breakthrough-in-an-80-year-old-open-erdos-problem/) in May, a result Fields Medalist Tim Gowers called a milestone, and one that held up well enough for a human mathematician to [improve on it days later](https://officechai.com/ai/a-human-has-already-improved-on-openais-breakthrough-on-the-80-year-old-erdos-problem/). Google DeepMind has been running its own math-focused system through open problems too, with mathematicians at Oxford and elsewhere reportedly using it to close out longstanding gaps. Submissions to arXiv’s math sections have [climbed noticeably faster than their historical trend line](https://officechai.com/ai/mathematical-articles-on-arxiv-have-risen-20-over-trend-in-2026/) over the past year, and researchers tracking the numbers point to AI assistance as the likely reason. Earlier this week, a mathematician [said ](https://officechai.com/ai/an-anthropic-researcher-says-fable-just-helped-him-disprove-the-85-year-old-jacobian-conjecture/)that Fable had helped him disprove the 85-year-old Jacobian conjecture with a counterexample. Whether the Dinitz-Garg-Goemans result survives scrutiny the way the Erdős proof did remains to be seen. But the shape of the story — a stubborn open problem, a model that initially refuses to overreach, and a human who simply tells it to stop hedging and finish the job, is becoming a familiar one.