GPT-5.6 Pro reportedly finds a counterexample to a 30-year graph theory conjecture
量子位 · wechat · 2026-07-23
A QbitAI post says GPT-5.6 Pro helped find a counterexample to the long-standing Dinitz-Garg-Goemans conjecture in graph theory. The task was framed as a routing problem: when flows that can be split must instead stay indivisible, can you keep congestion within bounds without making the total cost worse?
According to the write-up, the model produced a 7-node, 9-edge directed graph that breaks the conjecture. The counterexample shows that the two desired constraints cannot both hold at once: to respect the load limits, you end up with a minimum cost of 60, while the conjecture expected the cost to stay at 58.
The most striking part is the interaction itself. Researcher Dmitry Rybin reportedly used just four prompts totaling 58 English words, repeatedly asking the model to keep searching and produce a complete, unconditional counterexample. The model initially failed several times, then eventually converged on the valid construction.
The post uses this to illustrate a broader point: AI-assisted math work is becoming capable of discovering compact counterexamples with surprisingly little prompting, provided the human knows how to keep pushing instead of settling for partial results.
Related event: GPT-5.6 Pro Claims Math Breakthroughs, But Faces Hallucination Backlash(11 posts)→
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