GPT-5.6 Pro falsifies a 30-year graph theory conjecture as Sol+Codex solves 6 Erdős problems
新智元 · wechat · 2026-07-24
GPT-5.6 Pro and Sol are used to break a 30-year graph theory conjecture and solve six open problems
A new Chinese article claims GPT-5.6 Pro produced a counterexample to the Dinitz-Garg-Goemans conjecture in graph theory, turning a 30-year-open cost-version problem into a false statement. The counterexample uses three terminals with costs structured so that any integral solution must pay at least 60, while a fractional solution reaches 58.
The same piece also says Shouqiao Wang used GPT-5.6 Sol + Codex to solve 6 of 13 attempted open Erdős problems in 5 days, including one that ran for 32 hours. His workflow emphasized:
- selecting problems mathematicians were already actively discussing,
- precisely redefining what counts as a solution,
- and using adversarial agents to attack each candidate proof before finalizing it.
The article frames these cases as evidence that AI is becoming a serious research partner in mathematics, and speculates about the implications for future human-only prizes like the Fields Medal.
Related event: GPT-5.6 Pro Reportedly Refutes 30-Year Graph Theory Conjecture(5 posts)→
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