ChatGPT cracks 30-year-old math conjecture with four prompts
Get the Tech newsletter
Daily tech — startups, AI labs, chips, the launches that shape the next decade. Free.
- Dmitry Rybin, co-founder of AI startup Autokernel, posted a counterexample on X disproving the 30-year-old Dinitz-Garg-Goemans conjecture in graph theory, which had asked whether a logistics-style splitting problem can always be converted to a non-splitting one without increasing cost
- ChatGPT 5.6 Pro cracked the problem in 5.5 hours using only four prompts under 60 words total, with the initial prompt instructing the AI to "do a breakthrough and find a structured counterexample" and the remaining three prompting it to continue searching
- Chris Bowman-Scargill at the University of York noted a running joke in mathematics that every graph-theory conjecture is false, because structural behavior can shift dramatically once one or two vertices are added — explaining how such conjectures slip past human scrutiny
- Abhishek Saha at Queen Mary University of London said AI is "already superhuman" at some mathematical tasks and there is "a fair bit of low-hanging fruit," but it cannot yet build the theory needed for the deepest open conjectures
- Alexander Yong at the University of Illinois Urbana-Champaign predicted AI will soon prove many conjectures through "superhuman energy in knowing the literature and trying many things at a prompt," leaving surviving conjectures as the genuine goals for human innovation
- AI math breakthroughs have piled up in recent months: an OpenAI model cracked a decades-old Erdős conjecture in May, an AI found a counterexample to the nearly century-old Jacobian conjecture earlier this week, and users claimed solutions to a Graffiti conjecture and another graph theory problem the same day
Why it matters: Mathematicians like Abhishek Saha acknowledge AI is "already superhuman" at certain tasks and the field has "a fair bit of low-hanging fruit" ripe for AI to clear, meaning the bottleneck on routine counterexamples has shifted from human effort to knowing which problems to point AI at. The consensus among researchers is that AI will handle the scrappy search work while humans focus on the deeper theoretical challenges that survive AI scrutiny — reframing the profession's near-term labor allocation.
