What's this about?
Two separate events, one theme. First, researcher Dmitry Rybin announced that the Dinitz-Garg-Goemans conjecture — a graph-theory problem that had been open for about 30 years — is false, and the counterexample was found in a ChatGPT session with GPT-5.6 Pro. Second, Fields Medalist Terence Tao published his own raw ChatGPT conversation in which he digs into last week's AI-found counterexample to the Jacobian conjecture, and that transcript became the top Hacker News story of the day.
What exactly is a "conjecture"?
A conjecture is a mathematical claim that experts believe is probably true but nobody has managed to prove or disprove. Some sit unresolved for decades. "Disproving" one means finding a single concrete counterexample — like finding one black swan after 30 years of people believing all swans are white. What's striking here is that the counterexample hunting was done by an AI chatbot, steered by a human expert.
What's the community saying?
- The prompts were shockingly lazy — "do a breakthrough", "continue the search", "enough, do it" — raising the question of how much credit belongs to the human vs. the model.
- Reading Tao's transcript, many said the AI behaves less like a tool and more like a colleague — and that watching a world-class expert prompt is itself a masterclass.
- Skeptics asked whether these results are revolutionary or just bricks in the wall; mathematicians answered that counterexamples to famous conjectures genuinely redirect research.
- A running joke: even Terence Tao pays for the Pro tier ("I've activated Pro. Can you continue…" — "another satisfied customer").