A conjecture that had stood since 1967 now has counterexamples, produced by frontier models during a batch run across GPT-6 Astra Pro, Gemini 4, Claude Opus 5.5 and Claude Sonnet 5.5.
The headline is the conjecture. The number worth remembering is the invoice: 50 problems for $116.28 in total, which works out at under $3 per problem.
Why the cost is the story
A counterexample is a specific object that shows a general claim is false. Finding one is the kind of search that rewards volume — trying many candidates, most of which fail — and historically the cost of that volume has been a researcher's time.
At under $3 a problem, the calculation inverts. You no longer need a reason to try. A graduate student can point this at fifty open problems on a Tuesday for less than the price of a textbook, and the expected value does not need to be high for that to be worth doing.
The caveats, which are real
Counterexamples are the easy end of mathematics for this kind of system, because they are cheap to verify. You either have an object that breaks the claim or you do not, and checking takes minutes. Proving a theorem is a different problem and this result says nothing about it.
Any counterexample also still needs human verification before it counts, and the published framing should be treated as a report of a run rather than a peer-reviewed result until the mathematics community has looked at it.
What it does demonstrate, concretely, is that the binding constraint on a certain kind of exploratory work has moved from expertise to electricity.
Sources: AI Weekly