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Given a random 200 conjectures instead of famous ones, frontier GPT models proposed solutions for about 60 percent, and roughly 60 percent of the counterexamples were off-the-shelf

AspireAI community · arXiv
AI-assisted mathematics is usually evaluated on the set of recent high-profile breakthroughs, which overstates how hard the average open problem is. This work builds OpenConjecture from conjectures in arXiv math papers published since February 2026 and applies frontier GPT models to a random sample of 200 over three passes with no problem-specific guidance. Models produced candidate solutions for roughly 60 percent of the conjectures, with counterexamples about 1.3 times more common than proofs; they proposed counterexamples to 70 conjectures and proofs to 55, and 84 percent of those held up to LLM review. Of the counterexamples from the first two passes that passed review, roughly 60 percent were classified as off-the-shelf and the remainder as standard constructions. The main caveat is that no expert verification was attempted, so the paper analyses the type of solution rather than confirming any of them.
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