Sample open problems instead of selecting successes
The OpenConjecture study examines mathematical conjectures drawn from recent arXiv papers. Rather than starting with a collection of celebrated successes, the authors sample two hundred conjectures and apply frontier GPT models over three passes using a reproducible protocol.
The purpose is to study the character of the resulting output. The paper explicitly does not attempt expert verification of every candidate solution. That choice is essential when interpreting its reported numbers: a model proposing a resolution is different from a mathematician or formal checker establishing that the resolution is correct.
A proposed answer may solve a different problem
The models produce candidate solutions for roughly sixty percent of the sampled conjectures, with counterexamples about 1.3 times as common as proofs. Those are output categories under the study protocol, not a verified claim that the models solved sixty percent of open mathematics problems.
The authors inspect whether proposed resolutions follow the intended statement, relate appropriately to existing literature or exploit an error or underspecification. Some answers sit outside what the original authors apparently intended, while some proofs closely follow known results. The paper also identifies proposals with at least moderate estimated novelty.
Keep correctness and contribution separate
A useful evaluation therefore needs more than a single success label. A candidate can be interesting to inspect without being correct, and a correct argument can contribute less novelty than its presentation suggests. Attribution and fidelity to the intended problem need their own assessment.
For a researcher following AI mathematics, retain the original conjecture alongside the proposed proof or counterexample and its cited dependencies. Ask what changed between passes and which validation was actually performed. The study provides a structured way to examine generated mathematical work; it does not replace expert review with a headline solve percentage or certify every candidate as a new result.
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