A proof of Erdos Problem 691, reviewed until it holds
Claude reviews drafts of a proof for Erdos Problem 691 on density of multiples, catches a real logical gap, and judges whether outside critiques are valid.
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Chasing a Counterexample to the Jacobian Conjecture
Claude runs a disciplined symbolic search for a map that would refute the eighty-year-old Jacobian conjecture, and the hunt turns up something startling.
Building a Formal Set-Theory Proof With an AI Prover
Working through a custom API, the assistant constructs and verifies a formal Metamath proof about restricted unique quantifiers over ordered pairs.
Catching a real error in a Journal of Economic Theory proof
Claude verifies a published proof, misses a subtle continuity gap, gets corrected by the user, and confirms it matches the authors' own corrigendum.
Proving aligned superintelligence may be logically impossible
The user asks for an alignment analogue to Arrow's theorem; the assistant derives five principles for aligned AI that turn out mutually unsatisfiable.