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.
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Proving A over root(A) equals root(A) in Metamath, then a self-audit
The user guides Claude through a Metamath tool to formally prove A over root(A) equals root(A), then has it explain its own search-syntax mistakes.
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.
Claude verifies a claimed counterexample to the Jacobian conjecture
Claude verifies a proposed counterexample to the 87-year-old Jacobian conjecture, confirms it holds, then reconstructs how it might have been derived.
Why Lebesgue integration needs the f+/f- split but Riemann doesn't
Explains why Lebesgue integration must split functions into positive and negative parts to avoid infinity minus infinity, a trap Riemann integration never hits.