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.
Claude
#proofs
9 entries with this tag.
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.
Claude★ Editor’s pick
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.
Claude★ Editor’s pick
Does a knowledge ontology dodge the Münchhausen trilemma?
A user argues all certain knowledge is stipulated definitions in an inheritance hierarchy, working through the Münchhausen trilemma turn by turn.
Claude
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.
Claude
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★ Editor’s pick
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.
Claude
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.
Claude
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.
Claude