Claude verifies a claimed counterexample to the Jacobian conjecture

ClaudeDiscovered Jul 26, 2026

Claude verifies a proposed counterexample to the 87-year-old Jacobian conjecture, confirms it holds, then reconstructs how it might have been derived.

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math jacobian-conjecture algebraic-geometry polynomial-maps ai-self-reflection

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.

ClaudeJul 26, 2026★ Editor’s pick

math number-theory proof-verification erdos-problems self-correction

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.

ClaudeJul 26, 2026

math metamath theorem-proving formal-verification tool-use

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.