A curated collection of rigor-audited proofs and proof repairs.
ProofZoom is a curated archive of mathematical proofs that have been carefully examined, logically audited, and—where necessary—repaired. Many standard proofs in textbooks and lecture notes contain small gaps, illicit steps, or quiet handwaving that are usually harmless, but pedagogically damaging. The goal of ProofZoom is to slow down, zoom in, and make every step honest.
Complex functions and Conformality
A clarifying note explaining how complex differentiability controls local angle behavior, and how parametrized curves behave under complex maps—carefully, step by step.
Lemma 1 — Existence of the complex line integral on rectifiable curves
A standard proof often “inherits” tags under refinement (not a legitimate tagged partition). We diagnose the issue and give a fully tag-honest repaired proof.
Each ProofZoom entry contains: (i) a commonly taught proof (or proof skeleton), (ii) identification of a subtle logical gap or illicit step, (iii) a diagnosis explaining why it is illegitimate, (iv) a repaired proof that respects all definitions, and (v) brief commentary on what changed and why it matters.
Proofs are developed through careful human analysis in collaboration with an AI proof-analysis and writing system.