Optimising Metamath Proofs for Human Working Memory

Abstract

Mathematical proofs vary in legibility. While most proof optimisation techniques seek to minimise proof size, the strategic reordering of inferences can reduce the working memory demand of proof checking without altering overall size. Metamath serves as a prime case study for this approach: its verification architecture requires proof steps to be ordered in a manner that prioritises algorithmic efficiency over readability. In this paper, we introduce algorithms to minimise both peak and cumulative memory consumption, applying the latter as a novel proxy for sustained human cognitive effort. We achieve this by representing proofs as directed acyclic graphs and modelling their execution as a p..