Freedman Seminar

Speaker: Mike Freedman, Harvard CMSA

Title: Compression Is All You Need: Modeling Mathematics

Abstract: The talk will exposit a recent eponymous arXiv posting with coauthors Vitaly Aksenov, Eve Bodnia, and Mike Mulligan. The approach is to think like a physicist and model a seemingly complex bit of reality: mathematics, by a simple toy model where exact computations can be carried out and then compared with observation.  The models are finitely generated monoids and the data is derived from MathLib a large Lean-based repository. The hierarchical nature of definitions and lemmas in math is modeled by adding redundant generators to the monoids – think of the powers of 10 within the natural numbers which support place notation. Place notation confers an exponential compression of how we describe numbers; exploration of MathLib shows that this theme persists to (human) mathematics writ large. We hope that the observables we describe will help our agents navigate to interesting mathematical destinations.