This work formalizes why 'human' mathematics is distinct from the space of all valid deductions using information-theoretic compression measurements on MathLib.
March 24, 2026
Original Paper
Compression is all you need: Modeling Mathematics
arXiv · 2603.20396
The Takeaway
It provides empirical evidence that human mathematical value is tied to exponential expansiveness through hierarchical compression. This offers a quantitative metric for 'mathematical interest' that could guide automated theorem provers toward discovering proofs humans actually care about.
From the abstract
Human mathematics (HM), the mathematics humans discover and value, is a vanishingly small subset of formal mathematics (FM), the totality of all valid deductions. We argue that HM is distinguished by its compressibility through hierarchically nested definitions, lemmas, and theorems. We model this with monoids. A mathematical deduction is a string of primitive symbols; a definition or theorem is a named substring or macro whose use compresses the string. In the free abelian monoid $A_n$, a logar