Compression is all you need: Modeling Mathematics
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 logarithmically sparse macro set achieves exponential expansion of expressivity. In the free non-abelian monoid $F_n$, even a polynomially-dense macro set only yields linear expansion; superlinear expan...
| Authors | Vitaly Aksenov, Eve Bodnia, Michael H. Freedman et al. |
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| Primary category | cs.AI |
| Published | 20 March 2026 |
| Last updated at source | 20 March 2026 |
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