AI-Augmented Formal Verification Replaces Polymath in Collaborative Mathematics — E8 Intelligence Research

FINDING: The frontier of collaborative mathematics has shifted from human-only "Polymath" crowdsourcing to AI-augmented, large-scale formal verification — Tao's Equational Theories Project (ETP) is the current exemplar, mapping the implication graph of equational laws in magmas. MATH: - ETP core object: the set of equational laws in a single binary operation (*), e.g. x*(y*z) = (x*y)*z (associativity), x*y = y*x (commutativity), x*(y*z) = (x*y)*(x*z) (mediality). - Central quantity: the implication relation E1 ⇒ E2 over ~4,694 distinct equations (after symmetry reduction from a larger raw set), yielding a directed graph with ~22 million candidate implications to resolve. - Key structural result: the implication graph is not a partial order — it contains cycles (equivalence classes) and a large "anti-implication" frontier. The number of distinct equivalence classes and the diameter of the implication poset's condensation are the primary combinatorial invariants. - Formal verification Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com