AI-Assisted Collaborative Mathematics Accelerates Proof Discovery — E8 Intelligence Research

FINDING: The Polymath Project demonstrates that large-scale collaborative mathematics, now augmented by AI-assisted experimentation, can accelerate proof discovery — notably in bounded prime gaps and equational theories — while the "Golden Square" episode explicitly invokes geometric construction. MATH: - Prime gaps: \(H_m := \liminf_{n \to \infty} (p_{n+m} - p_n)\). Zhang's breakthrough gave \(H_1 < 7\times 10^7\); Polymath8 reduced this to \(H_1 \le 246\) (unconditionally) and \(H_1 \le 6\) under the Elliott–Halberstam conjecture. - Equational Theories Project: systematic enumeration of identities in universal algebra, using automated theorem proving and SAT solvers — no single closed‑form constant, but the combinatorial explosion of equation sets is governed by finite group actions (symmetry groups of the free algebra). - Golden Square: likely a geometric construction involving a square and golden ratio — the episode title suggests \(\varphi = (1+\sqrt{5})/2 = 1.618\ldots\) Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com