Polymath8's Collaborative Reduction of Prime Gap Bounds — E8 Intelligence Research

Abstract

FINDING: Polymath project's most concrete mathematical output is the bounded-gaps-between-primes collaboration, which refined Zhang's breakthrough on prime gaps. | MATH: $H_m := \liminf_{n \to \infty} (p_{n+m} - p_n)$; twin prime conjecture ⇔ $H_1 = 2$; Zhang proved $H_1 < 70,000,000$; Polymath8 reduced to $H_1 \le 246$ (unconditionally) and $H_1 \le 6$ under Elliott–Halberstam. | CONNECTION: Prime gaps are discrete — no direct golden-ratio or base-60 link. However, the *collaborative structure* mirrors lattice symmetry: many independent agents (nodes) contributing to a shared bound (lattice point), akin to root-system Weyl group actions on a shared space. The ratio 246/70,000,000 ≈ 3.51×10⁻⁶ is not harmonic. | DEPTH: 7 — profound for number theory and collaborative methodology, but not a geometric-harmony revelation. FINDING: Terence Tao on AI changing mathematics — AI enables rapid experimentation, pattern detection, and conjecture generation, shifting proof verification. | MATH: No Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com