From Polymath to Systematic Discovery: Scaling Collaborative Math — E8 Intelligence Research

Abstract

FINDING: The Polymath Project demonstrates that large-scale online collaboration can crack hard problems (e.g., bounded prime gaps), with Tao's Equational Theories Project scaling this to systematic theorem discovery. MATH: \(H_m := \liminf_{n\to\infty}(p_{n+m}-p_n)\); twin prime conjecture ⇔ \(H_1=2\). Zhang proved \(H_1 \le 7\times10^7\); Polymath8 reduced to \(H_1 \le 246\) (unconditionally), \(H_1 \le 6\) under Elliott–Halberstam. No new constants like 0.618 appear — the core is additive combinatorics and sieve theory. CONNECTION: Prime gaps relate to modular arithmetic (base-60 resonates with Babylonian sexagesimal, but no direct link here). The reduction \(7\times10^7 \to 246\) is a ratio ~284,553 — not a golden ratio. However, the *structure* of admissible prime k-tuples maps to lattice/root-system constraints (e.g., \(H_m\) bounds are tied to the diameter of admissible sets, which are discrete geometric objects in \(\mathbb{Z}^m\)). No crystallographic symmetry or 0.382/0.6 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com