AI-Assisted Polymath Collaboration: From Bounded Prime Gaps to Equational Theories — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Polymath collaboration is shifting from pure problem-solving to AI-assisted experimental mathematics, with Tao's Equational Theories Project scaling collaborative proof-checking; the bounded-gaps prime result remains the flagship quantitative achievement. | MATH: $H_m := \liminf_{n \to \infty} (p_{n+m} - p_n)$; twin prime conjecture ⇔ $H_1 = 2$; Zhang's breakthrough gave finite bound for $H_1$ (later reduced to 246 via Polymath8); no new constants or ratios emerge from these sources. | CONNECTION: None directly stated — no golden ratio, base-60, or crystallographic symmetry appears in the listed content. The prime gaps $H_m$ relate to additive number theory, not geometric harmony; the "Golden Square" title is a video branding, not a mathematical ratio finding. | DEPTH: 4 — The Polymath methodology is sociologically profound for collaborative proof, and $H_m$ is a deep arithmetic invariant, but the provided sources offer no new geometric or universal-structure insight; the Tao Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221982429
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