Structural Gaps in Unsolved Mathematics: A Survey of Key Problems — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Survey of unsolved problems (Collatz, Millennium Problems, Riemann Hypothesis, Navier-Stokes, P vs NP, Goldbach, twin primes) reveals no new solved equations, but exposes structural gaps in number theory and analysis. | MATH: Collatz: f(n)=n/2 if even, 3n+1 if odd — no closed form, no cycle proof. Riemann Hypothesis: ζ(s)=0 ⇒ Re(s)=1/2. Navier-Stokes: ∂u/∂t + (u·∇)u = -∇p + ν∇²u — existence/smoothness unproven in 3D. P vs NP: no polynomial-time algorithm for NP-complete problems proven impossible. Goldbach: every even integer >2 = sum of two primes — unproven. Twin primes: infinitely many p such that p+2 prime — unproven. | CONNECTION: Collatz dynamics show no stable ratio; but the 3n+1 map's orbit lengths statistically cluster near log(n) with a constant ~1.253 (Terras' constant), not a golden ratio. Riemann zeros align with a 1/2 critical line — a symmetry axis, but not a crystallographic one. No 0.382, 0.618, 0.786, 1.618, 2.618, or base-60 appears in any of these problems' 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: W7212177752
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