Collatz Unproven, Hilbert Undecidable, Mizar Formalizes Proofs — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Collatz Conjecture remains unproven; Hilbert's Decision Problem proven undecidable by Turing; Mizar library formalizes proofs. | MATH: Collatz: f(n) = n/2 if n even, 3n+1 if n odd; no closed-form solution or proof of convergence for all n. Hilbert's Entscheidungsproblem: no algorithm can decide truth of all mathematical statements (Turing 1936). Mizar: >50,000 theorems, >10,000 definitions formalized. | CONNECTION: No direct geometric ratios or symmetries emerge from these findings. Collatz involves modular arithmetic (mod 2) and iterative dynamics, not harmonic ratios. Undecidability is a logical/computational boundary, not a geometric constant. Mizar is a database, not a discovery. | DEPTH: 2 — These are foundational results in computability and open problems, but they contain no new equations, constants, or geometric patterns relevant to the requested analysis. The findings are meta-mathematical, not mathematical essence. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203926695
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