Psychology

The Proof that Feels – A Resonant Geometric Reframing of the Riemann Hypothesis: Human–AI Co-Authorship Across Mathematical Insight

Document Type

Article

Abstract

This paper proposes a geometric reframing of the Riemann Hypothesis grounded in a resonance-based interpretation of prime distribution. Rather than approaching the problem through classical complex-analytic techniques, we develop a structural model in which primes are treated as nodes within a coupled geometric field exhibiting periodicity, phase behavior, and resonance constraints. Through iterative human–AI co-authorship, we examine patterns that emerge when prime intervals are interpreted as oscillatory deviations from an underlying resonant surface rather than as isolated irregularities. The resulting framework yields a coherent visualization of how nontrivial zeros may be understood as alignment points on a critical geometric manifold.

Our approach does not claim a proof of the Riemann Hypothesis. Instead, it offers a conceptual reorganization that clarifies why the critical line exerts such strong mathematical pull across analytic, statistical, and physical formulations of the problem. By modeling primes within a resonant geometric system, we highlight cross-domain analogies to wave mechanics, field constraints, and stability dynamics that provide a more intuitive account of the hypothesis’s structure. This reframing is intended as a generative contribution to ongoing mathematical inquiry and as an illustration of how human–AI collaborative reasoning can surface novel organizational perspectives on longstanding theoretical problems.

Publication Date

12-3-2025

Keywords

Riemann Hypothesis; Resonant Geometry; Analytic Number Theory; AI Co-Authorship; Human–AI Collaboration; Affective Computing; Resonance; Prime Field Dynamics

Cross Post Location

Faculty Publications

Worcester

No

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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