What question did this study set out to answer?

The aim is to provide a geometric proof of the Riemann Hypothesis through symmetry and trajectory analysis.

April 3, 2026Open Access

A Geometric Approach to the Riemann Hypothesis based on Four-fold Symmetry and Trajectory Monotonicity

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Demonstrates a geometric proof of the Riemann Hypothesis, suggesting fundamental insights into number theory.

The aim is to provide a geometric proof of the Riemann Hypothesis through symmetry and trajectory analysis.
Analyzed the structure of the Riemann zeta function $(s)$ for symmetry and dynamics.
Defined a new functional $I(s)$ exhibiting four-fold symmetry.
Utilized a dynamic exclusion boundary $R(t)$ to analyze the positioning of zeros.
Demonstrated that the zeros are geometrically constrained onto the critical line $ = 1/2$.
Validated the geometric framework through numerical simulations involving 10,000 points.

YilWook Kim (2026) studied this question.

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