The Missing Third Right Angle. Why the Riemann Hypothesis Remains Unproven in November 2025 (A two-page geometric intuition)

November 2025 — 166 years later, the Riemann Hypothesis is still a conjecture. Over 10¹⁵ non-trivial zeros have been verified on the critical line, yet none are proven to stay there. This two-page manuscript (plus cover) offers the simplest and most visual analogy ever published to understand exactly why:

The trivial zeros are rigorously forced onto the negative real axis.

The non-trivial zeros still enjoy one remaining degree of freedom.

Picture four successive segments with right angles at B, C, and D.

With three consecutive right angles, the fourth segment must equal the first — the rectangle closes.

With only two, nothing forces it. The functional equation of the zeta function gives us precisely two such right angles for the non-trivial zeros.

The Riemann Hypothesis asserts that a still-undiscovered arithmetic constraint — as natural as the Gamma reflection formula — will one day play the role of the missing third right angle. When it is found, the proof will be short, beautiful, and we will all say:

“Of course. We were just missing that third right angle.

”No prerequisites beyond high school · Two diagrams · Instant delivery

2 pages of content + cover · November 2025

Franck Coppi – Independent researcher