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This survey examines Alain Connes's program addressing the Riemann Hypothesis through noncommutative geometry and its unifying frameworks.

July 14, 2026Open Access

Noncommutative geometry and the Riemann Hypothesis: a survey of ten papers in Connes's program (1998—2026)

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This survey examines Alain Connes's program addressing the Riemann Hypothesis through noncommutative geometry and its unifying frameworks.
Survey of ten papers spanning from 1998 to 2026 focusing on noncommutative geometry and the Riemann Hypothesis
Analysis of foundational works and the realization of critical zeros as a spectrum
Evaluation of geometric objects and their implications on the Riemann Hypothesis framework
The foundations of Connes's approach establish the zeros as an absorption spectrum
A spectral realization of the zeros is numerically verified through a geometric framework
The definitive positivity mechanism remains unresolved, indicating gaps in the current framework

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Survey reviews ten papers discussing Connes's noncommutative geometry framework for the Riemann Hypothesis, highlighting ongoing challenges.

Guo Chen (2026) studied this question.

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Survey reviews ten papers discussing Connes's noncommutative geometry framework for the Riemann Hypothesis, highlighting ongoing challenges.