2018-The_Riemann_Hypothesis.pdf


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2024-03-08
ing techniques solve Abel 机器 methods universality power Attack motivation
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THE RIEMANN HYPOTHESIS
MICHAEL ATIYAH
1. Introduction
In my Abel lecture [1] at the ICM in Rio de Janeiro 2018, I explained how to solve a
long-standing mathematical problem that had emerged from physics. The problem was to
understand the fine structure constant α.
The full details are contained in [2] which has been submitted to proceedings A of the
Royal Society. The techniques developed in [2] are a novel fusion of ideas of von Neumann
and Hirzebruch. They are sophisticated and powerful, based on an infinite iteration of
exponentials, while having an inherent simplicity.
Attacking the mystery of α was the motivation, but the power and universality of the
methods indicated that they should solve other hard problems, or at least shed new light
on them if they are insoluble. In expanding my Abel Lecture for the ICM Proceedings I
speculated that the techniques of [2] might lead to the new subject of Arithmetic Physics.
The Riemann Hypothesis RH is the assertion that ζ(s) h


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