More than two thirds of the zeros of the Riemann zeta function are simple and on the critical line

The talk will be aimed at a general mathematical audience

The Riemann Hypothesis asserts that all non-trivial zeros of the Riemann zeta function lie on the critical line Re(s)=1/2. In the absence of a proof of the Riemann hypothesis, a fundamental problem has been to determine what proportion of the zeros can be shown to lie on the critical line.

Three weeks ago, an internal research version of Claude developed by Anthropic announced a breakthrough result, later verified by Anthropic mathematicians Levent Alpöge and Ralph Furman, showing unconditionally that more than (67.25%) of the zeros are simple and lie on the critical line. Their argument is technically intricate and its main mechanism is not transparent. I will present a new, shorter and conceptually simpler proof of this result.