New from Alain Connes. His "Letter to Riemann" is fun.
https://arxiv.org/abs/2602.04022
He is honest about the fact we cannot prove the RH, and that it's not clear if his preferred approach will be the way, but also:
"Our discovery of a large class
of functions directly related to the Weil quadratic form and with zeros provably on the critical line, combined with the extraordinary numerical evidence linking truncated Euler products to the actual zeros of zeta, suggests that Riemann’s original insights may contain more power than previously realized. The accuracy achieved using only primes less than 13—with errors as small as \(2.6 \times 10^{-55}\)—cannot be dismissed as coincidence"
Apparent numerical coincidences in number theory like this at very minimum demand an explanation.
theHigherGeometer
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2026-02-05 06:14:51 UTC
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"content": "New from Alain Connes. His \"Letter to Riemann\" is fun.\n\nhttps://arxiv.org/abs/2602.04022\n\nHe is honest about the fact we cannot prove the RH, and that it's not clear if his preferred approach will be the way, but also: \n\n\"Our discovery of a large class\nof functions directly related to the Weil quadratic form and with zeros provably on the critical line, combined with the extraordinary numerical evidence linking truncated Euler products to the actual zeros of zeta, suggests that Riemann’s original insights may contain more power than previously realized. The accuracy achieved using only primes less than 13—with errors as small as \\(2.6 \\times 10^{-55}\\)—cannot be dismissed as coincidence\"\n\nApparent numerical coincidences in number theory like this at very minimum demand an explanation.",
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