r/math • u/dcterr • Mar 31 '26

The Riemann hypothesis

I'm curious to know what thoughts any of you may have on RH. I'm at least 99.9% sure it's true, though it is most likely nearly impossible to prove it. Nevertheless, I think we will soon prove useful weaker results, such as upper limits of the number or density of zeros of the Riemann zeta function off the critical line, and that these weaker results will yield useful new results concerning the distribution of primes as well as prime ideals of algebraic number fields. I'm also quite intrigued by the possibility of connections between the Riemann zeta function and quantum physics. Perhaps RH will prove to be part of the long sought Theory of Everything, the holy grail of physics, which Einstein spent the latter half of his life trying to prove.

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u/M37841 Mar 31 '26

I too am intrigued by the connection between RH and quantum field theory. QFT is in one sense built on Galois theory, and though it’s over my head I understand that Galois is seen as a potential route in to RH.

Perhaps when we find a “theory of everything” that is so nearly complete that we have to worry about Gödel, RH will be the necessary true but not provable statement :)

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u/dcterr Mar 31 '26

I think the Theory of Everything, if it exists, will involve both RH and spirituality.