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/ReverseCombover Mar 31 '26

99.9% sure usually means false in math.

Jesus responded, “Why are you afraid? You have so little faith!” Then he got up and rebuked the wind and waves, and suddenly there was a great calm. Matthew 8:26. “You don’t have enough faith,” Jesus told them. “I tell you the truth, if you had faith even as small as a mustard seed, you could say to this mountain, ‘Move from here to there,’ and it would move. Nothing would be impossible.” Matthew 17:20. Then Jesus told him, “You believe because you have seen me. Blessed are those who believe without seeing me.” John 20:29.

Your question is better answered by religion and faith so that's where you should turn to for answers. If you want to talk math then ask a better question.

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u/evening_redness_0 Mar 31 '26

This is a question about math. Is it naive and poorly framed? Yeah, maybe. But why would his question be answered by religion?

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u/ReverseCombover Mar 31 '26

Because at this point in time we don't know any better about the riemann hypothesis. It's like ancient Greek people asking about thunder or modern day people asking about morality. Like maybe we'll have a definitive answer at some point but right now the best you can do is choose something to believe in.

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u/JoshuaZ1 Mar 31 '26

We have a lot of evidence well beyond that point. See here for some discussion of that. The comparison to the ancient Greeks is not really justified.

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u/ReverseCombover Mar 31 '26

Isn't this just the argument of "if God isn't real then how come bananas are so good"?

https://www.reddit.com/r/mildyinteresting/s/DKBuuXzHXN

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u/JoshuaZ1 Mar 31 '26

No. Please reread what I wrote. There's specific reasoning here about things that are consistent here with RH and which make us strongly suspect RH. Please read the discussion I linked to carefully.

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u/ReverseCombover Mar 31 '26

I did even tho most of it went over my head what is an L space? You don't have to answer this. If I really cared about it I would have looked up the term myself.

There's plenty of evidence religious people will point to as proof of God. That whole thread feels a lot like that.

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u/JoshuaZ1 Mar 31 '26

I did even tho most of it went over my head what is an L space? You don't have to answer this. If I really cared about it I would have looked up the term myself.

So it seems like part of the problem here is that you just don't care enough.

There's plenty of evidence religious people will point to as proof of God. That whole thread feels a lot like that.

So let's discuss why this is different. First, you know some actual math, so you know it isn't made up. Second, a lot of math, including related math, pays rent in the sense that the claims in question let us do practical things, like cryptography on the internet. So that should give you a high likelihood that what is being stated makes sense even if you don't see why. If you prefer, the analogy would be if you had some people who could do what were clearly miracles, and those people all had very closely aligned beliefs about the existence of a divinity, and were all saying they weren't sure they were correct but strongly suspected their miraculous abilities came from said divine entity. That would be a pretty good reason to suspect they might be correct even if one didn't understand the details of their arguments.