That arxiv comment is hilarious
A proof of the Riemann Hypothesis on the horizon.
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https://arxiv.org/pdf/2111.02792.pdf
the plot thickensAndre Unterberger is actually a legitimate mathematician - PhD 1971, student of Laurent Schwartz. Not wildly successful but has done reasonable work on functional analysis. He is close to 80 years old, though.
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There are currently 4 teams of people, all well-known and respected, competing towards being the first to have a proof of the Riemann Hypothesis. A proof is in sight in the next few years. Stay tuned!
Next few years is now. What’s the status?
All hype. There has not been one single good idea for how to approach the Riemann hypothesis since it was formulated, and it'll probably remain that way for a while.
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All hype. There has not been one single good idea for how to approach the Riemann hypothesis since it was formulated, and it'll probably remain that way for a while.
I think the Deligne/Grothendieck proofs of Weil conjectures is a good idea.
It's a neat analogy, but that's all it is. An analogy. You need to be able to say something concrete about the RH over number fields, and nobody has the slightest clue what the first step here should be.
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It's a neat analogy, but that's all it is. An analogy. You need to be able to say something concrete about the RH over number fields, and nobody has the slightest clue what the first step here should be.
What about this then?
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It's a neat analogy, but that's all it is. An analogy. You need to be able to say something concrete about the RH over number fields, and nobody has the slightest clue what the first step here should be.
What about this then?
https://www.cambridge.org/core/journals/forum-of-mathematics-pi/article/de-bruijnnewman-constant-is-nonnegativeTao actually commented on this. The paper confirms a heuristic about the problem that if the RH is true, it's "barely so". It does not give us a concrete strategy but just says that the problem, if true, is as hard as possible to prove. It's a nice result though for giving us more context on the problem, which is better than nothing. See his post starting with "added later"
https://terrytao.wordpress.com/2018/01/19/the-de-bruijn-newman-constant-is-non-negativ/
Btw there're many reformulations of the RH besides the one you linked, even as a deceptively "simple" looking integral. See
https://mathoverflow.net/questions/39944/collection-of-equivalent-forms-of-riemann-hypothesis
So far though, it hasn't gave anyone good ideas.
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Seems the RH could actually be false, after all: https://figshare.com/articles/preprint/Untitled_Item/14776146
A remarkable paper. During its 14-version arXiv history it seems to have oscillated between proof and and disproof of RH.
For completeness, let's not forget the 21 versions (so far) of another proof: https://arxiv.org/abs/1708.02653
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Seems the RH could actually be false, after all: https://figshare.com/articles/preprint/Untitled_Item/14776146
A remarkable paper. During its 14-version arXiv history it seems to have oscillated between proof and and disproof of RH.
For completeness, let's not forget the 21 versions (so far) of another proof: https://arxiv.org/abs/1708.02653
Oh, the HRM version. Why is he still posting versions on arXiv? Didn't even the retraction of his paper convince him?