Is it possible proof of RH is undecidable?
So what if it’s undecidable? Doesn’t mean you can’t prove or disprove it. You just can’t do it with a Turing machine. But even the dumbèst human is infinitely more powerful than a Turing machine.
A proof of the Riemann Hypothesis on the horizon.
-
Seems the RH could actually be false, after all: https://figshare.com/articles/preprint/Untitled_Item/14776146
This paper seems to be quite serious. I wonder why we haven't yet heard about it in the mainstream mathematical community.
The mathematical community is usually very careful with such claims, even if the paper concerned is correct.
-
Seems the RH could actually be false, after all: https://figshare.com/articles/preprint/Untitled_Item/14776146
This paper seems to be quite serious. I wonder why we haven't yet heard about it in the mainstream mathematical community.
It's not serious at all. The author's previous work consists entirely of incorrect papers on the Riemann hypothesis, and this one was shunted to the "General Mathematics" section of the arXiv, the home for crackpots who somehow manage to get around the rules preventing them from posting to the arXiv. See here, and note that we're now on version 18: https://arxiv.org/abs/2006.12546
-
It's not serious at all. The author's previous work consists entirely of incorrect papers on the Riemann hypothesis, and this one was shunted to the "General Mathematics" section of the arXiv, the home for crackpots who somehow manage to get around the rules preventing them from posting to the arXiv. See here, and note that we're now on version 18: https://arxiv.org/abs/2006.12546
I think you are responding to someone who is not serious at all.
-
Seems the RH could actually be false, after all: https://figshare.com/articles/preprint/Untitled_Item/14776146
This paper seems to be quite serious. I wonder why we haven't yet heard about it in the mainstream mathematical community.
It's not serious at all. The author's previous work consists entirely of incorrect papers on the Riemann hypothesis, and this one was shunted to the "General Mathematics" section of the arXiv, the home for crackpots who somehow manage to get around the rules preventing them from posting to the arXiv. See here, and note that we're now on version 18: https://arxiv.org/abs/2006.12546
It takes consistent rising and falling to solve a scientific problem like the RH ( in analogy, Edison needed 1000 attempts to invent the light-bulb). The question is, does the author learn from their mistakes and use that experience to perfect their approach ?
I have rigorously gone over this paper, and being a professional number theorist, i can tell you that thi paper deserves a lot of respect (to say the least). Credit where it's due.
-
Seems the RH could actually be false, after all: https://figshare.com/articles/preprint/Untitled_Item/14776146
This paper seems to be quite serious. I wonder why we haven't yet heard about it in the mainstream mathematical community.
It's not serious at all. The author's previous work consists entirely of incorrect papers on the Riemann hypothesis, and this one was shunted to the "General Mathematics" section of the arXiv, the home for crackpots who somehow manage to get around the rules preventing them from posting to the arXiv. See here, and note that we're now on version 18: https://arxiv.org/abs/2006.12546
It takes consistent rising and falling to solve a scientific problem like the RH ( in analogy, Edison needed 1000 attempts to invent the light-bulb). The question is, does the author learn from their mistakes and use that experience to perfect their approach ?
I have rigorously gone over this paper, and being a professional number theorist, i can tell you that thi paper deserves a lot of respect (to say the least). Credit where it's due.Very weird troll pushing persistently a crackpot paper.
-
being a professional number theorist
Suppose f is a univariate irreducible polynomial with integer coefficients and has degree at least two. Are there infinitely many primes p such that f mod p has no root in Z/pZ? Explain why.
Is there a more elementary way than Chebotarev?
-
Is there a more elementary way than Chebotarev?
Chebotarev is the magic word I was looking for. I'm no number theorist but I assume any number theorist would know this in an instant.
The troll/crackpot didn't and responded with an insult that the mods deleted. So at least it's now clear that he's no "professional number theorist" --- no need to waste time on his arXiv paper.
-
Is there a more elementary way than Chebotarev?
Chebotarev is the magic word I was looking for. I'm no number theorist but I assume any number theorist would know this in an instant.
The troll/crackpot didn't and responded with an insult that the mods deleted. So at least it's now clear that he's no "professional number theorist" --- no need to waste time on his arXiv paper.Chebotarev is the typical answer from a random grad student who has taken a number theory class and thereby regarding himself as a "professional number theorist". A mathematician at the caliber of solving Riemann hypothesis would have a different answer.
For example, Peter Scholze was once asked about motivic cohomology. He simply replied "It doesn't do it for me. The definition just doesn't seem right." Those words would have been considered trolling or an insult if uttered by a lesser mathematician.
-
Algebraist here, so take this skeptically. Say we have a real analytic function on R^2 (or maybe {(x,y) with x>c} for some c). Say f decays reasonably quickly along vertical lines (like 1/|y|^(1+\epsilon), say). Then we can integrate along vertical strips to get a function on R. Is it again real analytic? I’m not seeing why it should be true.
-
Just to add: the paper definitely isn’t right. Holistically, the functions considered here are not exotic enough to justify an assertion that RH is “dramatically wrong” given the numerical evidence. The results used are all quite standard and essentially 19th century. But it is much less crankish than most, and imho deserves someone engaging with it to say what the issue is.
-
Chebotarev is the typical answer from a random grad student who has taken a number theory class and thereby regarding himself as a "professional number theorist". A mathematician at the caliber of solving Riemann hypothesis would have a different answer.
When you hear hooves, think horse, not zebra. What do you think is more likely? Scholze lurking around on EJMR or a crackpot who knows less than a grad student?
-
Just to add: the paper definitely isn’t right. Holistically, the functions considered here are not exotic enough to justify an assertion that RH is “dramatically wrong” given the numerical evidence. The results used are all quite standard and essentially 19th century. But it is much less crankish than most, and imho deserves someone engaging with it to say what the issue is.
Indeed, it would be interesting to see a proper evaluation of it.