Ask HN: My professor thinks he solved Riemann Hypothesis. how to validate it?
15 comments
The proof is flawed: https://empslocal.ex.ac.uk/people/staff/mrwatkin//zeta/herri...
Looks like this is responded by Raghavan and this is what I had seen on research gate comments
Dr. Kumar's response to the above: I certainly know that the lambda - sequence is fixed and unalterable because each lambda(n) is obtained by factorizing n into prime factors and then defining lambda(n)=+1 if there are even factors else, lambda(n) =-1 if n is a prime or has odd prime factors.
In the paper for very long sequences, the lambda-sequence is treated as one instance of a hypothetical random walk. If this analogy is true then the magnitude of L(N), which is the sum of the first N terms of lambda(n)’s, (where N is very large) can be likened to the expected distance travelled by a random walker in N steps which is given by C .N^(1/2) (see S. Chandrasekhar(1943)).
However, for this analogy to be really meaningful and accurate, one must prove the lambda(n), for large and arbitrary n, must satisfy the criteria: (i) equal probabilities of being +1 or -1 , (ii) the lambda-sequence has no cycle and (iii) unpredictability.
In the paper I provide mathematical proofs for all the above criteria, after which one can deduce the asymptotic expression for L(N) as C. N^(1/2+e). We then invoke (i) Littlewoods Theorem 1 (proved in the paper) and then (ii) use Khinchin (1924) and Kolmogorov’s (1929) law of the iterated logarithm, for evaluating the bound ‘e’ and to show that e tends to zero as N tends to infinity, thus finally proving R.H.
One last comment: Herrington quotes Borwein’s statement as an “Equivalence to RH”, in actuality the condition stated by Borwein (2008) is only a necessary condition for RH to be true. The additional criteria (above) needs to be satisfied and hence need to be proved as done in my paper.
Dr. Kumar's response to the above: I certainly know that the lambda - sequence is fixed and unalterable because each lambda(n) is obtained by factorizing n into prime factors and then defining lambda(n)=+1 if there are even factors else, lambda(n) =-1 if n is a prime or has odd prime factors.
In the paper for very long sequences, the lambda-sequence is treated as one instance of a hypothetical random walk. If this analogy is true then the magnitude of L(N), which is the sum of the first N terms of lambda(n)’s, (where N is very large) can be likened to the expected distance travelled by a random walker in N steps which is given by C .N^(1/2) (see S. Chandrasekhar(1943)).
However, for this analogy to be really meaningful and accurate, one must prove the lambda(n), for large and arbitrary n, must satisfy the criteria: (i) equal probabilities of being +1 or -1 , (ii) the lambda-sequence has no cycle and (iii) unpredictability.
In the paper I provide mathematical proofs for all the above criteria, after which one can deduce the asymptotic expression for L(N) as C. N^(1/2+e). We then invoke (i) Littlewoods Theorem 1 (proved in the paper) and then (ii) use Khinchin (1924) and Kolmogorov’s (1929) law of the iterated logarithm, for evaluating the bound ‘e’ and to show that e tends to zero as N tends to infinity, thus finally proving R.H.
One last comment: Herrington quotes Borwein’s statement as an “Equivalence to RH”, in actuality the condition stated by Borwein (2008) is only a necessary condition for RH to be true. The additional criteria (above) needs to be satisfied and hence need to be proved as done in my paper.
Here is Herrington's response to Raghavan: https://empslocal.ex.ac.uk/people/staff/mrwatkin//zeta/herri...
I have a degree in mathematics so after brief research, so I am inclined to believe the proof is indeed flawed, especially if it addresses a problem as high-profile as RH. There is a good point in his reply which actually applies to academia everywhere:
"Assuming this media report is accurate then it raises an issue mentioned in Note 1 which is that Eswaran 2018 contains no evidence, such as an acknowledgement, of independent expert review. As a professor, presumably with contacts in academia, and also with many senior scientists approving the proof, it seems reasonable to assume that Professor Eswaran could have found at least one suitably qualified person to review the proof. "
Media attention cannot be a substitute for rigorous peer review.
I have a degree in mathematics so after brief research, so I am inclined to believe the proof is indeed flawed, especially if it addresses a problem as high-profile as RH. There is a good point in his reply which actually applies to academia everywhere:
"Assuming this media report is accurate then it raises an issue mentioned in Note 1 which is that Eswaran 2018 contains no evidence, such as an acknowledgement, of independent expert review. As a professor, presumably with contacts in academia, and also with many senior scientists approving the proof, it seems reasonable to assume that Professor Eswaran could have found at least one suitably qualified person to review the proof. "
Media attention cannot be a substitute for rigorous peer review.
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So the previous discussion link is from 2016. Why does this smell like a desperate attempt to get mathematical fame? Why does this post smell like a "For your consideration" promotion? The previous discussion also talked about what a quirky guy the prof is, as if trying to make it about personality.
The context here is we are based out of Hyderabad(india) we do not have easy access to top universities mathematicians where the fundamental research happens in math.
We are trying : https://www.thehansindia.com/posts/index/Young-Hans/2018-11-...
As far as I know, I think he might have sent it to journals and conferences. but the problem is for them to consider it as it is a very big problem in math they look for some initial validation from the community I may be wrong.
This is my attempt to understand how the hacker news community would validate it.
We are trying : https://www.thehansindia.com/posts/index/Young-Hans/2018-11-...
As far as I know, I think he might have sent it to journals and conferences. but the problem is for them to consider it as it is a very big problem in math they look for some initial validation from the community I may be wrong.
This is my attempt to understand how the hacker news community would validate it.
What is a 'For your consideration' promotion? I feel like I've heard that term before but can't quite place it.
When studios send DVDs (Blurays?) of their movies to members of the Academy (who vote who gets the Oscar), they say "For your consideration", in the hopes the member watch and like (and vote for) their movie.
Yeah, the post is very odd. What math professor doesn't know how to get his proof/work validated or published?
Has it not been submitted to a journal and/or conference? Typically these things are peer-reviewed and tested over time, no?
Your professor will know how to get the proof validated. Post it on arxiv and submit it to a good journal like he would for any other paper.
its there on arxiv. https://arxiv.org/pdf/1609.06971v4.pdf
Modestly named "The Final and Exhaustive Proof".
I am not a mathematical expert but few of the mathematicians we had access to have confirmed that this could be a possible proof.
So I wanted to ask how do we get this proof validated the by the larger scientific community?
Dr. Kumar has used the properties of primes and analytic continuation and had a new way of handling slowly converging series and was able to use (at the crucial point) concepts borrowed from Donald Knuth regarding random numbers and random sequences. Knuth had said that for any sequence to be truly random it has to be non-cyclic. The proof required to show that a sequence of +1's and -1's , obtained from the prime factorization of the infinite sequence of integers, had to be shown to be random and to asymptotically behave like the tosses of a coin.
Previous discussions: https://news.ycombinator.com/item?id=12889009