
Ask HN: My professor thinks he solved Riemann Hypothesis. how to validate it? - sandeepeecs
https:&#x2F;&#x2F;www.researchgate.net&#x2F;publication&#x2F;325035649_The_Final_and_Exhaustive_Proof_of_the_Riemann_Hypothesis_from_First_Principles<p>I am not a mathematical expert but few of the mathematicians we had access to have confirmed that this could be a possible proof.<p>So I wanted to ask how do we get this proof validated the by the larger scientific community?<p>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&#x27;s and -1&#x27;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.<p>Previous discussions:
https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=12889009
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primitivesuave
The proof is flawed:
[https://empslocal.ex.ac.uk/people/staff/mrwatkin//zeta/herri...](https://empslocal.ex.ac.uk/people/staff/mrwatkin//zeta/herrington_eswaran_2018.pdf)

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jey
Source:
[https://empslocal.ex.ac.uk/people/staff/mrwatkin/zeta/RHproo...](https://empslocal.ex.ac.uk/people/staff/mrwatkin/zeta/RHproofs.htm)

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sandeepeecs
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.

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primitivesuave
Here is Herrington's response to Raghavan:
[https://empslocal.ex.ac.uk/people/staff/mrwatkin//zeta/herri...](https://empslocal.ex.ac.uk/people/staff/mrwatkin//zeta/herrington_eswaran_2019.pdf)

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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netsharc
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.

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anitil
What is a 'For your consideration' promotion? I feel like I've heard that term
before but can't quite place it.

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netsharc
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.

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aeriklawson
Has it not been submitted to a journal and/or conference? Typically these
things are peer-reviewed and tested over time, no?

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azhenley
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.

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sandeepeecs
its there on arxiv.
[https://arxiv.org/pdf/1609.06971v4.pdf](https://arxiv.org/pdf/1609.06971v4.pdf)

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quickthrower2
Modestly named "The Final and Exhaustive Proof".

