Update on 12/10/2024
The video and document below are provide as 15th attempt .
I have reviewed this document for numeric counterexample, and confirmed the author failed, to provide a numeric counterexample. Below are highlights, and you can see more details in note.
In general, the main challenge the author seems to face is not understanding how to properly handle infinity, when they are unequal, and when and why they are. The author claims that two infinite sums are equal, while at the same time proving that they are not equal when making this claim, contradicting himself and ignoring the fact that it was his mistake to obtain two different results. It is like a person take different to obtain a different answer for an integral, claiming the integral is false due to the contradiction. Note: The Identity theorem definitely doesn’t provide any basis to claim that infinity equals infinity. Infinites are not equal by default as you can see below.
If we perform one mathematical operation and obtain a result, then do a different operation or equation and get a different result, it is not a contradiction, but generally a mistake. In other words, there is a fine line between contradiction and bad math. In this version, all errors are considered contradictions.
Additionally, the author continues to present arguments without providing numeric counterexamples, which would help clarify the discussion and prevent confusion. If the argument were valid in any form, we would expect it to generate a numeric counterexample.
Update on 2/12/2024
The video and slides below are provide as 14th attempt .
In Version 14, the argument contradicts Version 13 as opposite arguments. This video and slide start with debunking a proof unrelated to this Riemann's last theorem. Then, from the middle to the end of the video, it starts explaining one of the interesting features of Riemann's last theorem (SEE https://www.0bq.com/se) and ends with a method for debunking the SEE using arguments from the Abridged Riemann's last theorem article. The core idea of debunking is that the author (of the video and Version 14 slide .pdf) does not explicitly say but claims that Version 13 is wrong. So, if Version 13 is wrong, thus the opposite is wrong. In other words, saying that because 13 or 14 are opposite versions, if one is false, it means the other one is true, which is a false logic. For example, if the goal is to get to the North Pole and you tell someone who is going east that they are in the wrong direction, it doesn't mean the west direction is the correct answer. In this case, in version 13, the author claims that through some error, he claims that two functions are equal by using the argument that ∞=∞ (east), then when referencing the video and argument, in version 14, the argument is ∞≠∞ and thus the SSE is wrong. Where you can see (The Riemann Hypothesis and a New Math Tool ) that depending on the rate of growth of infinity, equality and non-equality are possible, and claiming that one of ∞≠∞ or ∞=∞ must be correct is false.
So overall, this is yet another failed attempt to prove Riemann's Last Theorem, as the article has fallen short and not achieved the proof of the Riemann Hypothesis. Note that the author falls short in proving a numeric counterexample after 14 attempts. Also, I must say that with the presented data in the video and slides, he appears to be a very intelligent individual. However, in no shape or form does this prove he can provide a numeric counterexample to the Riemann's Last Theorem. I do strongly agree with him that his best work yet to come.
Update on 1/25/2024
@artificialresearching4437 Said :
"Hey, Aric, I've written you an email, but you're not responding, so I shall try reaching out to you through comments here. You see, the 18th of January was my 24th birthday, so I tried my best to revise all of the things I did the previous year. Of course, the biggest of my claims was the disproof of RH. And of course, I tend to question myself constantly. That is why I tried to understand the biggest proofs of RH and see if I missed something. I have already found a flaw in the proof by Jeffrey N. Cook, which I have posted to the comments under his video. Now I've tried to understand your proof better. I had some problems with dealing with your counter-example, since the series for the zeta-function is not defined in the critical strip, but that is what you have already been told. Then I thought "Hey, maybe, this guy is eventually correct in some way", so I started playing with SSE. I have discovered that if SSE is correct, then Riemann zeta-function cannot have zeros in the critical strip, so any non-trivial zero is the counter-example to SSE. To derive this I have accepted all of your proving methods and conventions about the series object that you have posted. Any of my steps is supposed by the similar steps of yours. You used a kind of Ramanujan intuition of analytical continuation, so I tried to test it if it can be actually legit. That is why I started playing with two representations of this series: \lim_{k-> \infty} sum_{n=1}^{8k^3} 1/n^s and \lim_{k-> \infty} sum_{n=1}^{8k^6} 1/n^s. They coincide on Re s>1, which consists of accumulation points. Thus, if the series objects are well-defined, those limits should coincide everywhere. Then I used ABC zeta representation for both of those, assuming the existence of the series on the domain 0<Re s<1. By the similar methods I obtained that if you are correct, then the non-trivial zero should be with the real part 1/3. But you have already obtained that the real part of this zero should be 1/2. Since 1/2 and 1/3 are different numbers, we deduce that non-trivial zeroes cannot exist, but Riemann himself found some of those with the real part 1/2. That is why we prove that any of those is the numerical counter-example to your statement, believe it or not. Here is the paper I wrote with the citations on each step taken. It was interesting to actually study your papers, thank you) The paper: https://drive.google.com/file/d/1z2n6W-zfi80VyKZEM84sep0FwyfAi0qC/view?usp=drivesdk"
Answer to version 13 ( Fresh attempt) :
To simplify, let's explain with an example. In this claim, there's confusion with functions. The author starts with f(x) = x^2 - 1/4 but mistakenly defines g(x) as x^2 - 1/9. Then, the author wrongly states f(x) = g(x). This leads to confusion when the author claims that because g(x) has a root at 1/3, it contradicts the findings of another paper. The conclusion that 1/3 is a root of f(x) doesn't make sense.
The proposition above it is the first one, and a similar fatal error has been repeated in this paper. Ironically, there is a video on "The Riemann Hypothesis and a New Math Tool (a new Indeterminate form)," particularly talking about this common error.
The fatal error is stating that the limit of 8K^3 is equal to the limit of 8K^6 as K goes to infinity. To put it simply, assuming all infinities (∞) are equal because we use the same notation for infinity is very wrong.
Consider the chronological progress table below:
K 8K^3 ≠ 8K^6
2 64 ≠ 512
3 216 ≠5832
4 512 ≠ 32768
5 1000 ≠ 125000
6 1728 ≠ 373248
…
Please see notes 4.pdf for an update on my personal notes on this subject.
Update on 10/26/2023
@artificialresearching4437 Said: "Dear all, some of you may have been spectators of our argument. I must admit. At this moment I resign. I am a theoretical mathematician and finding the precise numerical counter-examples is something beyond my abilities. I can only hope that my work would give someone any new and interesting ideas. Thank you!"
Aaswer to version 12 : 7/21/2023 The user provided Iteration Version 12 via email. This version starts with a major problem where the author ignores the fact that ζ(s) is the analytic continuation of the series ∑(n=1 to ∞) 1/n's in the critical strip(This fact has been clarified in the Super Symmetric and Transcendental Zeta Function pages) . This is sufficient to debunk this version of the claim. The claim at the beginning of the video is analogous to someone saying that 1+2+3... - 1/12 = 0, which is false for obvious reasons, as someone misinterprets the meaning of equality. -1/12 is the analytic continuation result for the series 1+2+3.... This is an invalid and unsupported operation that does not appear in any paper or argument by anybody, and for the same reason, it never occurs in the YouTube.com/@rslt nor in Riemann's last theorem article. Please consider see my personal notes for more detail.
The good point is that the numeric counterexample claim has disappeared from this version, which is a step in the right direction. However, the argument for version 10 and earlier is still present, where it remains merely a claim without any proof.
This user consistently exhibits incredibly rude behavior and shows no respect for others. Despite clear evidence provided during the contest, which includes requesting numeric counterexamples, he decides to ignore it and instead asks for reviews of his alleged disproof, citing his refugee status as a reason. In ten instances, I have demonstrated the errors in his claims. Subsequently, he becomes derogatory, only to later admit he was wrong and introduce additional nonsensical arguments. His behavior follows a repetitive pattern.
Please consider an oversimplified version of the numeric counterexample. The author argues that if we input the function f(x) = x - 1/2 into the machine approximation algorithm, for example, 'Muller,' it finds a root at 0.050000000000000076299623. Based on this result, the author concludes that there must be a root other than 1/2 for the function f(x). However, in his analysis, they fail to take into account the limitations of the machine and misunderstand the context of the root found.
Aaswer to version 11 : 7/10/2023 :I have no reason to believe that SSE is incorrect. This is the strongest point of RSLTbased on the Uniqueness of Analytic Continuation and Identity theorem. If you have any claim, you need to demonstrate why you believe zeta(s) and zeta(1-s*) are equal, even though you claim they originated from different series. Again, it makes no sense to assert that the analytic continuation of ∑(n=1 to ∞) 1/n^s and ∑(n=1 to ∞) 1/n^(1-s*) are equal, and yet also claim that ∑(n=1 to ∞) 1/n^s and ∑(n=1 to ∞) 1/n^(1-s*) are different.
Regarding your paper up to version 10, it was wrong( as you know since you said above) , and I have no interest in reviewing version 11 before publish my next video. There are several fundamental problems with you paper that I have listed in my notes (pdf below).
Regarding your last version, I have some concerns that you haven't addressed critical aspects, such as:
Could you kindly provide a clear proof (paste it on youtube) for Φ(s) = e^{i α}? Additionally, could you explain why this proof is not applicable to other functions, for example, s^2 = e^{i α}? I have mentioned multiple times that it is necessary to prove both |Φ(s)| = 1 and |e^{i α}| = 1 independently. Simply stating that |e^{i α}| = 1 does not sufficiently justify the claim that |Φ(s)| = 1 as well. Your arguments appear flawed and confusing when you say |Φ(s)| = 1 because |e^{i α}| = 1.
For a correct argument, it is essential to demonstrate rigor in proving both |Φ(s)| and |e^{i α}| equal to 1 independently. Only then, based on the fact that 1 = 1, one can claim that there exist values α (s) (the useless curve) that make Φ(s) = e^{i α} possible. I believe you are capable of presenting a more robust analysis. This is an undergraduate problem, and I don't expect you to get stuck on this for so long.
Please address these concerns adequately while I'm working on SSE vedio.
5/24/2023: You possess an exceptional level of intelligence and expertise in the field of mathematics, far surpassing my own capabilities. I humbly acknowledge that there is much for me to learn and grow in my understanding. Consequently, I find it challenging to engage in a meaningful discussion without further knowledge and proficiency. While I acknowledge that there may be valid points within your claim, as a whole, it has been thoroughly refuted and deemed false due to various reasons, as exemplified below. I appreciate the effort you have invested thus far, and I understand that you may be reluctant to accept my explanation, such as the one provided here . However, I have made the decision to abstain from delving deeper into this topic. I sincerely thank you for your time, and I extend my best wishes to you in all your future endeavors.
Also, I must say, I was quite surprised by the lack of interest shown by the mathematical community in my proofs. However, upon reflecting on my experience with some people, I can now understand why they might feel annoyed and be unresponsive.
To begin with, it is important to acknowledge that the mathematical community consists of individuals with diverse backgrounds, areas of expertise, and personal interests. This vast diversity can contribute to differences in priorities and the level of attention given to certain proofs or mathematical contributions. While my proof may have been significant to me, it is possible that it did not align closely with the current focus or research interests of the mathematical community at that time.
Additionally, the mathematical community receives a considerable number of submissions, proofs, and research papers on a regular basis. With such a high volume of information to evaluate, it can be challenging for individuals within the community to allocate sufficient time and attention to every single submission. This may result in delayed responses or, in some cases, no response at all.
It is also worth considering the clarity and presentation of my proof. Mathematical proofs require a rigorous structure, logical coherence, and clear explanations to be readily understandable and verifiable by others. If my proof lacked these qualities or was not effectively communicated, it could have contributed to the lack of interest or response from the mathematical community.
While it can be disheartening to experience a lack of interest or response from the mathematical community, it is essential to remember that the field of mathematics is continuously evolving. Research interests, trends, and priorities change over time, and what may not have garnered attention in the past could potentially become relevant and influential in the future.
In light of this, it may be beneficial for me to reassess my proof, consider feedback from colleagues or experts in the field, and explore alternative avenues to share my work. Collaboration, engagement in relevant mathematical communities, and participation in conferences or seminars could provide opportunities to present my proof to a more receptive audience.
Overall, it is crucial to recognize that the lack of interest or responsiveness from the mathematical community does not necessarily reflect the value or validity of my proof. It is a multifaceted community with various factors influencing their attention and response. By adapting and persevering, I can continue to engage with the mathematical community and potentially gain the recognition and interest my work deserves.
Version 10 5/242023
Version 9 5/18/2023
5/6/2023 Again: You are incredibly intelligent and knowledgeable in mathematics, and I cannot match your talent and expertise. I recognize that I need to learn more, and until then, I have no reason to communicate. I understand that there may be some correct statements in your claim, and I recognize that. However, as a whole, your claim has been debunked and is completely false for several reasons, such as the example below. I understand that you have been working hard despite my requests, and for that reason, you may not be willing to accept a simple explanation as below. I will not be elaborating on this matter any further, and my decision is final. Thank you for your time, and I wish you all the best.
