Riemann Hypothesis Puns

Whenever I read or watch anything on the Riemann Hypothesis, it always says that the zeros of the Riemann zeta function are related to the distribution of prime numbers, but they never seem to actually explain how or why they are related and what it means.

If anyone could explain this, I would be extremely grateful

Someone called K. Eswaran from a little-known college near Hyderabad claimed to have proved the Riemann hypothesis (here we go again), and this is currently receiving a lot of media coverage in India, though most are just regurgitating the same press release.

The preprints with the claim have been online for a few years:

Researchgate (May 2018): https://www.researchgate.net/publication/325035649_The_Final_and_Exhaustive_Proof_of_the_Riemann_Hypothesis_from_First_Principles

Arxiv (Oct 2017), The Dirichlet Series for the Liouville Function and the Riemann Hypothesis: https://arxiv.org/abs/1609.06971

A few more links in case you are interested:

• https://www.researchgate.net/publication/324828748_A_Simple_Proof_That_Even_and_Odd_Numbers_of_Prime_Factors_Occur_with_Equal_Probabilities_in_the_Factor-ization_of_Integers_and_its_Implications_for_the_Riemann_Hypothesis
• https://www.researchgate.net/publication/329539660_On_the_Generalized_Riemann_Hypothesis
• Seven 1-hour lectures to explain his supposed proof to a general audience: https://youtube.com/playlist?list=PLRsxymPrOKUAk3eXhK9FZdGAPmgGGrhfb
• An example of the press coverage: https://timesofindia.indiatimes.com/city/hyderabad/hyd-physicist-claims-to-prove-161-year-old-hypothesis/articleshow/83905877.cms

Edit: If you’ve spent enough effort reading the paper and have the time and inclination to do so, it would be great if someone wrote a careful rebuttal note to debunk this claim of proving RH soon.

The media coverage is still going on, for example this “news” was just retweeted by a prominent Member of Parliament with 8M followers, who was once in running to be the Secretary-General of the United Nations: https://twitter.com/ShashiTharoor/status/1409757057264144386?s=20

Edi

I would not consider myself to be very good at math. I work in what might be considered a STEM field, but I failed Calc 1, and never had a need or a reason to really delve back into higher mathematics, so I haven't. But I do very much enjoy thinking about physics, and how mathematics plays out in the real world, how patterns can be understood in 2D, or 3D, or sometimes higher dimensions. I just watched this video about The Riemann Hypothesis, and specifically found myself thinking about the zeta graph plotting shown in the first 30 seconds. I have some questions, hopefully someone out there can offer some answers. (I did Google and check the FAQ, noted below.)

As I understand it, imaginary numbers are nothing more than what happens when you take the line of real numbers and move it into 2D space. It was just that the mathematicians at the time hadn't understood it as such, so they created "imaginary numbers" to do a number of things, with the end result that someone eventually realized what I just said. This is obviously simplified to what is probably an offensive level to many who are reading this, but please set that aside for the moment.

I'm also aware of certain concepts in math making more sense when I visualize them as conversions from 2D into 3D space (for example, how photons 'spiral' through space and how this relates to electromagnetic waves). When I saw the zeta plot in those first 30 seconds something seemed familiar. It reminded me of orbital resonances. It seems like the numbers being plotted are moving as if they're "orbiting" around some other number that's also in motion. That made me wonder:

• What is this other number/constant/function the zeta function is "orbiting" around? Is it a known number/constant/function, or something currently unknown?
• What would knowing this number/constant/function tells us (both about prime numbers and anything else)?
• Is this other number/constant/function moving in the same 2D plane as the zeta function? Yes or no, what insights does that uncover?
• Has anyone already looked into this? If so, what did they find?

Also, I'm not 100% positive, but I actually think this might be (at least) a three body problem. I lack the proper vocabulary to explain it, but ... I see variations in the periodicity of the movements that I don't think would be representative of a two body system. It reminds me of the "loops" astronomers thought were present in

Hope it works this time. Answer to the paper claiming a proof of RH hypothesis posted by u/balance_chai :https://arxiv.org/abs/1609.06971 sorry about the images, reddit won't let me upload a pdf and i don't want to make an arxiv alt.

footnote 1: [...] This holds for i.i.d. sequences [...]

there is another version on researchgate with the same flaw in its mathematical reasoning.

Hello, I would like to study (out of curiosity) the necessary to understand the Rieman hypothesis well. I have basic knowledge of calculus of one variable, several variables and complex numbers. I would like to know what other areas of knowledge i should get involved in (If you have recommendations for books in these areas, I would appreciate it as well.). Thank you!

Is it reasonable to consider the chance that the "unprovable truthes" implied by Godel's Incompleteness Theorems could include the Riemann Hypothesis? Have mathematicians tried to write a non-proof of the hypothesis along these lines?

How would anyone even go about writing a proof that something cannot be proven given the axioms in use? Is this even possible?

I remember hearing about a proof of a theorem that worked off the assumption that the Riemann Hypothesis was true, and then later the mathematician went back and created a second proof using the opposite assumption, thereby ensuring that their theorem was true regardless of the truth of the Riemann Hypothesis. I can't remember where I heard this though or what it was about. I was wondering if anyone knew which theorem this was?

Hi guys

I just finished my first math course and I've decided to prove the Riemann hypothesis, however I'm having a bit of trouble getting started.

Any hints would be appreciated

Whenever I watch or read anything on the Riemann Hypothesis, it is always mentioned that the zeros of the Riemann Zeta function are related to the distribution of prime numbers, but they never seem to explain why or how they are related.

If anyone could explain this, I would be extremely grateful

Why do we care about the placement of prime numbers? Could someone explain what proving the hypothesis means?