A very noteworthy HP-15C mention

[Valentin Albillo]

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Hi, floppy,

(04-19-2023 08:10 PM)floppy Wrote:  Perhaps a peer review of this will bring a bit light in the tunnel? (far over my skills) https://vixra.org/pdf/2208.0089v1.pdf

There are dozens upon dozens of alleged "proofs" of the Riemann Hypothesis, even in arXiv, and hundreds more in other less reputed sites (like the one you linked from viXra) and the Internet at large. For instance, these are a few of the most recent ones submitted to arXiv:

A Simple Proof of the Riemann Hypothesis

Proof of the Riemann Hypothesis

A Proof of the Riemann Hypothesis Using Bombieri's Equivalence Theorem

All Complex Zeros of the Riemann Zeta Function Are on the Critical Line: Two Proofs of the Riemann Hypothesis

Local geometric proof of Riemann Hypothesis

A Proof of Riemann Hypothesis

A Simple Proof of the Riemann's Hypothesis

A Proof of the Riemann Hypothesis Through the Nicolas Inequality

A Proof of the Riemann Hypothesis

A proof of Riemann Hypothesis

Proof of Riemann hypothesis

A Proof of the Riemann Hypothesis and Determination of the Relationship Between Non- Trivial Zeros of Zeta Functions and Prime Numbers

A proof of the Riemann hypothesis using the remainder term of the Dirichlet eta function

Proof of the Riemann's hypothesis

Modeling the creative process of the mind by prime numbers and a simple proof of the Riemann Hypothesis

A Simple Solution to a Major Problem: Proof of the Riemann Hypothesis

One page proof of the Riemann hypothesis

A short Brownian motion proof of the Riemann hypothesis

etc., etc.

so most mathematicians wouldn't bother to waste their time peer-reviewing any of those unless submitted by authorities on the matter, and even so. Thus, the most advisable thing to do is to wait for the big news to appear in newspapers all over the world before committing any of your time to review them or in fact pay any attention at all. Oh, and don't hold your breath while you wait ...

By the way, this has already happened a number of times, most famously with the Squaring the Circle problem ("constructing a square with the area of a circle by using only a finite number of steps with a compass and straightedge",) where prestigious institutions were swarmed with zillions of alleged solutions (which they were eventually forced to reject for lack of resources to review them,) until Ferdinand von Lindemann proved the transcendence of \(\pi\) in 1882, thus showing the impossibility of constructing \(\pi\) within the requirements of the problem.

Same here, but there's also the fact that perhaps the Riemann Hypothesis is false, in which case it would be impossible to try and prove it, no matter who and no matter how many attempts, as happened with the problem of algebraically finding roots of a quintic equation, which resisted all attempts to solve it for longer than 200 years until Niels Henrik Abel attempted (and succeeded !) to prove that perhaps it was actully impossible, against all expectations.

V.
Edit: corrected typos.