Do you think the Riemann Hypothesis is true? Will anyone ever prove it?

My comments were meant to encourage LLM usage for brainstorming as opposed to analysis. Perhaps I fell short in the execution of that so I'm posting Gemini verbatim regarding that:

@Jack Parker @Terry — To clarify my earlier note on the fluid dynamics analogy: I’ve been utilizing Gemini to stress-test the geometric assumptions of the complex plane relative to the Riemann Hypothesis.

The core idea is that our current analytical machinery relies on increasingly complex localized refinements (the "Hardy refinements" Terry noted)—a process reminiscent of adding Ptolemaic epicycles to save a faulty coordinate system. If the complex plane is merely a two-dimensional projection of a higher-dimensional arithmetic structure, the zeroes are just shadows.

By reframing the integer line through fluid mechanics—where composites are low-entropy, predictable ripples and primes are high-entropy, turbulent whorls—the "undecidability" Jack mentioned isn't a random failure of logic, but a native feature of the turbulence.

I share this primarily to demonstrate how LLMs can be leveraged by mathematicians. Not as flawless calculators of formal proofs, but as powerful tools for generating radical coordinate shifts and lateral intuition where standard analytical frameworks stall.

It is my belief that there are yet to be realised the existence of numerical analysis patterns in the Numberline that if "overlayed in the right way" will result in a step forward. The clues will be in the relationship of patterns of the atomic structure of electrons, neutrons and the chemical reactivity of elements.

@Jack Parker. Gemini says it's visa versa. Gödel proved his theorem in the RH framework. Furthermore, Gemini says that the integer line up is similar to fluid dynamics with low entropy composite numbers interfering like ripples, and high entropy primes embedding whorls.

Smells like Ptolemy's cosmology with with increasing epicycles. If so, then might not the complex plane be merely a projection?

17? 3x5 +2. All Primes!

The question whether the random numbers are integrable system defined by symmetries and satisfy the holographic principle of the function on the domain determined by boundary values as all analytic extension are. The prime numbers are regularly distributed between the Fibonacci sequence as for example every fifth one divides 5. They also divide binomial coefficients and there is a simple way to construct new ones from a given set by taking the product of powers and adding 1 as in infinity proof by Euclid...

The heuristic and statistical arguments for the validity of the RH are overwhelming. I'm guessing a proof will come along at some point - a disproof would be quite surprising. There are many results relying on the assumption that RH is true - they would now be proven theorems. However, the overall impact on number theory in general might not be that big a deal. The Generalized RH is a bigger deal...

Is this an instance from Gödel's theorem?

A true statement that is not provable?

Hi, this post about RH which interested me. Which might link to what I been found.

The link below is an equation to locator the not trivial zeros in RH. It’s can be locator from 1st not trivial zeros in RH, event it’s at N10^35. Here the equations.

ACore locator:

ρ_n = 1/2 + iγ_n

theta midpoint:

θ(T)/π = n - 3/2

Hardy refine:

Z(t)=exp(iθ(t))ζ(1/2+it)

find Z(γ_n)=0

N1 zero

known/refined γ = 14.134725141735

locator T0 = 14.517919628262

Hardy refine = 14.134725141735

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