Tuesday, August 8, 2023

Symmetricity : Riemann Hypothesis


The problem at the heart of mathematics and physics. 

So some brief background what I was taking to you last time. I try to look at the mathematical system here as a game where one has defined the rules for operators like addition, multiplication, subtraction, division etc. There can be made different games by tweaking the rules of algebra and numbers. Probably that’s the reason why David Hilbert looked at advanced maths as the game of symbols. 

Since, it’s the game I tried to look at the physical structure behind the RZ function on he basic of symmetry aspects in the game.

Last time I showed that Riemann Zeta function Satisfies the Functional Equations and by using Functional Equation I tried to show why RH is true . But then you came back with wonderful counter examples to that using Dirichlet L functions , Polya etc. 

Then I also reverted after my thoughts that somewhere I am trying to link Symmetricity in the structure of Equations and the Graphical Plots. By Structural Symmetricity in the Equation of RZ, I tried to relate that to the game rules and also conservation of physicalities in the graph where 0 represents the singularity and physicalities is collinearity of non trivial zeros too. 
I then found that these counter examples have asymmetric aspects unlike Riemann zeta function in their structures and hence their game theory strategies would get distorted and hence also the graphical characteristics would likely be asymmetric and that’s why these counter examples might violate RH due to asymmetry and heterogenous in their structure of equations. 


On that basis, as per the Game theory rule or physical characteristics conservation, I tried to show that RH would be true for RZ function but may not be true for other Counter examples. There can be created many Counter examples but not as symmetric as RZ.

On that intuition and principle I tried to show RH is true for RZ ! I tried to conserve the symemtricity that were assumed while defining the arithmetic and algebraic rules of addition, multiplication, subtraction etc.. and establish the link between the symmetricity,homogeneity in algebraic equations and the graphical representation like for example the equation of circle is symmetric and homogeneous in algebraic structure and hence also symmetric and homogeneous in graphical representation.similarly for RZ function and Other Counter Examples satisfying the RZ functional Equations. I don’t see that an asymmetric equations will have graphical symmetry and symmetric equations curve will have asymmetric graphical structure !! That’s my main point.


So, I would kindly request to have some imaginative thoughts on my humble idea and reimagine Mathematics from a different angle. 



(I am trying to look from Natural Point of view not from Conventional approaches employed by expert number theorist. Because I see some possible fundamental limitations there . It’s like trying to lift the bucket by standing inside the bucket which won’t be possible !! 

This is because I believe that in mathematics one can prove many things but may not prove the axioms itself on which they have been defined. For that one has to possibly imagine the mathematical problem by treating it like a physical system externally as an observer not internally using arranging equations. 

Let's discuss mathematics unconventionally..


 

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