Riemann Hypothesis

Many entries, written over a 10-year period, that are designed to reveal the truly remarkable (inherent) dynamic synchronous nature of the number system

2010

2011

The Trivial Zeros (1)
The Trivial Zeros (2)
The Trivial Zeros (3)
The Trivial Zeros (4)
The Trivial Zeros (5)
The Trivial Zeros (6)
The Trivial Zeros (7)
The Trivial Zeros (8)
2-Dimensional Proof
Odd Numbered Integers (1)
Odd Numbered Integers (2)
Odd Numbered Integers (3)
Odd Numbered Integers (4)
Odd Numbered Integers (5)
Odd Numbered Integers (6)
Odd Numbered Integers (7)
Odd Numbered Integers (8)
Odd Numbered Integers (9)
A Deeper Code
The Critical Region (1)
The Critical Region (2)
The Critical Region (3)
The Mystery of the Primes
New Perspective on Mathematical Proof
Calculating ζ(- 1) and ζ(- 3)
The Strange Case of η( - 1)
Finite and Infinite
Interesting Squares Connection
A Strikingly Simple Prime Number Relationship
The Harmonic Series Again
Riemann's Zero
Spiral Waves
Sum of Reciprocals of Primes
Vibrating Primes
Changing Our Idea on the Primes
The Number Big Bang

2012

Frequency of Non-Trivial Zeros
Addendum on Frequency of Non-Trivial Zeros
Brief Further Addendum
Further Considerations
Music of the Primes
The Mystery of e
Further Thoughts on Non-Trivial Zeros
Connecting Positive (Even) Negative (Odd) Integers of Zeta Function
Approximation Formulae for Zeta Function (Negative Odd Integers)
Fundamental Implications of Nature of Primes
Approximate Nature of Prime Numbers
Momentous Change
Clarifying the Riemann Hypothesis
Quantum Mechanics
Role of Unconscious
Two Number Systems
The Nub of the Matter
At the Crossroads
Imaginary Numbers and Qualitative Understanding
Jungian Connections
Startling Implications
Reason and Intuition (1-Dimensional Interpretation)
2-Dimensional Interpretation
Feminine Archetypes
Prime Numbers (Local and Non-Local Identity)
Riemann Zeta Function (1)
Riemann Zeta Function (2)
Riemann Zeta Function (3)
Deep Prime Connections
Riemann Zeta Function (4)
Riemann Zeta Function (5)
The Music of Pi
Marvellous Vistas
Riemann Zeta Function (6)
Number Uncertainty
Implications for Mathematical Proof
Addition, Multiplication and Exponentiation
Issues with Respect to Cardinal and Ordinal Numbers
From Triviality to Ineffable Mystery
Looking Inside the Primes!
The Remarkable Secret of the Primes
Alternative Riemann Hypothesis!
The Hidden Zeta Function
Unveiling the Zeta 2 Function
The Startling (Unrecognised) Significance of the Riemann Zeta Function
Interpreting Number for s <0
Interpreting Numerical Result for ζ(0)
Number Inconsistency (1)
Number Inconsistency (2)
Number Inconsistency (3)
Number Inconsistency (4)
Number Inconsistency (5)
Number Inconsistency (6)
Why the Trivial Zeros are not so Trivial
Riemann Zeta Function and Odd Integer Values (1)
Another Perspective on the Riemann Hypothesis
Nature of Number System (1)
Nature of Number System (2)
Nature of Number System (3)
Nature of Number System (4)
Nature of Number System (5)
Nature of Number System (6)
Through the Looking Glass of Number
Emergence of Zeta 1 and Zeta 2 Functions
Interesting Prime Result
Prime Numbers and Zeta 2 Function
Interpreting Riemann Function Denominator Values (for Negative Odd Integer Values of s)
The Central Issue for Mathematics
A New Mathematics
Prime Number Theorem: Alternative Formulation
Remarkable Relationships
Remarkable Relationships (2)
Remarkable Relationships (3)
Remarkable Relationships (4)
Incredible Nature of the Zeta Zeros (1)
Incredible Nature of the Zeta Zeros (2)
Incredible Nature of the Zeta Zeros (3)
Incredible Nature of the Zeta Zeros (4)
Incredible Nature of the Zeta Zeros (5)
Incredible Nature of the Zeta Zeros (6)
Incredible Nature of the Zeta Zeros (7)
Incredible Nature of the Zeta Zeros (8)
Incredible Nature of the Zeta Zeros (9)
Incredible Nature of the Zeta Zeros (10)
Incredible Nature of the Zeta Zeros (11)
Incredible Nature of the Zeta Zeros (12)
Incredible Nature of the Zeta Zeros (13)
Incredible Nature of the Zeta Zeros (14)
Incredible Nature of the Zeta Zeros (15)
Incredible Nature of the Zeta Zeros (16)
Incredible Nature of the Zeta Zeros (17)
Incredible Nature of the Zeta Zeros (18)
Incredible Nature of the Zeta Zeros (19)
Incredible Nature of the Zeta Zeros (20)
Incredible Nature of the Zeta Zeros (21)
Incredible Nature of the Zeta Zeros (22)
Incredible Nature of the Zeta Zeros (23)
Incredible Nature of the Zeta Zeros (24)
Incredible Nature of the Zeta Zeros (25)
Subatomic Structure of the Primes
Mathematical Revolution

2013

Calculating the Shadow Deviation
The Truly Remarkable Nature of the Number System
The Perfect Shadow Number System
Mysterious Role of 6 and 12
The Number 2
In a Nutshell
Two Complementary Zeta Functions (1)
Two Complementary Zeta Functions (2)
Two Complementary Zeta Functions (3)
Two Complementary Zeta Functions (4)
The Shadow of Mathematics
Two Complementary Zeta Functions (5)
Two Complementary Zeta Functions (6)
Two Complementary Zeta Functions (7)
Brief Interlude
More on Complementarity
Filling in the Picture (1)
Filling in the Picture (2)
Filling in the Picture (3)
Addition and Multiplication - Cardinal v Ordinal Interpretation of Number
Mathematics at the Crossroads
Stunning Accuracy
Number as Energy
Zeta 2 Formulation of Euler Product Formula
Addition and Multiplication as Complementary Facets of Same Phenomenon
No Longer Fit for Purpose!
Functional Equation for Zeta 2 Expression
Significance of 1/2 in Context of Riemann Hypothesis
Reformulating the Riemann Hypothesis
The True Holistic Nature of the Zeta Zeros
Precise Nature of Zeta 1 Zeros
Addendum on Formula for Zeta Zeros
Meaning of Imaginary
The Central Issue
The True Significance of the Zeta Zeros (Zeta 1 and Zeta 2)
Number as Dimension
Holistic v Analytic Interpretation
The Emperor Has No Clothes (1)
The Emperor Has No Clothes (2)
The Emperor Has No Clothes (3)
What It's All About
The Simple Explanation
Qualitative Nature of Prime Music
Central Message
Illustrating the Holistic Approach
The Holistic Nature of the Number System (1)
The Holistic Nature of the Number System (2)
The Holistic Nature of the Number System (3)
The Holistic Nature of the Number System (4)
The Holistic Nature of the Number System (5)
The Holistic Nature of the Number System (6)
The Holistic Nature of the Number System (7)
The Holistic Nature of the Number System (8)
The Holistic Nature of the Number System (9)
The Holistic Nature of the Number System (10)
The Holistic Nature of the Number System (11)
Where Science and Art Coincide (1)
Where Science and Art Coincide (2)
Where Science and Art Coincide (3)
Where Science and Art Coincide (4)
Where Science and Art Coincide (5)
Where Science and Art Coincide (6)
Where Science and Art Coincide (7)
Where Science and Art Coincide (8)
Where Science and Art Coincide (9)
Where Science and Art Coincide (10)
Where Science and Art Coincide (11)
Where Science and Art Coincide (12)
Where Science and Art Coincide (13)
Where Science and Art Coincide (14)
Where Science and Art Coincide (15)
Where Science and Art Coincide (16)
Where Science and Art Coincide (17)
Where Science and Art Coincide (18)
Where Science and Art Coincide (19)
Where Science and Art Coincide (20)
New Vision of the Number System
The Original Number System

2014

Important Role of Euler Identity
Return of Shadow Deviations
Simple Estimate of Frequency of Riemann Zeros (1)
Simple Estimate of Frequency of Riemann Zeros (2)
Further Considerations
Estimation of Frequency of Prime Numbers
Conversion Between the Two Aspects of the Number System
Ordinal Nature of Prime Numbers
Estimation of Frequency of Prime Numbers (2)
Where Addition and Multiplication Meet
More on Type 1 and Type 2 Conversions
Holistic Appreciation of the Riemann Zeros
Alternative Approach to Frequency of Primes
The Limits of Conventional Logic
Randomness and Order Among the Primes
Estimating the Total Sum of Composite Factors
Important Connections!
Complementary Views of Same Reality
Estimating Sum of Riemann Zeros
Estimating Sum of Riemann Zeros (2)
Unexpected Link
Interesting Observations
New Perspective on Prime Number Theorem (1)
New Perspective on Prime Number Theorem (2)
New Perspective on Prime Number Theorem (3)
New Perspective on Prime Number Theorem (4)
New Perspective on Prime Number Theorem (5)
New Perspective on Prime Number Theorem (6)
More on Randomness and Order (1)
More on Randomness and Order (2)
More on Randomness and Order (3)
More on Randomness and Order (4)
More on Randomness and Order (5)
More on Randomness and Order (6)
More on Randomness and Order (7)
New Perspective on Riemann Zeros
Complementary Formula for Zeta 2 Zeros (1)
Complementary Formula for Zeta 2 Zeros (2)
Complementary Formula for Zeta 2 Zeros (3)
Complementary Formula for Zeta 2 Zeros (4)
Complementary Formula for Zeta 2 Zeros (5)
Another Interesting Connection
Interesting Log Relationships (1)
Interesting Log Relationships (2)
Interesting Log Relationships (3)
Interesting Log Relationships (4)
Using Frequency Formula to Estimate Location of Riemann Zeros
Holistic Synchronous Nature of Number System (1)
Holistic Synchronous Nature of Number System (2)
Holistic Synchronous Nature of Number System (3)
Holistic Synchronous Nature of Number System (4)
Holistic Synchronous Nature of Number System (5)
Addendum on Erdős–Kac Theorem
More on Erdős–Kac Theorem
Interesting Connections
A Simple Example
Do Numbers Evolve (1)
Do Numbers Evolve (2)
Do Numbers Evolve (3)
Do Numbers Evolve (4)
Do Numbers Evolve (5)
Do Numbers Evolve (6)
Do Numbers Evolve (7)

2015

Slight Modification
Mathematical Revolution Required!
Zeta Zeros - Psychological and Mathematical Connections
The Zeta Zeros and Affective Appreciation
Number as the Theory of Everything
The True Nature of the Zeta Zeros (1)
The True Nature of the Zeta Zeros (2)
The True Nature of the Zeta Zeros (3)
The True Nature of the Zeta Zeros (4)
Connection Between Zeta 1 and Zeta 2 Functions
More on Dynamic Nature of Number (1)
More on Dynamic Nature of Number (2)
More on Dynamic Nature of Number (3)
More on Dynamic Nature of Number (4)
More on Dynamic Nature of Number (5)
Zeta Zeros Made Simple (1)
Zeta Zeros Made Simple (2)
Zeta Zeros Made Simple (3)
Zeta Zeros Made Simple (4)
Zeta Zeros Made Simple (5)
Zeta Zeros Made Simple (6)
Zeta Zeros Made Simple (7)
Zeta Zeros Made Simple (8)
Zeta Zeros Made Simple (9)
Zeta Zeros Made Simple (10)
Zeta Zeros Made Simple (11)
Zeta Zeros Made Simple (12)
A Brief Addendum
Zeta Zeros and the Changing Nature of Number (1)
Zeta Zeros and the Changing Nature of Number (2)
Zeta Zeros and the Changing Nature of Number (3)
Zeta Zeros and the Changing Nature of Number (4)
Zeta Zeros and the Changing Nature of Number (5)
Zeta Zeros and the Changing Nature of Number (6)
Zeta Zeros and the Changing Nature of Number (7)
Zeta Zeros and the Changing Nature of Number (8)
Zeta Zeros and the Changing Nature of Number (9)
Complementarity of the Number System
Clarifying Analytic and Holistic Interpretations of "2" (1)
Clarifying Analytic and Holistic Interpretations of "2" (2)
Clarifying Analytic and Holistic Interpretations of "2" (3)
Clarifying Analytic and Holistic Interpretations of "2" (4)
Clarifying Analytic and Holistic Interpretations of "2" (5)
Clarifying Analytic and Holistic Interpretations of "2" (6)
Clarifying Analytic and Holistic Interpretations of "2" (7)
Clarifying Analytic and Holistic Interpretations of "2" (8)
Clarifying Analytic and Holistic Interpretations of "2" (9)
Clarifying Analytic and Holistic Interpretations of "2" (10)
Clarifying Analytic and Holistic Interpretations of "2" (11)
Clarifying Analytic and Holistic Interpretations of "2" (12)
Clarifying Analytic and Holistic Interpretations of "2" (13)
Clarifying Analytic and Holistic Interpretations of "2" (14)
Clarifying Analytic and Holistic Interpretations of "2" (15)
Clarifying Analytic and Holistic Interpretations of "2" (16)
Clarifying Analytic and Holistic Interpretations of "2" (17)
Clarifying Analytic and Holistic Interpretations of "2" (18)
Clarifying Analytic and Holistic Interpretations of "2" (19)
Clarifying Analytic and Holistic Interpretations of "2" (20)

2016

Holistic Synchronicity (1)
Holistic Synchronicity (2)
Holistic Synchronicity (3)
Riemann Hypothesis: New Perspective (1)
Riemann Hypothesis: New Perspective (2)
Riemann Hypothesis: New Perspective (3)
Riemann Hypothesis: New Perspective (4)
Riemann Hypothesis: New Perspective (5)
Riemann Hypothesis: New Perspective (6)
Riemann Hypothesis: New Perspective (7)
Riemann Hypothesis: New Perspective (8)
Riemann Hypothesis: New Perspective (9)
Riemann Hypothesis: New Perspective (10)
Riemann Hypothesis: New Perspective (11)
Riemann Hypothesis: New Perspective (12)
Riemann Hypothesis: New Perspective (13)
Riemann Hypothesis: New Perspective (14)
Riemann Hypothesis: New Perspective (15)
Riemann Zeta Function: Important Number Relationships (1)
Riemann Zeta Function: Important Number Relationships (2)
Riemann Zeta Function: Important Number Relationships (3)
Riemann Zeta Function: Important Number Relationships (4)
Riemann Zeta Function: Important Number Relationships (5)
Riemann Zeta Function: Important Number Relationships (6)
Riemann Zeta Function: Important Number Relationships (7)
Riemann Zeta Function: Important Number Relationships (8)
Riemann Zeta Function: Important Number Relationships (9)
Riemann Zeta Function: Important Number Relationships (10)
Riemann Zeta Function: Important Number Relationships (11)
Riemann Zeta Function: Important Number Relationships (12)
Extended Riemann Connections (1)
Extended Riemann Connections (2)
Extended Riemann Connections (3)
Extended Riemann Connections (4)
Extended Riemann Connections (5)
Extended Riemann Connections (6)
Zeta 1 and Zeta 2 Functions - Complementary Nature
Prime Number Magic (1)
Prime Number Magic (2)
Prime Number Magic (3)
Zeta 2 Zeros - Key Significance (1)
Zeta 2 Zeros - Key Significance (2)
Zeta 2 Zeros - Key Significance (3)
Zeta 2 Zeros - Key Significance (4)
Zeta 2 Zeros - Key Significance (5)
Zeta 1 Zeros - Key Significance (1)
Zeta 1 Zeros - Key Significance (2)
Zeta 1 Zeros - Key Significance (3)
Zeta 1 Zeros - Key Significance (4)
Zeta 1 Zeros - Key Significance (5)
Zeta 1 Zeros - Key Significance (6)

2017

Zeta 1 Zeros - Key Significance (7)
Zeta 1 Zeros - Key Significance (8)
Zeta 1 Zeros - Key Significance (9)
Zeta 1 Zeros - Key Significance (10)
Zeta 3 Zeros - Key Significance (1)
Zeta 3 Zeros - Key Significance (2)
Zeta 3 Zeros - Key Significance (3)
Zeta 3 Zeros - Key Significance (4)
Reduced Zeta 1 Functions (1)
Reduced Zeta 1 Functions (2)
Enhanced Zeta 2 Functions (1)
Enhanced Zeta 2 Functions (2)
Enhanced Zeta 2 Functions (3)
True Significance of the Pi Connection in the Riemann Zeta 1 Function (1)
True Significance of the Pi Connection in the Riemann Zeta 1 Function (2)
Return of the Zeta 2 Function (1)
Return of the Zeta 2 Function (2)
Extending to Negative Values
True Dynamic Nature of Riemann Zeta Function
Where s = 0 (1)
Where s = 0 (2)
Where s = – 1
Where ζ– 1) = – 1/12!
More on the Significance of ζ– 1) = – 1/12!
Missing Piece of the Jigsaw
Analytic and Holistic Interpretation of Mathematical Dimensions
Product Formulation of Alternative Zeta 2 Function

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