Spectrum of Mathematics

Contributions that involve further reflections on the number system, closely related to my "Riemann Hypothesis" blog 

2011

• Three Types of Mathematics

• Three Types of Mathematics (2)

• Three Types of Mathematics (3)

• Basic Problem

• A New Number System

• Resolving Inconsistency

• Addendum on Squares

• Reformulating Basic Notions

• Imaginary - Hidden Qualitative Notion

• The Number System Revisited

• Importance of Dimensions

• Holistic Mathematical Dimensions (1)

• Nature of Prime Numbers

• Holistic Values

• Differentiation and Integration

• The Number e

• The True Nature of Prime Numbers

• Natural Logs

• The Imaginary Concept

• Euler's Identity

• Interesting Comments

• Spiritual Illumination

• When 0 is not Nothing!

• Avoiding Contradiction

• A New Number System (1)

• A New Number System (2)

• Alain Connes

• A New Number System (3)

• Parallel Riemann Hypothesis!

• More on Euler Identity

• Nature of Number as Dimension

• Multiplication and Addition

• Mathematical Dimensions and Psychological Development (1)

• Mathematical Dimensions and Psychological Development (2)

• Three Levels of Appreciation of Transcendental Numbers

• Number as Dynamic Interaction

• Wholes and Parts

• Cardinal and Ordinal Numbers

• Cardinal and Ordinal Numbers (2)

• Partition Numbers

• Fibonacci Sty[e Relationships as Fractals

2012

• New Role of Mathematics

• Three Mathematical Interpretations

• Generalising New Approach

• The Square Root of 1

2013

• Tapestry of the Number System

• Cyclic Primes

• Cyclic Primes (2)

2014

• Generating Primes

• Interesting Number Relationships

• Reflections on Experience (1)

• Reflections on Experience (2)

• Reflections on Experience (3)

• Reflections on  Experience (4)

• Reflections on  Experience (5)

• Reflections on Experience (6)

• Reflections on Experience (7)

• Reflections on Experience (8)

• Reflections on Experience (9)

• Reflections on Experience (10)

• Reflections on Experience (11)

2015

• Reflections on Experience (12)

• Reflections on Experience (13)

• Intricacies of Addition and Multiplication (1)

• Intricacies of Addition and Multiplication (2)

• Intricacies of Addition and Multiplication (3)

• Intricacies of Addition and Multiplication (4)

• Intricacies of Addition and Multiplication (5)

• Intricacies of Addition and Multiplication (6)

• Intricacies of Addition and Multiplication (7)

• Reflections on Number (1)

• Reflections on Number (2) 

• Reflections on Number (3) 

• Reflections on Number (4) 

• Reflections on Number (5) 

• Wholes and Parts (1)

• Wholes and Parts (2)

• Wholes and Parts (3)

• Wholes and Parts (4)

• Wholes and Parts (5)

• Wholes and Parts (6)

• Wholes and Parts (7)

• Wholes and Parts (8)

• Wholes and Parts (9)

• Wholes and Parts (10)

• Wholes and Parts (11)

2016

• Wholes and Parts (12)

• Wholes and Parts (13)

• Remarkable Features of Number System (1)

• Remarkable Features of Number System (2)

• Remarkable Features of Number System (3)

• Remarkable Features of Number System (4)

• Average Frequency of All Prime Factors of a Number

• Predicting Frequency of Factors

• Surprising Result

• (Distinct) Prime Factors

• Illustration of Remainders

• The Generalised Fibonacci Sequence

• Fascinating Connections

• Approximating ζ(s) between 0 and – 1

• Approximating ζ(s) between – 1 and – 2

• Approximation Formulas for Negative Values of ζ(s)

•  Approximating the Non-Trivial Zeros

• Approximating the Non-Trivial Zeros (2)

• More Interesting Relationships

• Another Interesting Relationship

• Further Investigation

• Buddhist Mathematics

2017

• Twin Primes (1)

• Twin Primes (2)

• Ramanujan's Letter (1)

• Ramanujan's Letter (2)

• Ramanujan's Letter (3)

• Ramanujan's Letter (4)

• Ramanujan's Letter (5)

• Ramanujan's Letter (6)

• Ramanujan's Letter (7)

• Polynomial Equations and Associated Number Sequences (1)

• Polynomial Equations and Associated Number Sequences (2)

• A  Special Case (1)

• A  Special Case (2)

• A  Special Case (3)

• A  Special Case (4)

• A  Special Case (5)

• Numbers - Distinguishing Rational and Intuitive Understanding

• Imaginary Numbers

• Ratios and Sums of Reciprocals

• Surprising Connections to the Zeta Function

• New Perspective on Zeta Function 

• Some Interesting Connections

• Some Number Magic

• Some Number Magic (2)

• Interesting Log Relationships (1)

• Interesting Relationships Continued

• Interesting Relationships Continued (2)

• Symmetrical Geometrical Objects

• Connections with Symmetry

• Further Interesting Connections

2018

• Testing for Primes

• Interesting Log Relationships (2)

• Interesting Log Relationships (3)

• Octagonal and Triangular Numbers (1)

• Octagonal and Triangular Numbers (2)

• Octagonal and Triangular Numbers (3)

• More on Octagonal Numbers

• Extending Relationships for Octagonal Numbers

• Extending Relationships (2)

• Extending Relationships (3)

• Calculating Frequency of Palindromes

• Fascinating Palindrome Connection (1)

• Fascinating Palindrome Connection (2)

• Pentagonal Number Theorem (1)

• Pentagonal Number Theorem (2)

• Pentagonal Number Theorem (3)

• Pentagonal Number Theorem (4)

2019

• Ramanujan's Tau Function and Euler's Pentagonal Number Theorem

2021

• Generalised Formulae for e

• Polygonal Numbers and e (1)

• Polygonal Numbers and e (2)