Introduction

The Riemann Hypothesis has fascinated and intrigued me for many years and over the past two years I am confident that I have resolved it to my own satisfaction.

However I am well aware that I will face great difficulties in communicating this fact for appreciation of my very approach requires acceptance of a new - and largely - unrecognised interpretation of Mathematics.

From my perspective, it is now quite clear why attempts to prove the Riemann Hypothesis (within the standard accepted understanding of mathematics) have met with continued failure, as quite simply these are not adequate for the task in question.

So the first great requirement in coming to appreciation of the true nature of the Riemann Hypothesis, is the realisation - and corresponding acceptance - that what is commonly referred to as Mathematics represents in fact just one important aspect of an overall comprehensive mathematical system.


It might help to appreciate this point with reference to the analogy of a scissors.

Clearly the scissors has two blades of equal importance. In like manner Mathematics - rightly understood - contains two aspects of equal importance. However, quite remarkably only one of these aspects is presently recognised!

In other words what is commonly referred to as Mathematics refers simply to the quantitative interpretation of mathematical symbols in what might therefore be referred to as Conventional Mathematics. We will see as we proceed how such mathematics is related philosophically to a linear use of logic!

However there is a corresponding qualitative interpretation of all mathematical symbols that is of equal importance. And it is this latter interpretation that has engaged my attention now for more than 40 years in what I refer to as Holistic Mathematics. By contrast this aspect of Mathematics is based on an alternative circular use of logic relating to the dynamic interaction of dimensions (or directions) in experience.

Of course for true functioning of a scissors, both blades must operate in conjunction with each other. Likewise for a truly comprehensive functioning mathematical system both the quantitative and qualitative aspects must be closely associated with each other in all mathematical interpretation. This combined third aspect I refer to as Radial Mathematics.

Now unless one is willing to considerably widen perspectives as to what is meant by Mathematics, there is little hope of appreciating the sublime secrets enfolded in the Riemann Hypothesis.

Indeed ultimately the Riemann Hypothesis serves as the fundamental axiom necessary for the consistent interaction of both the quantitative and qualitative aspects of Mathematics.

Needless to say therefore, the Hypothesis (which properly relates to the necessary relationship between both aspects) cannot thereby be proved with respect to just one (i.e. the standard quantitative aspect).

So the Riemann Hypothesis has no solution in conventional mathematical terms. However the real message of what follows is how extraordinarily limited in fact is the present conception of mathematics.

As we know the binary system which potentially can be used in computers to encode all information is based on the quantitative use of the two digits 1 and 0.

Likewise a comprehensive mathematical system is based on a holistic binary system that incorporates both linear (1) and circular (0) logic. And such a dynamic system has the power potentially to scientifically encode all transformation processes.

Just imagine how limited digital technology would be if we confined ourselves to the use of just one quantitative digit (i.e. 1)!

This in fact should indicate how limited is in fact current mathematical understanding that is solely based on just the qualitative digit of the linear logical system (1).


So ultimately, what is even more important than the attempt to resolve the Riemann Hypothesis is the realisation of the true nature of mathematical activity (that combines distinctive quantitative and qualitative interpretations).

And paradoxically with this realisation (i.e. of the true nature of mathematics) comes a remarkably simple solution to the Riemann Hypothesis!