Unity Root Matrix Theory (URMT)
Unity Root Matrix Theory is an integer-based theory that has both a pure number-theoretic side, with connections to Fermat’s Last Theorem and the Riemann Hypothesis, and a physical side by virtue of the similarity of its equations and phenomenology to that of Physics. It offers a possible discrete formulation of the laws of nature without recourse to real numbers or continuous equations.
URMT Overview
A complete overview of URMT, including Special Relativity
and Quantum Mechanics. PDF download
Number Theory and Physics
“The Laws of Physics are those of Number Theory”
This is the view of the author (Richard J Miller) of Unity Root Matrix Theory (URMT).
Whilst there is absolutely no denying the Standard Model and General Relativity,
his belief is that nature is ultimately discrete and any quantum theory of gravity
will have to embrace this. In the author’s opinion, current physical laws are merely
a continuous-valued, macroscopic approximation to what is ultimately a discrete form.
Any such discrete formulation should have no concept of physical laws at its lowest
level and, instead, such laws, including the very concepts of space and time, only
materialise as the numbers grow larger.
April 2021
Fermat’s Last Theorem and Pythagoras
as an Eigenvector Problem
PDF download
April 2021
The Coordinate Equation & Fermat’s Last Theorem
PDF download
Mar 2026 Latest, Book 6
Work has resumed on a sixth book, tentatively titled Higher Order Extensions, that
seeks to extend to cubic and higher order exponents, both the number-theoretic and
physical results already obtained for a quadratic exponent, notably Pythagoras, as
published in books two to five. Work for this sixth book actually started in 2021,
with publication of the two papers given in the links below. The work was then suspended
for a few years whilst the author pursued other commitments - always in mathematics
and physics!