Unity Root Matrix Theory (URMT)
This site was updated 3rd Mar 2026
Contact: Richard Miller, richard@urmt.org
Free PDF downloads
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.

Published Books

 

Why bother with URMT?

URMT Overview

A complete overview of URMT, including Special Relativity

and Quantum Mechanics. PDF download

 

Miscellaneous related topics

Number Theory and Physics

Errata: books 1 to 5

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“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

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April 2021

The Coordinate Equation & Fermat’s Last Theorem

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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!