What question did this study set out to answer?

The study aims to redefine the concept of zeros in addition and multiplication through a new model. It explores the interplay between existence and non-existence using a monadic framework.

March 21, 2026Open Access

UMA-Monad Theory: A sketch for the zeros of addition and multiplication

Key Points

The study aims to redefine the concept of zeros in addition and multiplication through a new model. It explores the interplay between existence and non-existence using a monadic framework.
Provides a speculative sketch on the concept of zeros in mathematics.
Establishes a model involving multiple universes and the Monad as a fundamental unit.
Explores the collision of additive and multiplicative worlds at the point of zero.
Redefines '0' as an exit point rather than a void in mathematics.
Introduces the concept of the Universal Mapping Absolute Monad to integrate addition and multiplication.
Highlights potential threats to universal equilibrium due to multiplicative proliferation.

Abstract

This paper is a speculative sketch by a painter attempting to redefine "zeros" in addition and multiplication. The author reimagines the origin of numbers not as static symbols such as "0" or "1," but as a multilayered universe model where the law of conservation of energy functions dynamically. In this model, Leibniz's "Monad" is established as the fundamental unit of existence, assuming five universal spaces: "Universe A (the Pole of Existence)," where the Monad manifests; "Universe E (the Pole of Non-existence)," where dimensions are infinitely folded; and "Universe C (the Neutral Mirror)," which serves as their boundary. In particular, this study focuses on the problem of the singularity where the additive world (parallel expansion) and the multiplicative world (dimensional generation) collide at "0," threatening universal equilibrium through the infinite proliferation of multiplicative dimensions. By reinterpreting "0" in standard mathematics not as a mere void, but as an "exit" through which energy from Universe E refluxes into Universe A, the paper argues for the necessity of the "Universal Mapping Absolute (UMA) Monad," which integrates addition and multiplication without contradiction. This paper aims to present these intuitive ideas as a preliminary stage to rigorous mathematical proof.

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