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This work investigates the necessity of a foundational beginning in mathematics and how it can arise from minimal generative activity.

May 13, 2026Open Access

Why Mathematics Must Have a Beginning Mathematical Genesis: From Generativity to Equations and Universal Functions

Key Points

This work investigates the necessity of a foundational beginning in mathematics and how it can arise from minimal generative activity.
Developed a conceptual pathway from Minimal Generative Events (MGE) to stable structures and proto-mathematical operations.
Introduced formal aspects, including definitions, axioms, and operator theory, to establish the mathematical framework.
Integrated both conceptual and formal components into a unified framework called GTii Version 2.
Established the first theorem of GTii, confirming the semigroup structure of iterates.
Demonstrated how mathematical concepts can emerge from generativity, indicating a foundational basis for mathematics.

Abstract

Mathematical Genesis: From Generativity to Equations and Universal Functions (GTii Version 2) presents a complete conceptual and formal reconstruction of how mathematics can emerge from minimal generative activity. The document begins with the foundational question: Why must mathematics havea beginning? GTii answers this by introducing generativity as the pre‑mathematical substrate from which stability, regularity, proto‑relations, functions, equations, and universal functional compressions arise. Part I develops the conceptual pathway from Minimal Generative Events (MGE) to stable structuresand proto‑mathematical operations.Part II provides the formal mathematical layer: definitions, axioms, operator theory, proto‑equations,and the first theorem of GTii, establishing the semigroup structure of iterates. GTii Version 2 integrates both layers into a unified framework, offering a generative foundationfor the emergence of mathematical structure. Author: Waldemar Superson

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Waldemar Superson (Mon,) studied this question.

synapsesocial.com/papers/6a04153d79e20c90b4445062 https://doi.org/https://doi.org/10.5281/zenodo.20112988

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