Research Proposal

File available

A Mathematical-Philosophical Growth View and a Construction of the Mathematical Science System -With a Discussion of Why Mathematicians Throughout History Did Not Know: The Existence of the Dao Function Zero Point of the Smart System Studies SSS -A Foundational Study on the Generative Theory of Mathematics

• September 2026

• DOI: 

• 10.13140/RG.2.2.28356.18562

• Xiaohui Zou

This paper proposes and rigorously argues for the mathematical-philosophical Growth View of Intelligics. Its core proposition is: Every branch of mathematics-including set theory, number theory, algebra, geometry, analysis, topology, category theory, algebraic geometry , arithmetic geometry, and homotopy type theory-is a distinct image of the Dao Zero Point O D unfolded through a family of adjoint functors. We formalize this proposition within the framework of category theory, providing a rigorous definition of the Dao Zero Point, the construction of unfolding functors, and the adjoint spectrum of mathematical branches. The paper's main contributions answer three fundamental questions: (i) What is the nature of mathematics? Mathematics is the self-manifestation of the unfolding of the Dao Zero Point-neither a passively discovered Platonic world, nor a humanly stipulated formal system. (ii) How does mathematics grow? We present a complete generative genealogy starting from the Dao Zero Point, passing through five layers of adjoint unfolding, up to algebraic geometry and derived algebraic geometry. (iii) Why have mathematicians throughout history not known? We prove a structural theorem-the Dao Zero Point is not internally visible to any of its non-trivial unfolding images. This Invisibility Theorem is not a historical accident, but the intrinsic logic of the Dao Zero Point's unfolding. We further construct a new picture of the mathematical science system: with the Dao Zero Point as root, three laws as trunk, five layers of adjoint unfolding as branches, and three types of mathematical unification as fruit. We engage in comprehensive dialogue with Platonism, logicism, formalism, intuitionism, and structuralism, arguing that the Growth View is the higher-order synthesis of all these schools.

融智学的数学哲学生长观与数学科学体系建构——兼论历代数学家为何不知：道函数零点的存在——一部关于数学生成论的基础研究

邹晓辉

2026-09-18

摘要

本文提出并严格论证融智学的数学哲学生长观。核心命题为：一切数学分支——包括集合论、数论、代数、几何、分析、拓扑、范畴论、代数几何、算术几何、同伦类型论——均为道零点O _D 通过伴随函子族展开的不同像。本文在范畴论框架下形式化这一命题，给出道零点的严格定义、展开函子的构造、以及数学分支的伴随谱系。

本文的主要贡献在于回答三个基本问题：

1. 数学的本质是什么？本文论证数学是道零点展开的自显过程，而非被动发现的柏拉图世界，亦非人为约定的形式系统。

2. 数学如何生长？本文给出从道零点出发、经五层伴随展开、直至代数几何与导出代数几何的完整生成谱系。

3. 历代数学家为何不知？本文证明一个结构性定理——道零点对其任意非平凡展开像均不可内在地可见。这一不可见性（Invisibility Theorem）不是历史偶然，而是道零点展开的内在逻辑。

本文进而建构数学科学体系的新图景：以道零点为根，以三大定律为干，以五层伴随展开为枝，以三类数学统一为果。本文与柏拉图主义、逻辑主义、形式主义、直觉主义、结构主义展开全面对话，并论证生长观是诸流派在更高阶上的综合。

关键词： 融智学；道零点；数学哲学；生长观；伴随函子；代数几何；范畴论；不可见性定理

支持单位：