A Conceptual Tower of Mathematical Structures: From Sets to Meta-Frameworks
Year: 2025
Type: article
Abstract: This paper proposes a structured overview of core mathematical structures, arranged in a conceptual tower from foundational to meta-theoretical frameworks. The classification aims to illuminate the relationships between key domains in mathematics, such as algebra, topology, geometry, analysis, and category theory. Emphasis is placed on the increasing levels of structural richness, abstraction, and applicability, with a view toward foundational clarity and unification.Note: There is a small typo — Riemannian manifold is listed under Geometric Structures, when it should be under the Manifold level. This will be corrected in future versions. Also, the natural place of manifold is after topology and before geometry.
Author: Azari, Ehsan
Language: English
Subfield: Theoretical Computer Science
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6949905604
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