Mathematics via Symmetry

TL;DR

This paper proposes viewing mathematics as a form of symmetry that preserves truth under certain transformations, aligning it with physical sciences and offering new insights into its philosophical foundations.

Contribution

It introduces a novel perspective of mathematics as symmetry-based, connecting it with scientific principles and clarifying philosophical issues.

Findings

Mathematics characterized by symmetry transformations preserving truth.

Aligns mathematical concepts with physical symmetry principles.

Provides new philosophical insights into the nature of mathematics.

Abstract

We state the defining characteristic of mathematics as a type of symmetry where one can change the connotation of a mathematical statement in a certain way when the statement's truth value remains the same. This view of mathematics as satisfying such symmetry places mathematics as comparable with modern views of physics and science where, over the past century, symmetry also plays a defining role. We explore the very nature of mathematics and its relationship with natural science from this perspective. This point of view helps clarify some standard problems in the philosophy of mathematics.