The Deeper Roles of Mathematics in Physical Laws

TL;DR

This paper explores how the success of mathematics in physics stems from our descriptive choices and the pursuit of quantification, illustrating this through the concept of additivity and symmetry constraints in physical laws.

Contribution

It offers a new perspective on the role of mathematical concepts like additivity in deriving physical laws from symmetry constraints.

Findings

Mathematics' utility is linked to our description and quantification of the physical world.

Physical laws can be derived as symmetry constraint equations.

Additivity plays a fundamental role in understanding physical laws.

Abstract

Many have wondered how mathematics, which appears to be the result of both human creativity and human discovery, can possibly exhibit the degree of success and seemingly-universal applicability to quantifying the physical world as exemplified by the laws of physics. In this essay, I claim that much of the utility of mathematics arises from our choice of description of the physical world coupled with our desire to quantify it. This will be demonstrated in a practical sense by considering one of the most fundamental concepts of mathematics: additivity. This example will be used to show how many physical laws can be derived as constraint equations enforcing relevant symmetries in a sense that is far more fundamental than commonly appreciated.