# The utterly prosaic connection between physics and mathematics

## TL;DR

This paper argues that the deep connection between physics and mathematics is practical and driven by physics questions, with mathematics developing in response to these questions and facilitating scientific progress.

## Contribution

It offers a pragmatic perspective on the physics-mathematics relationship, contrasting with more speculative views like the Mathematical Universe Hypothesis.

## Key findings

- Mathematics is developed in response to physics problems.
- Utilitarian mathematics correlates with significant physics progress.
- The connection is practical rather than mysterious or purely philosophical.

## Abstract

Eugene Wigner famously argued for the "unreasonable effectiveness of mathematics" for describing physics and other natural sciences in his 1960 essay. That essay has now led to some 55 years of (sometimes anguished) soul searching --- responses range from "So what? Why do you think we developed mathematics in the first place?", through to extremely speculative ruminations on the existence of the universe (multiverse) as a purely mathematical entity --- the Mathematical Universe Hypothesis. In the current essay I will steer an utterly prosaic middle course: Much of the mathematics we develop is informed by physics questions we are tying to solve; and those physics questions for which the most utilitarian mathematics has successfully been developed are typically those where the best physics progress has been made.