---
pubDate: 2019-09-04
title: Mathematical Manifestation
abstract: |
  How can we expect expect mathematical explanations to manifest in real
  phenomenon in the actual world?
tags:
  - mathematics
  - philosophy
  - science
---

## Introduction

Question: _Why is mathematics useful for, and often seemingly prophetic of,
physics?_

There are bevies of examples where even the most esoteric
[pure mathematics](https://en.wikipedia.org/wiki/Pure_mathematics) finds its way
into physical theories. Many times the pure mathematics is developed long before
the physical theories and with no intention of the physical use. Just to name a
few:

- TODO

To me, and I would assume many others, this suggests a sense of fundamental
truth about physical reality that pure mathematics can expose. It feels like a
mystical revelation, especially when the particular instances are not rigorously
understood.

One resolution, from the perspective of physics, is that the relations to
results in pure mathematics are only trivial. There are cases, certainly, where
this resolution applies. The sum of _integers_ 1 and 1 is 2, just as the count
of a pair of _physical_ atoms is 2.

So, are there results from pure mathematics that inspire physics in a nontrivial
way? In this article I argue that this is possible and will offer a few possible
examples.

## Nontriviality

What would it mean for such a relationship to be _nontrivial_?

## Mathematical Mirror

Physics mirrors mathematics.

## Trends

Trends of this phenomenon.