# 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 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:

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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.