(Opening disclaimer: as with most of my writings on science, I have no formal training in the area. Perhaps someday, but for now I am merely a curious bystander. What I present below is my best attempt at understanding the topic, but for detailed information (and fact-checking), follow the various provided links.)
Mathematics is a language with its own grammar and syntax. Mathematicians work to see what coherent sentences can be written with that language. Many times they do not know what to do with the sentences they compose, and many times those sentences later turn out to be accurate depictions of physical phenomena. Because they form complete sentences, they can also reveal things previously unknown in physics.
Imagine you are working on a physics problem and you are able to string together a theory that looks something like, “The quick brown fox…” You are absolutely certain that this phrase is part of the solution to your problem, but you are also certain that it is incomplete. Your friend the mathematical grammarian happens to stop by for a visit and she looks at your discovery. “Well that’s funny,” she says, “that looks just like the first part of a sentence I uncovered with the language of mathematics.” You look at her sentence, “The quick brown fox jumped over the lazy dog,” and you realize her complete sentence is not only a perfect match to the fragment you already have, it helps to explain things you previously could not figure out. Your friend had no idea that her sentence corresponded to the real world. To her it was just a beautiful formulation from mathematical grammar. For you, this abstract piece of math helps to open a new window into the world.
This basic analogy points toward a broader reality: mathematics has the uncanny ability to describe the world around us.Continue Reading