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Untangling Knots
The Awesome World of Mathematical Knot Theory
One of my favorite things about mathematics is how it can show up in the most unexpected places. Fundamentally, math is the study of numerical patterns. We humans are very good at finding patterns and can find math just about everywhere. This includes common examples like geometry and algebra, but it also includes some less obvious examples like biology, social sciences, and ocean processes. In this article, I’m going to talk about the appearance of math in one of the most ancient human arts: knots.
Knots have been around for a long time. We estimate that the first knots began to be created at least 100,000 years ago by early humans through indirect fossil evidence¹. The first direct appearance of knots shows up in the form of fossils and artwork that contain knots. Knots had their heyday during the Age of Sail (roughly 1550 to 1850) when massive sailboats dominated European civilization. A rigorous knowledge of many different knots was required by the sailors operating these ships. Knots continue to be extremely useful in a variety of fields. Ask any climber or enthusiast of a similar outdoor sport and they will rattle off several key knots they use in their craft.
It may come as no surprise to you that mathematicians have sought to come up with a framework for describing knots. This…
