Wrapping your head around  Knot Equivalence Theory can make untangling earphones seem like child's play. This theory explores whether two knots are essentially the same by transforming one into the other through a series of twists and stretches, without any breaking. Consider it this way: according to knot equivalence theory, two twisty pretzels are the same if you can squish and stretch one to look exactly like the other without breaking it.

So, why would anyone study knots? Well, way back, in the 1800s, Lord Kelvin had a theory that atoms were knots in space, and that properties of the elements were related to knotting between atoms. Kelvin turned out to be wrong, but by then, knot theory was already growing as its own field of math.