Unknotting knot theory

New techniques are beginning to unravel the mysteries of knots, revealing a great mathematical superstructure in the process

Sometimes, a simple, even childish question turns out to be connected to the deepest secrets of the universe. Here’s one: How many different ways can you tie your shoelaces?

Mathematicians have been puzzling over that question for a century or two, and the main thing they’ve discovered is that the question is really, really hard.