Every Knot is a Closed Circular Braid

Mathematician Mike Fellows thought up this demonstration of why every knot is a closed circular braid while riding on his bicycle.

This is an important lesson for all mathematicians: when you are stuck, don't bang your head on the table! Go outside, take a walk, ride your bike, play catch and gently be aware of the problem you are working on. Make a relaxed place in your brain where a creative solution can build itself.

If you have a problem-solving story like this one, send it in!

Mike's Problem-Solving Story

In order to get into graduate school, Mike had to show that he was mathematically capable and promising. His teacher suggested that he try to prove a theorem from Knot Theory: Every knot is a closed circular braid. Knowing that the theorem was true was a good start. Of course Mike could have looked it up, but the idea was to think it up on his own.

One day, he was thinking about it while he was riding his bike. The idea for a way to turn any knot into a closed circular braid ocurred to him. He kept thinking about it, and found a reason why it will always work and wrote it up as a proof. It turned out that Mike's proof wasn't the one that his teacher had in mind. He had thought up a proof that was brand new!

The Demonstration that Mike Thought Up