Bridge Numbers: A Knotty Journey

Take a long string, tie it in a complicated knot, and fuse the ends together. This gives you a mathematical knot. In your knot, you will have sections which go over other sections, and only over. These are called bridges. The least number of bridges in any drawing of a knot is called the bridge number of that knot. We can use the bridge number to tell knots apart. We are studying ways to draw the knot so that we have the fewest number of bridges. There are a large number of knots with unknown bridge numbers, including the knots with 12 crossings. Because these bridge numbers are unknown, there is a gap in the knowledge in knot theory. We are trying to fill that gap