Why knot?

Thomas Mattman

You may have heard of string theory, but have you ever heard of knot theory? Thomas Mattman, a professor of mathematics and statistics at Chico State, has a passion for knots and the mathematical study of them, and shares it with colleagues and students alike at the annual Topology Conference at Chico State (happening May 2-4), where knot theorists from all over the continent come to talk knots. Mattman, a native of Canada, has two young daughters with his wife, local jazz pianist Shigemi Minetaka. He has been teaching at Chico State for 13 years and has been working with knot theory for nearly 20 years.

What exactly is knot theory?

We look at knots, which are what you think, but, the question is, when somebody gives you two jumbles of string, you want to know—is there a way to move this one around to make it look just like that one? It’s hard to tell just by looking at it, so what we usually do is find different ways of associating a number or some equation with the two knots, so that if they’re different, then the equations will be different.

Where does knot theory come from?

It started with chemists about a hundred years ago. Before they had the atomic theory, they had this idea that substances were different because they were represented by different knots, and that’s what made nickel different from iron. So they started to make a table of knots, like a periodic table. But then, pretty soon after that, they started to know more about atoms, so the chemists put it aside and the mathematicians got interested and started making it their own.

What is it that fascinates you about the theory?

For me it’s like a puzzle. Some people do crossword puzzles, some do Sudoku; it’s an intellectual challenge. It’s like Mount Everest—you do it because it’s there.

What are some of its practical applications?

One of the main things that people have been doing is using it to study DNA. It turns out that there’s an enzyme that will grab two pieces of DNA and make a little break in one of them and pass through the other and then refasten. This enzyme is really clever because it can take a complicated bit of DNA, that’s really tangled up, and untangle it very efficiently. Mathematicians can help biologists understand how this enzyme works.

Anything else you’d like to add?

Mathematics has a lot of creativity and beauty to it, and it’s unfortunate that many people don’t have a chance to see that. Knot theory doesn’t feel like math for a lot of people, so it’s a nice way to make contact with those who maybe had a bad experience with math before.