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We’re talking about knots here, and while some can be quite simple and easily come undone, others require hours of plotting and patience, while the toughest remain impossible to untie.

From little kids learning to tie their shoes, to scientists studying DNA strands to seek treatments for serious illness, to artists creating mosaics, knots are all around us.

They’re also a fun and tangible way to test and explain complicated math concepts. This summer, Ana Wright, a 51���� professor, and student researcher Vincent Reynolds ’26 are using knot theory to explore and develop knot games and puzzles.

Wright didn’t plan on being a math major in college, but a knot theory course helped change that path. Now an assistant professor of mathematics and computer science at 51����, it’s one of her favorite things to teach and research. 

“I always liked solving puzzles and thinking about different logical problems but did not like math as a kid,” Wright said. “As the courses became more creative and open-ended, I liked math a lot more.”

Knot theory, a subset of topology, is the study of how one-dimensional circles can be tangled up in three dimensional spaces.

Reynolds, who double majors in mathematics and educational studies, loved math growing up and came to 51���� to pursue that interest. He plans to earn a doctorate after college and become a mathematics professor.

Knot or Unknot

The two have been recreating new versions of The Knotting-Unknotting game that came out in 2010. In the game, one player tries to untie the knot, and the other tries to create a knot that can’t be untangled. You can play the game with simple strands of string or rubber, or a pencil and paper. They also wrote codes to help crack thousands of potential outcomes.

Reynolds had the idea to put mosaics on slide puzzles, which they’ll make on a 3-D printer. A single slide puzzle can have multiple solutions — brain twisters they hope will appeal to everyone from young kids to aging adults.

He said the summer research has been a challenging and lively way to study math — far more fun than formulaic. It’s also made him think differently about the importance of knots.

“In biology and chemistry, you think about how DNA is folded into knots,” he said. “We can also think about fishing — we have to tie knots so the hook stays on the line. Knot theory can help tell us what’s a better knot to tie so the fish doesn’t take the hook with it.”

And knots are easy to explain to non-math types.

Knowing knot theory can also be a sought-out source of expertise.

“Often when I tell people I teach knot theory, they’ll bring up things like having tangled up headphone cables or garden hoses,” Wright said. “Those problems in life are a little easier to deal with because they’re always going to have a loose end.”