Knot theory began as an attempt to understand the fundamental makeup of the universe. In 1867, when scientists were eagerly trying to figure out what could possibly account for all the different kinds ...

Three high schoolers and their mentor revisited a century-old theorem to prove that all knots can be found in a fractal called the Menger sponge. In the fall of 2021, Malors Espinosa set out to devise ...

Consider the plight of a gardener struggling with a recalcitrant tangle of garden hose. Sometimes, no amount of pulling or twisting unsnarls the coils. At other times, the tangles readily come apart, ...

Conway’s knot, a famous mathematical problem, was a tricky one to untangle. Mathematicians have been arguing about how to solve it for more than 50 years—until 2018, when graduate student Lisa ...

Find a string. Really. Do it. Now twist, tie and tangle it as much as you like. Finally, attach the two loose ends of your string together to make a closed loop. (This is a crucial step.) What you ...