At the heart of every resonator — be it a cello, a gravitational wave detector, or the antenna in your cell phone — there is a beautiful bit of mathematics that has been heretofore unacknowledged.

2/11/1991 “All Tied Up in Knots (Knotting Theory in the Natural Sciences: Untangling some of the Knotty Mysteries of DNA)” ...

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 ...

MIT researchers develop a mathematical model to predict a knot’s stability with the help of color-changing fibers. Photo by Joseph Sandt Knots are some of the oldest and most-used technologies that ...

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 ...

Scanning the crowd at a fancy soiree may reveal a wide array of neckties, each fastened with a highly complex mathematical object masquerading as fashion. An entire field of mathematics is devoted to ...

Color-changing fibers are helping scientists to understand, for the first time, the exact ways some knots hold tighter than others. In 2018, researchers developed pressure-sensitive fibers in part to ...

Mathematicians say knots cannot exist in four-dimensional space. (Image: Canva) Knots cannot exist in four-dimensional space, say mathematicians. In 4D, any knot can be untied without cutting the rope ...

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, ...