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 ...

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 ...

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 ...

The artificial intelligence (AI) program DeepMind has gotten closer to proving a math conjecture that's bedeviled mathematicians for decades and revealed another new conjecture that may unravel how ...

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 ...

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, ...