Knot theory, a branch of topology dedicated to the study of embeddings of circles in three-dimensional space, intersects deeply with homotopy theory—the study of continuous deformations between ...

Knot theory, a branch of topology, examines the intricate properties of closed curves embedded in three-dimensional space. At its core is the study of knot invariants—quantitative measures that remain ...

You may not have heard of knot theory. But take it from Bill Menasco, a knot theorist of 35 years: This field of mathematics, rich in aesthetic beauty and intellectual challenges, has come a long way ...

For over 50 years, mathematicians have argued over the nature of a complex knot. The tangled problem, known as Conway’s knot, is so fabled among mathematicians that a depiction of the knot even graces ...

Scientists have developed a new method using knot theory to find the optimal routes for future space missions without the need to waste fuel. Just as sat-nav did away with the need to argue over the ...

For Elisabetta Matsumoto, knot theory is knit theory. Elisabetta Matsumoto holds a Geared Cuboctahedral Jitterbug that she designed with mathematician Henry Segerman.Credit...Johnathon Kelso for The ...

When a spacecraft is circling a planet or sailing among a set of moons, navigating between different orbits can be tough – but a trick from knot theory may help. It can be used to identify points ...