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 ...

Many of the processes essential to life involve proteins -- long molecules which 'fold' into three-dimensional shapes allowing them to perform their biological role. Many of the processes essential to ...

Knots are everywhere—from tangled headphones to DNA strands packed inside viruses—but how an isolated filament can knot itself without collisions or external agitation has remained a longstanding ...

(Nanowerk News) Consider a short piece of rope: could you guess which knots are more likely to form if you crumple and shake it? Synthetic chemists have long been working on a molecular version of ...

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 ...

Special fibers that change color when they are under strain have helped scientists come up with some simple rules that can predict how a knot will perform in the real world. People have used knots ...