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 ...

(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 ...

As chemists tie the most complicated molecular knot yet, biophysicists create a “periodic table” that describes what kinds of knots are possible. The world is tied up in knots. They form spontaneously ...

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 ...

How can mathematical theory predict the strongest knots in real life? The answer to that question has remained elusive despite humans relying on knots for thousands of years while fishing, hunting, ...

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 ...