Tie a trefoil knot in a piece of string, seal the ends together, and try to wiggle it free without cutting. In three-dimensional space, the knot holds firm. Add a fourth spatial dimension, however, ...

Knot theory, a vibrant branch of topology, investigates the properties of knots viewed as embeddings of circles in three-dimensional space. Central to this field are knot invariants—algebraic or ...

Sometimes, a simple, even childish question turns out to be connected to the deepest secrets of the universe. Here’s one: How many different ways can you tie your shoelaces? Mathematicians have been ...

When Lisa Piccirillo solved a decades-old mystery about the “Conway knot,” she had to overcome the knot’s uncanny ability to hoodwink some of the most powerful tools mathematicians have devised. Known ...

Virtual Knot Theory extends classical knot theory by incorporating virtual crossings alongside traditional over‐ and under‐crossings. Originating from Kauffman’s work in the late 20th century, the ...

Add Yahoo as a preferred source to see more of our stories on Google. Find a string. Really. Do it. Now twist, tie and tangle it as much as you like. Finally, attach the two loose ends of your string ...

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, ...

Q: When is a knot not a knot? A: When it's a quantum computer. Steve Simon explains how a remarkable link between knot theory and certain quantum systems may be useful for quantum information ...