Knot theory

John Pardon sees connections between different areas of math that others don’t. For that vision, he’s now been awarded a Fields Medal.

With a newly discovered mathematical tool, researchers are hoping to gain unprecedented insight into the structure of complex knots.

Two mathematicians have proved that a straightforward question — how hard is it to untie a knot? — has a complicated answer.

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.

A new proof shows that a knot some thought would contradict the famed slice-ribbon conjecture doesn’t.

Far from being an abstract mathematical curiosity, knot theory has driven many findings in math and beyond.

For decades mathematicians have searched for a specific pair of surfaces that can’t be transformed into each other in four-dimensional space. Now they’ve found them.

“Ribbon concordance” will let mathematicians compare knots by linking them across four-dimensional space.

Steven Strogatz explores the mysteries of knots with the mathematicians Colin Adams and Lisa Piccirillo.