Knot theory

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.

The noted mathematician and author Steven Strogatz explains how the conversations with experts in his new Quanta Magazine podcast address his lifelong fascination with timeless mysteries.

Two recent collaborations between mathematicians and DeepMind demonstrate the potential of machine learning to help researchers generate new mathematical conjectures.

Even as mathematicians and computer scientists proved big results in computational complexity, number theory and geometry, computers proved themselves increasingly indispensable in mathematics.