Topology

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

Four Fields Medals were awarded for major breakthroughs in geometry, combinatorics, statistical physics and number theory, even as mathematicians continued to wrestle with how computers are changing the discipline.

A quantum approach to data analysis that relies on the study of shapes will likely remain an example of a quantum advantage — albeit for increasingly unlikely scenarios.

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

A comprehensive mathematical framework treats wrinkling patterns as elegant solutions to geometric problems.

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.

Using ideas borrowed from graph theory, two mathematicians have shown that extremely complex surfaces are easy to traverse.

“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.