Mathematicians say knots cannot exist in four-dimensional space because the extra dimension allows a rope to move around itself and untangle, revealing surprising insights into geometry and topology.

From mathematical cookie cutters to wormholes, we pick favourite 3D-printable objects. Also, download an exclusive New Scientist Christmas tree ornament – a ...

When most people think of shapes, they imagine a triangle, a rectangle, or maybe even a fancier-sounding rhombus or trapezoid. But to mathematicians, shapes encompass a vast universe of surprising ...