When is a coffee mug a donut? Topology explains it

A topologist is a person who cannot tell the difference between a coffee mug and a donut -- so goes a joke about a little-known scientific field crowned Tuesday with a Nobel Physics Prize. The quip describes it perfectly: topology explains how a material's shape can be completely deformed into new one without losing its core properties. In the metaphor, the mug and the donut are one and the same.