The shapes of everyday things, like a tangle of string or a coffee mug, don't seem to require sophisticated math to understand. But there's an entire field of study, called topology, that examines how different shapes are related. Amazingly, some of this same math applies to quantum behavior that emerges near absolute zero. And this year's physics prize goes to three researchers that identified this relationship.
The basic concepts of topology are deceptively simple. Let's say you have a tangle of string. If you find the two ends and pull to remove any slack, how many knots will end up in the string? And how many different configurations of tangles will produce the same number of knots? Answering those questions mathematically is where topology comes in.
Similar math can be applied to three-dimensional items. For example, a bowl shape can be transformed into a variety of other different shapes, but not a coffee mug, since the latter has a single hole in it. Neither of those can be transformed into a traditional pretzel, which has three. Again, topology can help identify equivalent shapes and the means of transforming one into another.