The Nobel Prize in Physics for 2016 has been awarded to three theoretical researchers for their insights into the odd behavior of matter in unusual phases, like superconductors, superfluid films and some kinds of magnets.

David J. Thouless receives half the prize, and Duncan M. Haldane and J. Michael Kosterlitz share the other half. All three used mathematics to explain the the properties of matter in certain states.

Their work relied on the field of topology, which describes properties that only change in integer steps. Thors Hans Hansson, a professor of theoretical physics who was on the Nobel Committe for Physics this year, pulled out a cinnamon bun, a bagel and a pretzel to explain the concept. "I brought my lunch," he joked, before explaining that the number of holes in each baked good represented a "topological invariant" — you can have no holes, one hole or two holes, but there's no such thing as half a hole.

Topologically, a plate, a cup and a cinnamon bun are categorically the same, with no holes, while a coffee cup and a bagel are in another category, with one hole.

The researchers' prize-winning insight was that concepts from topology could explain what was happening when matter changed phases in unusual situations. They weren't looking at familiar phase changes, like ice melting into water, but strange changes that occur with very thin layers of matter, very cold substances or extreme magnetic fields.

Hansson set aside his bagel for a new metaphor — a tornado — to explain how a topological phase transition works. A swirling vortex in a thin layer of liquid is like a hole, he said, in that you either have one or you don't; you count it in integers. And a switch from paired vortices to solitary vortices could explain a puzzling phase transition in helium fields.

The discoveries that won the Nobel are theoretical — and beautiful, a Nobel spokesman said. They could have concrete, practical applications in electronics and computing, but the Nobel isn't being awarded for those benefits, Hansson noted, but for the "profound insights into physics" on a theoretical level.

Here's more on the award-winning research, from the Nobel Prize website:

"The three Laureates' use of topological concepts in physics was decisive for their discoveries. ... Using topology as a tool, they were able to astound the experts. In the early 1970s, Michael Kosterlitz and David Thouless overturned the then current theory that superconductivity or suprafluidity could not occur in thin layers. They demonstrated that superconductivity could occur at low temperatures and also explained the mechanism, phase transition, that makes superconductivity disappear at higher temperatures."In the 1980s, Thouless was able to explain a previous experiment with very thin electrically conducting layers in which conductance was precisely measured as integer steps. He showed that these integers were topological in their nature. At around the same time, Duncan Haldane discovered how topological concepts can be used to understand the properties of chains of small magnets found in some materials."We now know of many topological phases, not only in thin layers and threads, but also in ordinary three-dimensional materials. Over the last decade, this area has boosted frontline research in condensed matter physics, not least because of the hope that topological materials could be used in new generations of electronics and superconductors, or in future quantum computers. Current research is revealing the secrets of matter in the exotic worlds discovered by this year's Nobel Laureates."

A longer description of the research, written for a general audience, is available here; if you'd like to see the math for yourself, the scientific background is here.

Copyright 2016 NPR. To see more, visit