Few explorers have delved into stranger worlds than the three newest Nobel Laureates, who just won this year’s Nobel Prize for Physics. These eminent physicists have been honored for their work on some the most exotic states of matter, making sense of its fundamental mysteries and opening doors for today’s era of exploration and development for new materials like topological metals, insulators, and superconductors.

The Royal Swedish Academy of Sciences jointly awarded the prize with one half going to David J. Thouless, of the University of Washington, and the other half to F. Duncan M. Haldane, of Princeton University and J. Michael Kosterlitz of Brown University “for theoretical discoveries of topological phase transitions and topological phases of matter.” If that sounds abstract to you, you’re not alone: The winners’ achievements were so esoteric that one committee member sought to demonstrate them using a host of breakfast breads.

Thouless, Haldane, and Kosterlitz work in a surreal part of the physical world that might be described as “the flatlands.” This world is found on the surfaces of matter, or inside layers so thin that they are essentially two-dimensional; in fact, some of Haldane's work focuses on threads so thin that they are basically one-dimensional. Here, matter takes some of its strangest forms.

During the 1970s and 1980s, the scientists revealed secrets of the strange forms found in this realm, including superconductors, superfluids and thin magnetic film. This morning, Stockholm University physicist Thors Hans Hansson, a member of the Nobel Committee for Physics, explained the elegant mathematical concept they used for the prize-winning discoveries using a cinnamon bun, a bagel and a pretzel.

Topology is a system of mathematics that focuses on properties which change only by well-defined increments. In Hansson's breakfast food example, what's important is that the bun has no hole, the bagel has one hole and the pretzel has two holes. “The number of holes is what the topologist would call a topological invariant,” Hansson explained at the news conference. “You can't have half a hole, or two and two-thirds of a hole. A topological invariant can only have integer numbers.”

It turns out that many aspects of exotic matter also adhere to this one-hole, two-hole concept.

In 1982, Thouless used this idea to explain the mysterious quantum Hall effect of electric conductance. Within a thin layer at very low temperatures and a high magnetic field, electric conductance was found to build in units that could be measured with extreme precision: first nothing, then one unit, then two units. Thouless proved that the steps of this effect can be explained by a topological invariant. It worked by multiples of an integer, much like the unchangeable numbers of holes in the breakfast food example.

In 1988, Duncan Haldane pushed this line of research to a new frontier, discovering that thin semiconductor layers can house the quantum Hall effect even without a magnetic field.

The laureates' research also revealed new phases of matter that can be seen at temperatures near absolute zero (-273 °C). In 1983, Haldane uncovered a set of magnetic atoms in a chain—the first type of new topological matter ever discovered. That feat launched an ongoing race to discover new topological phases of matter hidden within layers, chains and ordinary three-dimensional materials.

These discoveries might today be considered abstract or exotic, but they could one day pave the way for the discovery of indispensable, commonplace materials, says Hansson. “What is exotic for us now might not be so exotic in 20 or 30 years,” he told journalist Joanna Rose moments after the announcement. “Electricity was very exotic when it first came around and it's not so exotic any longer.”

Topology has revamped our traditional understanding of how matter changes states. Generally, a phase change occurs when the temperature changes, i.e. when water freezes. But at extremely cold temperatures, the familiar states of matter—gases, liquids and solids—give way to bizarre new phases and behaviors. Electric currents can flow with no resistance, making possible the superconductor. New material phases like superfluids (for which Russian Pyotr Kapitsa won the 1978 Nobel Prize in Physics) can spin in vortexes that never slow down.

During the 1970s, Thouless and Kosterlitz discovered a completely new way in which matter can move from one state to another in this strange area—a topological transition driven by small vortexes, like tiny tornadoes within the flat material. At low temperatures the vortexes form pairs, which then suddenly separate from one another to spin off on their own when the temperature rises to a transition point.

This transition, dubbed the “KT transition,” became a revolutionary tool that allowed scientists to study condensed matter, atomic physics and statistical mechanics.

When phoned by the Academy, Haldane declared himself surprised and gratified by the honor. “This work was a long time ago, but it's only now that a lot of tremendous new discoveries that are based on this original work ... are now happening,” he said. Hansson echoed those thoughts, noting that scientists around the world now use these tools to work towards practical applications in electronics, new materials and even components in a new quantum computer.

But first and foremost, Hansson stressed, the prize was meant to honor exceptional science. “They combined beautiful mathematics and profound insights into physics, achieving unexpected results. That's what the prize is for,” he added. “It's really beautiful and it's deep.”