This year’s Nobel Prize in physics goes to David Thouless from the University of Washington, Duncan Haldane from Princeton University, and to Michael Kosterlitz from Brown University for their work in mathematical topology — “opening the door on an unknown world where matter can assume strange states”.
Topology describes shapes and structures by breaking them down into their fundamental characteristics, such as number of holes or faces. Topologically speaking, a bucket, a doughnut, and a bagel are the same because they have one hole — but they’re distinct from a pretzel, which has two. The trio used topology to analyze the properties of exotic states of matter, such as superconductors or superfluids. Their work could underlie future advances in material science and electronics, such as quantum computers.
Thirty years ago, it was widely believed that superconductivity (zero electrical resistance) couldn’t occur in thinly layered mediums. Thouless and Kosterlitz showed otherwise using topological means. They showed that thin conductive layers could form in materials by taking the form of discrete topological steps, where going up one step is like changing from a bagel to a pretzel.
Using similar concepts, Haldane explained the magnetic properties of several materials — the work “seemed very abstract” in the beginning, said Haldane, but as time went by more and more properties could be explained by topology.
“It turned out that many materials people had been looking at for years had these properties,” said Haldane, “they just hadn’t been seen.”
The work the trio did is pertinent to several different materials, but it’s still too early to understand the full implications of topology. “What these discoveries show,” said Haldane, “is that we have a long way to go to discover what’s possible.”
Haldane “was very surprised and very gratified” when he was informed about the decision. Much of this work took place in the late 70s and the 80s, but Haldane said “it’s only now that lots of tremendous discoveries based on this work are now happening.”