Dave Knott writes: David J. Thouless, F. Duncan M. Haldane and J. Michael Kosterlitz were awarded the Nobel Prize in Physics on Tuesday for discoveries in condensed-matter physics that have transformed the understanding of matter that assumes strange shapes. All three were born in Britain but work in the United States. Using advanced mathematical models, the three scientists studied unusual phases, or states, of matter, such as superconductors, superfluids or thin magnetic films. Their findings have relevance for materials science and electronics. The Royal Swedish Academy of Sciences in Stockholm awarded the prize for "theoretical discoveries of topological phase transitions and topological phases of matter." Topology is a branch of mathematics that describes properties that change only in increments. In the early 1970s, Dr. Kosterlitz and Dr. Thouless "demonstrated that superconductivity could occur at low temperatures and also explained the mechanism, phase transition, that makes superconductivity disappear at higher temperatures," the academy found. In the 1980s, Dr. Thouless showed that the integers by which the conductivity of electricity could be measured were topological in their nature. Around that time, Dr. Haldane discovered how topological concepts could 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," the academy said. "Over the last decade, this area has boosted front-line 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."