A Revolutionary Material

Abstract

T he 2011 Nobel Prize for Chemistry was awarded to Dan Shechtman for the discovery of quasicrystals, an exotic class of materials. The discovery was published in 1984 and was quickly treated as revolutionary, with front-page headlines in newspapers. While the award was for chemistry, the revolution was more broadly based within the interdisciplinary subject of materials science. This can be described easily, and we will begin with a sketch of the idea. The multifaceted implications for mathematics are more complicated, and we will try to elucidate them afterwards. The basic fact is that quasicrystals are equilibrium solids which are not crystalline. Not only is their pattern of atoms not crystalline, the pattern has a fascinating hierarchical structure. However, we emphasize that the hierarchical pattern is not essential to the revolutionary significance of quasicrystals to materials science. It had been understood for many years, following the development of X-ray diffraction, that common inorganic solids (for instance all solids composed of only one chemical element) are crystalline, and great practical success followed from incorporating this into standard modeling, essentially by analyzing various perturbations of a crystalline atomic configuration. This is evident from basic textbooks on solid state physics from the 1970s. The startling fact uncovered by the discovery of quasicrystals was the existence of a previously unknown class of inorganic solids, of unknown