Quasicrystals: A brief history of the impossible

The 30-year history of quasicrystals is one in which, time after time, the conventional scientific view about what is possible has been proven wrong. First, quasicrystals were thought to be mathematically impossible; then, physically impossible; then, impossible unless synthesised in the laboratory under carefully controlled conditions. One by one, these strongly held views have been disproven, the last only recently as the result of the discovery of a natural quasicrystal found in a meteorite dating back to the formation of the solar system. This paper is a brief personal perspective on this history of misunderstanding and discovery.