Distorsion, Dislocation and Disclination or Why Liquid Crystals are disinclined to be disinclined

The original observation of liquid crystals in 1888 emphasised that the materials in question underwent a double melting phenomenon. A new cloudy fluid phase interposed itself between solid and liquid phases. Under a polarising microscope, however, the cloudy phase turned out to exhibit quite beautiful patterns, which became known as textures. The interpretation of these textures in terms of defects in a director field of an anisotropic fluid was one of the triumphs of twentieth century physics. More recently it has also provided a paradigm for the application of methods of topology to condensed matter physics. In this talk I shall begin by giving surveying the history of liquid crystals, and of the idea of a defect, concentrating on issues of interest to a mathematical audience. I shall conclude by discussing some of my own recent work in this area.