Direct methods - from birth to maturity

The award of the Nobel Price for Chemistry to two pioneers of direct methods, H. Hauptman and J. Karle, has been a recognition of the importance that these methods have attained, in crystallography in particular and in science generally. The development of direct methods is traced from its first beginnings with Harker-Kasper inequalities and the Karle and Hauptman determinantal inequalities. The range of application of these methods to centrosymmetric structures was much increased by the introduction of the sign relationship by Sayre, Cochran and Zachariasen and an ACA Monograph by Hauptman and Karle to which the origins of the application of direct methods may be traced. Sayre's paper, in 1952, developed an exact equation which applied to both centrosymmetric and non-centrosymmetric structures as did the Karle and Hauptman determinantal inequalities. (orig./BHO)