Herbert Hauptman and Jerome Karle, a mathematician and a physicist respectively at the United States Naval Research Laboratory, develop from 1953 onward a mathematical method that solves one of the most persistent technical problems of X-ray crystallography: determining the three-dimensional structure of a molecule from the X-ray diffraction patterns produced by a crystal, without needing prior approximate knowledge of that structure. The fundamental problem — known as the "phase problem" — lies in the fact that X-ray detectors record only the intensity of the diffracted radiation, not its phase, information mathematically essential for reconstructing the exact position of atoms using the conventional techniques available until then, which required laborious successive approximations or prior structural knowledge of the type of molecule. Hauptman and Karle demonstrate that it is possible to derive phase information directly from statistical and probabilistic relationships among the measured intensities, without needing that prior knowledge — hence the name "direct methods". The technique, initially met with considerable skepticism from the established crystallographic community and taking almost thirty years to be widely adopted, becomes, once sufficiently powerful computers arrive, the standard method for determining the structures of small and medium-sized molecules, drastically accelerating the pace of structural determination in organic and pharmaceutical chemistry.