Until 1934, materials physics faced an unresolved mathematical contradiction: theory predicted that plastically deforming a perfect metal crystal required a stress thousands of times greater than that observed experimentally in real metals. The Italian physicist Vito Volterra had introduced in 1907 the abstract mathematical concept of a line defect in a continuous medium, with no explicit connection to the plasticity of real crystals. In 1934, with no knowledge of each other's work, three scientists resolve the contradiction by applying that same geometric idea to real crystal structure: in Cambridge, Geoffrey Ingram Taylor publishes in July a mathematical and mechanical theory of plastic deformation based on the displacement of line defects, also introducing the phenomenon of work hardening; in Berlin, Egon Orowan, a recently graduated Hungarian physicist, publishes in September a series of papers describing the same defect from a thermal-kinetics perspective, treating its motion as a temperature-activated process; and, in the same journal and at practically the same time, Michael Polányi, a Hungarian-British physical chemist, publishes a formulation centered on the stress needed to move the defect through an otherwise perfect crystal lattice. All three papers describe, with different mathematical emphasis, the same physical object: a linear defect in the atomic lattice — the dislocation — whose displacement, rather than simultaneous slip of entire atomic planes, explains why real crystals deform at stresses far lower than predicted by the theory of an ideal, defect-free crystal. None of the three worked in collaboration with the other two, and the near-exact coincidence in time — the same year, the two German papers in the same volume of the same journal — is considered in the history of materials science the textbook example of an independent, simultaneous discovery. None of the papers alone exhausted the problem; together they found dislocation theory, a conceptual framework that over the following two decades would develop into the foundation of modern physical metallurgy, allowing systematic explanation and control of properties such as ductility, alloy hardening, and the mechanical behavior of materials under stress. In 1934, however, the dislocation remained a purely theoretical hypothesis: no one had observed one directly. It would not be until 1956, with the development of high-resolution transmission electron microscopy, that Hirsch, Horne, and Whelan would achieve the first direct observation of real dislocations moving within a metal crystal.