A new investigation into an unresolved mathematical procedure in the 1905 paper on special relativity

For decades, historians have debated the origins of Einstein’s special theory of relativity. The derivation of the Lorentz Transformations given by Einstein in 1905 is studied in detail; and it is found to be mathematically inconsistent, and thus in error. Therefore, he must have been aware of the transformations at the time of writing the paper, which is an extremely minority opinion in the general literature. His attempt to rederive them starting from the synchronization condition is incorrect. Though the derivation is flawed, it does not affect many of the concepts he put forth that flow from the Lorentz Transformations. The observations given here will help resolve a long-standing dispute over the priority of the discovery of various parts of the theory. The priority, which is presently concentrated with Einstein, may need to be redistributed between Einstein, Lorentz, Poincaré, Larmor, Voigt, and others.