This paper traces Einstein's discovery of "the equivalence of mass [m] and energy ["E[subscript 0]"]." He came to that splendid insight in 1905 while employed by the Bern Patent Office, at which time he was not an especially ardent reader of physics journals. How then did the young savant, working outside of academia in semi-isolation, realize that these two seemingly disparate concepts were actually "identical"? Until now little attention has been given to exploring the physics that guided his thinking in this remarkable endeavor. That work culminated (1907) in the equation "E[subscript 0] = mc[squared]", where "E[subscript 0]" is "rest energy" and "m" is "invariant mass." Despite claims to the contrary, Einstein did not write this equation, or its ambiguous variant, "E = mc[squared]", in 1905. Furthermore, we will propose a compelling reason for his otherwise inexplicable caution. This paper is meant to help clarify the contemporary literature in the service of an informed pedagogy.