On November 25, 1915, Albert Einstein presented to the Berlin Academy of Sciences the explicit, complete and correct, generally-covariant field equations of gravitation, lying at the heart of his General Theory of Relativity. This was the fourth time in which he presented, at consecutive weekly meetings of the Academy, what he believed to be the culmination of many years of intense efforts to generalize his principle of relativity, so that it would apply to gravitation as well. Soon after each of the three previous presentations, Einstein had realized that the equations were in need of further improvement. The fourth time he was certain, and after the talk he was truly euphoric about this achievement, which he ever since considered to be the most important one of his entire scientific career.
Five days prior to Einstein's fourth Academy talk, on November 20, David Hilbert had presented in Göttingen his own version of the equations that, in the published version that appeared in print several months later, contained the correct and explicit equations of the theory. According to a view that was commonly accepted for many years, Hilbert had anticipated Einstein by five days in correctly formulating this important part of the latter's work. Recent archival research, however, has shown that this was not really the case, and the actual historical situation was much more complex.
Based on such recent historical research, this talk addresses several historical questions related with this seminal moment in the history of twentieth -century physics. It analyzes the interesting interaction between these two prominent scientists whose overall research programs started from substantially different points, and eventually found themselves converging to a most difficult and challenging common problem.
