The derivation of Einstein's field equations of general relativity is a topic that has been the subject of historical debate. Both Albert Einstein and David Hilbert made significant contributions to the development of these equations.
Einstein published his field equations in a paper titled "Die Grundlagen der allgemeinen Relativitätstheorie" ("The Foundations of the General Theory of Relativity") in November 1915. In this paper, Einstein presented his field equations in the form known as the Einstein field equations.
David Hilbert, a renowned mathematician, also worked on the problem of gravitation and formulated a set of equations that were equivalent to Einstein's field equations. Hilbert's work was presented in a talk on November 20, 1915, just a few days after Einstein's paper was published. However, the written version of Hilbert's work was published later, in March 1916.
The priority and credit for the discovery of the field equations have been the subject of debate and controversy. Einstein and Hilbert corresponded during this period, and there is evidence to suggest that Hilbert's work was influenced by discussions with Einstein. The exact sequence of events and the extent of the influence between the two scientists is not entirely clear.
In the scientific community, the general consensus is that Einstein's contribution to the field equations is more substantial, as he developed the theory of general relativity as a whole and published his results first. However, both Einstein and Hilbert made important contributions to the formulation of the field equations.