From what I remember, Hilbert actually got the equations first by applying the principle of least action, so a much more mathematical than Einstein's physical a

From what I remember, Hilbert actually got the equations first by applying the principle of least action, so a much more mathematical than Einstein's physical approach. However, everybody agreed that Einstein did all the heavy lifting (he worked closely with mathematicians for years to figure things out), so that's why they aren't called the Einstein-Hilbert equations.