  We compute the Mellin amplitude of the planar four-point correlator of
weight-two half-BPS operators in $\mathcal{N}=4$ SYM at one and two-loop orders
in the small 't Hooft coupling expansion. The two-loop Mellin amplitude has an
infinite number of poles, as expected from a stringy bulk dual. We then perform
a Mellin conformal block expansion of the amplitude and extract the one-loop
anomalous dimensions and OPE coefficients of the exchanged twist-two singlet
multiplets. Our results match those of Dolan and Osborn \cite{Dolan:2004iy} but
the computation is rather straightforward in Mellin space.
