  For each $d\geq 0$, we prove decoupling inequalities in $\mathbb R^3$ for the
graphs of all bivariate polynomials of degree at most $d$ with bounded
coefficients, with the decoupling constant depending uniformly in $d$ but not
the coefficients of each individual polynomial. As a consequence, we prove a
decoupling inequality for (a compact piece of) every smooth surface in
$\mathbb{R}^3$, which in particular solves a conjecture of Bourgain, Demeter
and Kemp.
