  We prove that smooth convex $\alpha$-noncollapsed ancient mean curvature flow
satisfies a quantitative curvature estimate $H(y,t)\leq
CH(x,t)(H(x,t)|x-y|+1)^2$ for any pair of $x,y$. In other words, the rescaled
curvature grows at most quadratically in terms of the rescaled extrinsic
distance.
