Yes, a child can do advanced math without knowing his "math facts". But having them down cold will save him time, and allow him to focus on the concepts instead.
I posted about this elsewhere on this board. Once a fact is known, it should be drilled until it is second nature. There should be no pause, no hesitation in bringing it up or using it. Numbers, problems, proofs, etc, all fall in this method.
Math should be known like one knows a piano piece or a dance or a combative - it should just flow.
If you do less, then you are not doing your best.
