Can one be a brilliant mathematician but be poor at arithmetic skills?

please help settle this friendly dispute with my friend, he is from US and only knows and understands technically operative arithmitic, where as I understand mathematics as a blissful exercise, divined sourced and philosophy etc etc, my friend thinks im ridicules, he does not understand higher order geometry and maths but is super fast at computation and thinks he is more learned than I in math. I am trying to tell him that there is another way to percieve and understand mathematics outside of mere arithmtic computations. My friend does not comprehend mathematical philosophy at all. please help