Forgive me, but I find it a little arrogant that mathematicians think God communicates to us through "mathematics or magic." Many people know hardly any math and of course God's communicating through "magic" seems to trivialize his communication.
God created the laws of the universe and could consequently change them as he saw fit, but I don't believe he ever does. His communication with us, though, may be the closest he comes to doing just that.
When he communicates in our thoughts, do you really think it's like a "still small voice," or a radio message? It seems to me his thoughts become ours....
Your question is interesting and thought provoking and I, of course, have no answer, but like to discuss it, and thank you for posing your question. It is very important, isn't it?
Allot of mathematicians claim that math is god's secret book. Math after all takes the complex and make them simple. If god had infinite knowledge then it would be in an equation.