Actually, I don't think he would.
He'd recognize it as a very impressive machine. But certainly not 'magic'.
Indeed, I have always disagreed with Arthur C. Clarke's "second law". The only people who mistake a phenomona for 'magic' are those who believe in magic. The others will always look for an explanation and try to figure out how it works.
The question of whether mathematics is "invented by man" (i.e. a posteriori) or not (a priori) is one of many interesting questions addressed in Immanuel Kant's Critique of Pure Reason. It's a bit of a sticking point at that interstice between philosophy and theology, and a deep indicator of how one sees the universe: to a religious purist it doesn't matter because if man invented it, God invented man; to an atheist it doesn't matter because if God invented it, man invented God. To the rest of us it's a little more opaque.