Why do we call the Pythagorean Theorem a theorem, not a law?
As far as I know, we call a theorem a theorem because though it's reliable in every observable case, its truthfulness cannot be proven for every case. However I've looked and it seems as though we (as the human race) have very extensive proofs of the Pythagorean Theorem, considering every case. Why is it that it hasn't made the transition from theorem to law? Is my terminology confused? Is it not as proven as I think it is? Is there some other condition for being a law that I don't know about?
You seem to have jumbled mathematical and scientific terminology. Theorems state what is mathematically proven. Various kinds of scientific conclusions, including laws, are well-evidenced (with the whole of the philosophy of science as a footnote to that).