TITLE: Why "De Morgan's laws", Why not De Morgan's theorems?
QUESTION [5 upvotes]: While we can prove both De Morgan's terms, they are called "law/rule" in many textbooks, references and also Wikipedia(+)! why law?


Aren't those terms theorem, in fact?

REPLY [5 votes]: The truth is that many results have non-standard names, like the ones you mention, the division algorithm, and Bertrand's postulate (which was not proved by Betrand). Then there are conjectures that will probably carry their names forevermore even after being proven (like Riemann's hypothesis); conjectures that were called "theorem" (like Fermat's last theorem, last because it was one of the few unproven results by Fermat that Euler wasn't able to prove, and withstood centuries of work). The strict theorem/lemma/corollary division is just fiction, there are people who prefer to call everything "proposition," there are plenty of lemmata which turned out much more important than the (now almost forgotten) results they led to. Mathemathics is a human endeavor, with plenty of quirks and vagaries.