Not to discount our zombie debate, but these guys used math and stuff:

Two physicists have published an academic paper where they demonstrate, by virtue of geometric progression, that vampires could not exist, since they would almost immediately deplete their entire food supply (a.k.a, all of us).

The best part is this argument has been going on since at least 1982 in the form of various scientific papers. See Physicists Prove That Vampires Could Not Exist at io9 for the entire article.