I'm not exactly dissing on Sumerians here, just point out that it's one thing to use something and the other explaining the 'why it works' part. Just as Euclid was stunningly close to discovering complex and dual numbers 20-some centuries ahead of schedule, but didn't consider implications of particular x y and z, I have no problem believing Sumerians et al. could have missed it. Maybe they didn't think it needed to be proven, "since anyone can see it works." Maybe they found it but seen as aeolipile of applicable mathematics. Still, it'd be nice to see a tad more than 'just' application, since they're so goddamned close. Proofs are important, because math gets counter-intuitive very quickly and very easily. My most recently favorite example of that fact is Kempner series. Message brought to you by applied maths lobby.