Sysyphus
Talk Tennis Guru
I'd like to also point out that the greatest advances of human kind, and the ones that paved the way for modern science, took place before the scientific method was even conceptualized. The concept of scientific method was unknown of in old civilizations, including Ancient Greece. That didn't stop seminal developments in Mathematics and Philosophy. Mathematics, in particular, as a discipline created mainly through internal mental processes in abstract ways independent of external observation, could be considered very "unscientific" in very peculiar ways. Yet, it's hard to argue with the fact that without Math there would have been no serious development in any other scientific field
Well, even in maths, the empirical factor can't be underestimated (in terms of checking new proofs etc).
That said, in isolation, mathematics isn't something that gives us new knowledge about the world. Math is a language, and the truths it produces are about internal consistencies within the system, i.e., tautological.
It's when we couple it with empirical science that we can discover knowledge about the world, and it works great for that. As an aside, you claim that without math we probably would have never had science: well, it's actually been shown that one can perform physics using completely different models as well (see Hartry Field who did some pretty weird and impressive work here. He holds that mathematics is just a "useful fiction"), it's just less convenient.
As for the progress in the ancient world, even if they hadn't formalized the scientific method, they were certainly doing empirical science, just in a less formalized way. Their progress still stemmed from the same mechanisms (testing ideas against experience). They didn't build Rome purely by metaphysical speculation.