How far back could the math be pushed? Wikipedia lists Alhazen as one of the originators of the idea that mirrors could do the same job as lenses, and also points to some earlier work by Hero of Alexandria and some other Greeks. What impacts would Alhazen's reflecting telescope (circa 1000 AD--just in time to observe the 1054 AD supernova) have? Or one by Hero?Nothing held reflectors back that much, any society that discovered bronze could make speculum metal for mirrors, but the math to know the correct shape and distances would take a good amount of effort. For refracting telescopes it's the same thing, the earliest known lenses (purely decorative) date to 2200 BC in Egypt and there are lenses from Crete dated to 500 BC that were most likely used as magnification lenses given their quality. (Also this has more information on ancient lenses.) But while they were probably good enough for telescope lenses there is no evidence that they ever built telescopes.

And, on a similar mathematical level, Wiki says that the Egyptians used a zero, and had developed something similar to Cartesian coordinates in that they understood negative (below datum) numbers. Could Egyptian numerals have been adopted more broadly in the ancient Mediterranean, and with them greater strides in numerical math?