Interesting you mention the ancients figuring all that stuff out. I really think we’ve lost a lot of that sort of mental capacity by having information at our fingertips.
Even back in the era you’re talking about, we had compasses and maps and the like, and we weren’t spending time studying the stars (possibly because we have TV and books and such to occupy us at night). I think that a lot of that sort of study comes from practice and frequent use, honestly.
It’s like how my grandfather could run a sum of figures in his head with complete accuracy that I would need a calculator to do. It’s just practice. He wasn’t any smarter than me, just practiced differently. Same thing goes for how they were able to build pyramids and such - their minds were just working at a vastly different level than ours in those areas.