I wonder if our culture will last as long as theirs did.

I don’t think so. As history moves on the circles of the helix of development are becoming smaller. Egyptian civilisation kept repeating itself, copying ancestors for thousands of years.
no civilisation in XXI century can afford this, it will be swept away. We are already witnessing the process of globalisation in which Classical Anglo-Saxon Culture is being transformed into something else, as parts of Roman Culture were moulded into European Christian Culture.