According to Konstantinos, concrete structures will last longer, since rust sets in long before concrete begins to crumble. Either way, Redford is not convinced. “I very much doubt it. They are functional structures for sure, but they will last only as long as there is a need for that function. And then they will simply be abandoned,” he says.

In the end, most skyscrapers are more likely to be torn down than fall down. In fact the Great Pyramid was not the only impressive building around 4,500 years ago.

One of them, known as The Labyrinth, was reportedly even more extraordinary. “When the Greek historian Herodotus saw it, it took his breath away. He could not describe the size and the weight of some of the huge blocks that went into construction,” says Redford. Try and find the building today and it’s been completely levelled. The rocks were plundered and used as building materials elsewhere. “If you wander the streets of old Cairo and look at the foundations of old buildings, you’ll sometimes see Hieroglyphic inscriptions which come from this very building,” says Redford.

If we don’t tear down any skyscrapers in say, New York – and they don’t fall over – then at the current rate of construction there will be 10,000 buildings over 160 metres tall in the city by the year 7,000. Perhaps it wouldn’t be so bad if some of them went the way of the Labyrinth after all.

Join 600,000+ Future fans by liking us on Facebook, or follow us on Twitter, Google+, LinkedIn and Instagram.

If you liked this story, sign up for the weekly bbc.com features newsletter, called “If You Only Read 6 Things This Week”. A handpicked selection of stories from BBC Future, Earth, Culture, Capital, Travel and Autos, delivered to your inbox every Friday.