[haylel]

I read about this a lot a while ago, the main solution I came across was that in the diamond age when we get to that point in societal development. We'll be able to make tiny diamond bubbles with a vacuum inside, and they can be used to create airships and floating platforms. The airship doesn't have to be a single large vacuum diamond hull, but could also be made from many smaller diamonds which would help prevent a catastrophic failure. The diamond bubbles would be strong and light enough to hold the vacuum.

[beautifulfreak]

The wikipedia entry on "vacuum airships, as they're called," is nicely detailed. https://en.wikipedia.org/wiki/Vacuum_airship

[gibspaulding]

If I remember correctly, one of Edgar Rice Burroughs' Pelucidar books involves a vacuum airship as well. His was just made of some sort of future super strong unobtainium type matterial though.