[Boogieman]

They’re not proposing a geosynchronous orbit, they aren’t proposing attaching it to the ground with a cable, they are proposing hanging a giant building from it that won’t reach the ground.

It’s not a space elevator and the concept won’t work even with infinitely strong materials.

[Telepathic Intruder]

A space elevator won't have to reach the ground either. The entire mass, cable + asteroid, would be centered in geosynchronous orbit. In the case of this article, it's still geosynchronous but not stationary because the orbit is inclined to the equator.

Carbon nanotubes are supposed to have enough strength, so they say. But what if it does snap because of a terrorist attack or a meteor impact? The cable would wrap around the earth as it falls, delivering the impact energy of a nuclear explosion where it hits.