Maybe not:

Laboratory tests have shown that individual nanotubes can withstand an average of about 100 GPa, an unusual strength that comes courtesy of their crystalline structure. But if a nanotube is missing just one carbon atom, this can reduce its strength by as much as 30%. And a bulk material made from such tubes is even weaker. Most fibres made from nanotubes have so far had a strength much lower than 1 GPa.

Recent measurements of high-quality nanotubes have found them to be missing one carbon atom out of every 1012 bonds; that’s about one defect over 4 micrometres of nanotube length1. Defects of two or more missing atoms are much more rare, but Pugno points out that on the scale of the space elevator they become statistically probable.

Using a mathematical model that he has devised himself, and which has been tested by predicting the strength of materials such as nano-crystalline diamond, Pugno calculates that large defects will unavoidably bring a cable’s strength below about 30 GPa. His paper has been posted to arXiv2, and will appear in the July edition of the Journal of Physics: Condensed Matter.

Pugno adds that even if flawless nanotubes could be made for the space elevator, damage from micrometeorites and even erosion by oxygen atoms would render them weak. So can a space elevator be made? “With the technology available today? Never,” he says.

This seems like kind of an oxymoronic statement, because “never” implies the technology available any time, not just today. I would think that devices that continuously repaired redundant cables at a molecular level could solve this problem, though they’re not “technology available today.” In any event, I remain an agnostic.