"The biggest challenge to the space elevator has been developing a cable tough enough to extend 62,000 miles without breaking. This, Edwards explained will be solved with carbon nanotube composites - tiny bundles of carbon weaved together to form a ribbon that will be stronger than steel. His startup company, Carbon Designs, Inc., is currently focused on developing this technology." So, they don't have a material that's strong enough, yet. But given the rate of progress in the nanotech field and the number of people working on it, it's only a matter of time.
So, they don't have a material that's strong enough, yet. But given the rate of progress in the nanotech field and the number of people working on it, it's only a matter of time. Essentially correct. Though it seems unlikely that an Islamic society would find much use for such a project. As private space exploitation grows, the profitability of such a project will become obvious.