One of the core challenges with the space elevator concept is that they need a cable that can reach from the earth's surface to somewhere beyond geostationary o

One of the core challenges with the space elevator concept is that they need a cable that can reach from the earth's surface to somewhere beyond geostationary orbit, with exactly how far depending on how they want to arrange the counterweight. The midpoint of that cable will have to support the weight of all of the cable that's below it, and that's around 10-15k miles of cable. So we need a material out of which you can make a 15k mile long cable that can hang free, supporting its own weight. Making it thicker doesn't help, because then you just add more weight that you'll have to support. We need a better material that has this level of strength when manufactured at scale.