Yep. And (if memory serves) he did it within the confines of Einsteinian physics.
Yup. The primary problem with his solution is energy. If I recall properly, his methodology requires an energy level that would be the equivalent of converting all the mass of Jupiter into energy. In other words, highly impractical.
But I have read a lot of other people have massaged his math to the point where they think it can be done with a lot less energy input, but still more than what mankind can currently manage.
At least they have a good theoretical foundation for looking in this direction anyway. Maybe they will achieve a breakthrough at some point.