Even if technically possible it might require near infinite amounts of energy. As I understand it the entire output of our sun wouldn't drive even a small capsule faster-than-light.
I'm not a physicist, and I'm not stellar at math (nice pun, huh?). But, I do remember from Calc II, that there was an equation you could rotate around an axis, determine it's volume, but if you tried to determine surface area, you would reach infinity. I may have reversed it. The point is, up to that point, I didn't know enough (and actually didn't need to take any other math, and was not motivated enough to care...) to solve the problem of infinity, but the professor said it would be taught in a later class.
So, my point is: Many times in the past, we just didn't have the right perspective.