There is no way to prove it's not boundless, but what if it wasn't? What would happen when a universe bumps into another?
The Big Bang
, according to one theory.
We can't currently prove that the universe is boundless, but someday we might. In fact, according to an episode of Through the Wormhole, at least one scientist believes he has found such proof. I'm not sure of the details, but something to do with patterns in the Cosmic Background Radiation that look the same in opposite directions, suggesting not only that the universe is finite and boundless, but also that it's not much larger (about 20% larger) than the observable universe.