Is it possible to travel faster than the speed of light?

So far, I have not been able to run a mile in under 30 minutes. 
That proves that I can't do it, but that does not necessarily mean
its impossible.  It doesn't prove that nobody else can do it.

Nobody and nothing has ever traveled faster than the speed of light. 
That doesn't prove that somebody or something that hasn't tried yet
can't do it.  But discoveries in Physics, Quantum Mechanics, Cosmology,
and Relativity, over roughly the past 125 years, which explain and predict
almost everything seen in hundreds of experiments and thousands of
observations since then, do all agree that the speed of light is, let's say,
nature's "speed limit", and that no matter how hard you try, nothing and
nobody CAN travel faster.