There's a LOT of problems to be overcome before we're anywhere close to this.
Columbus died in 1506, according to
Wikipedia, still believing he had reached Asia. That is, by 1506, he was still underestimating the magnitude of his own problem.
In 2006, we're still crawling into orbit on experimental spacecraft, awed by still further distances that boggle the imagination. 500 years and we stand on an ocean vastly different than any previously imagined.
Now, if his ships had a top speed of between 5 and 15 knots, I'll generously say they went 25 km/h. The space station orbits at about 27,000 km/h, or roughly 1000 times the speed of ships 500 years ago, in a vastly different environment.
A 1000-fold increase over that would be, say, 25 M km/h, or 6.94x10
6 m/s gives a little more than 0.2c or 500 years from now, 1000 times the speed of ships today, in a vastly different environment (interstellar space).
Now sometimes, no matter what resources you throw at a problem, you encounter physical limits. A good example is transistor scaling. However, there is usually someone willing to look at workarounds, such as increasing die size if transistor density isn't improving, different semiconductor and interconnect technologies, etc.
...
drkitten and I have crossed on this before (specifically, FTL at the time). My two wild analogies are a little glib, but I maintain that
impossible is a very strong word.
Impossible is radically different from, "There's a LOT of problems." In fact, impossible doesn't even mean the same as a LOT
LOT of problems. You'd have to have a googolplex of problems without even the wild imaginings of a solution before you got anywhere near impossible.
I wouldn't let the failure of realizing the movie 2001 inform wild speculation about events 500 or more years from now...
ETA: Just to be clear, my love for interstellar travel is fuelled much more by science fiction than science fact, which I freely admit. I think there is an interesting enough set of problems with interplanetary travel, and should I be lucky enough to do any instrumentation work on any spacecraft that actually flies, I will consider myself to be more than fulfilled.