@Ionus,
The answer is both a yes and a no.
Yes, nothing exists. It exists in the dictionary, under the definition of nothing. You can read it, so you'll have concrete, empirical proof, as long as you have a dictionary handy. Or you can check out the definition in Wikipedia.
And:
No, in reality, nothing does not exist. There is always something, no matter how simple, that serves to negate nothing. Not even a true vacuum exists. Supposed vacuums are teeming with quantum particles, popping into and back out of existence, apparently uncaused, but not out of nothing--but out of something, like perhaps another dimension not open to our scrutiny.
Also, at the very instant that you attempt to think nothing, you automatically negate nothing.
A Buddhist attempting to empty themselves of all thought, is inevitably brought back to reality and something because reality is ever present, whereas nothing is only an Ideal state that can never be actualized, not even in the mind of the most accomplished Buddhist monk.