Do you believe nuclear weapons will ever be eliminated?

No, I do not think this will ever happen. If we totaly disarm ourselves, we have nothing to threaten those who may build a bomb in secret. However, the current numbers are much to high.

Reminds me of what Einstein said: "The position in which we are now is a very strange one which in general political life never happened. Namely, the thing that I refer to is this: To have security against atomic bombs and against the other biological weapons, we have to prevent war, for if we cannot prevent war every nation will use every means that is at their disposal; and in spite of all promises they make, they will do it. At the same time, so long as war is not prevented, all the governments of the nations have to prepare for war, and if you have to prepare for war, then you are in a state where you cannot abolish war." Meaning: In order to prevent (nuclear) war, you have to prepare for (nuclear) war, but if you prepare for (nuclear) war, you get stuck into a perpetual state of fear of (nuclear) war.