Nuclear Numbers

What actually happens when inspectors go into a country to verify the existence or nonexistence of nuclear weapons? They can't examine the warheads themselves, so how can they know for sure? A new method involves what's known in mathematics as a zero-knowledge proof, basically a way of testing weapons without learning what's in them: http://blogs.discovermagazine.com/d-brief/2014/06/25/a-new-way-to-verify-nuclear-weapons-with-math/#.U6soDqi5bgc