The EPR paradox is a thought experiment proposed by Albert Einstein, Boris Podolsky, and Nathan Rosen. It was proposed in a 1935 paper in Physical Review titled, "Can quantum-mechanical description of physical reality be considered complete?"
The EPR paradox was created with the intention of demonstrating that quantum mechanics is incomplete because it violates local realism. Einstein, Podolsky, and Rosen felt that an underlying theory incorporating "hidden variables" must exist. However, subsequent experiments showed that locality is indeed violated (action at a distance), and most physicists today consider "hidden variable" theories intractable.
- PDF version of EPR paper.