In this paper an exploratory map of what intelligent natural language processing systems can achieve will be drawn up, given the advances that have been made in recent years as revealed in the latest developments in practical applications of natural language technology in areas as diverse as natural language generation, natural language understanding, machine translation, dialog system etc. Here a mathematical exploration of the issue in question will lay out the constraints on what they can achieve in their goal of automatizing language processing that humans do. It will be shown that these constraints together constitute a fundamental limit which these systems seem to fail to cross.