Maya as a contradiction

Swami Vivekanada describes a new perspective into the meaning of Maya - it being a contradiction of our intellect. He further mentions that "Maya is not a theory for the explanation of our world - in fact, it is a statement of facts as they exist, that the very basis of our being is contradiction..." Hethen procedes to talk about a problem that we all face - based on Swami jee's arguments, I was failing to see what exactly was this problem, what was its nature, how could I write it down. Perusing the rest of the article gave me solace. Swami jee revealed: It is impossible to find a solution to this problem. It is impossible to answer this problem, because the question itself cannot be logically formulated. There is neither a how nor why, we only know that it is and that we cannot help it. Even to grasp it, to draw an exact image of it in our minds is beyond our power. Thus it cannot be solved. The key then is to get to someplace that is not bound by Maya and where we shall be free of all contradictions of our intellect. Is Vedanta the map that can get us there?