Einstein said that the most incomprehensible thing about the universe is that it is comprehensible. But was he right ? Can the quantum theory of fields and Einstein's general theory of relativity, the two most accurate and successful theories in all of physics, be united in a single quantum theory of gravity ? Can quantum and cosmos ever be combined ? On this issue, two of the world's most famous physicists -Stephen Hawking (A Brief History of Time) and Roger Penrose (The Emperor's New Mind and Shadows of the Mind) -disagree. Here, they explain their positions in a work based on six lectures with a final debate, all originally presented at the Isaac Newton Institute for Mathematical Sciences at the University of Cambridge.