Albert Einstein, whose Theory of Relativity had made him the most famous scientist in the world, remarked towards the end of his career that he only went in to his office at Princeton 'just to have the privilege of walking home with Kurt Godel'. He and Godel had both fled Europe and the clutches of Nazism and had found rare solace in each other's company in foreign exile. They argued as equals and reinspired their respective interests in pure mathematics and physics. Godel's 'Incompleteness Theorem' had been described at Harvard as the 'most significant mathematical result of the century'. He was one of the few people to understand the philosophical implications of Einstein's theories of the universe - and would later honour Einstein's seventieth birthday by addressing his theories directly, proving time to be an ideal. This extraordinary friendship is one of the most remarkable of the twentieth century, all the more so for remaining so unremarked.