Palle Yourgrau, professor of philosophy at Brandeis University, writes in an essay from his book, Without Time: The Forgotten Legacy of Gödel and Einstein (in The Chronicle of Higher Education):
Washed up onto America’s shores by the storm of Nazism that raged in Europe in the 1930s, the two men awakened to find themselves stranded in the same hushed academic retreat, the Institute for Advanced Study [at Princeton], the most exclusive intellectual club in the world, whose members had only one assigned duty: to think. But Gödel and Einstein already belonged to an even more exclusive club. Together with another German-speaking theorist, Werner Heisenberg, they were the authors of the three most fundamental scientific results of the century.
Each man’s discovery, moreover, established a profound and disturbing limitation. Einstein’s theory of relativity set a limit — the speed of light — to the flow of any information-bearing signal. And by defining time in terms of its measurement with clocks, he set a limit to time itself. It was no longer absolute but henceforth limited or relative to a frame of measurement. Heisenberg’s uncertainty principle in quantum mechanics set a limit on our simultaneous knowledge of the position and momentum of the fundamental particles of matter. This was not just a restriction on what we can know: For Heisenberg it signified a limit to reality. Finally, Gödel’s incompleteness theorem — “the most significant mathematical truth of the century,” as it would soon be described in a ceremony at Harvard University — set a permanent limit on our knowledge of the basic truths of mathematics: The complete set of mathematical truths will never be captured by any finite or recursive list of axioms that is fully formal.
More here.