Here’s one that’s bugging me. I read it a long time ago so I might not have all the details right.
A long term space mission sets out for a planet orbiting another star. The crew is a bunch of scientists, and to pass the time they are given some math/science problems to work on. It later turns out that the whole mission is a sham – there is no planet at the destination and the only point of the mission was to isolate the scientists so they could focus completely on these important problems. The fact that the crew will perish when they reach the nonexistent planet is considered acceptable by the mission planners. The crew makes astounding progress during the mission, and radios some of their results back to earth. Eventually they discover the ruse but by then they have advanced so far beyond earth science that they are able to survive anyway (I think that they actually CREATE a planet when they arrive at the destination star). One specific incident I recall is they radio one of their most important results (controlled fusion or something of that order) as a Godel-encoded number, and one of the crew comments that the Earth people are probably “too dumb” to de-Godelize it.
Anyone got this one?