As I understand, it is the (relatively new) theory of how the way a piece of information can be reproduced by an algorithm relates to the "randomness" or complexity of the piece of information. Gregory Chaitin, stepping in the footsteps of Kurt Goedel and Alan Turing, invented and published the theory when he was nineteen. The way the theory relates to Godel's theorem and Turing's Halting Problem is that Chaitin proved that there is no algorithm for testing whether any algorithm is the shortest way to compress a given peice of information, and therefore no true measure of the complexity of any sort of formal numeric entity.