Manifolds in the Genesis mission "Ed Pegg Jr. gives a wonderful history of the mathematical research leading up to the recently recovered Genesis spacecraft in his latest column. The story began in the late 19th century when King Oscar II of Norway and Sweden offered reward money to anyone who can solve a number of problems. One such problem was to prove whether Newton's and Kepler's equations were stable for our solar system. Poincare accepted this challenge and submitted a proof which, although it contained a large error which he later fixed, won the prize money (Poincare had to spend more money to stop publication of his original proof than what he won). The error in the paper itself led to the origins of chaos theory. The mathematics he used to solve the problem became the tool used in space exploration today. "