In the event of his milestone birthday, a certain 19th century King once offered a monetary accolade to anyone who could solve this specific conundrum. It was subsequently found to be ill-written and thus unsolvable. The award was given to the man who recognized this. What was the conundrum, who won the prize, and what ultimately did all this lead to the beginning of?

zbeckabee

Chaotic Motion In 1887 the King of Sweden and Norway, Oscar II, initiated a mathematical competition to celebrate his 60th Birthday in 1889. Henri Poincaré selected the 3-Body problem (actually, he considered a 9-Body problem: the then known about 8 planets plus the Sun. However, he realised that the minor components of the solar system would produce perturbations on the planets and thus the problem was closer to a 50-Body problem. He immediately saw the difficulty with this and restricted himself to the 3-Body problem.) Poincaré was familiar with the then current algebraic techniques and their limitations. However, he started to look at the problem from a different point of view and decided to try a geometric approach. This approach was ground-breaking and although he had failed in solving the problem, he was awarded the prize. His revolutionary work was to be published in Acta Mathematica. However, during the publication process, Edvard Phragmen (a Swedish Mathematician) noticed a serious error in Poincarés work. The editor of Acta Mathematica immediately stopped publication and asked Poincaré to review his work. With further effort, Poiincaré looked again at his data (primarily patterns on the slices in phase space) and realised that the orbit of a planet in a case such as his could not be calculated far into the future. He was shocked by the results and rewrote his paper http://www.irit.fr/COSI/training/complexity-tutorial/henri-poincare.htm Aug 06 06, 9:19 AM

peasypod

Well done zbee, the banana is being Fed-Ex'ed right on over. Incidently, the second time around, the King's Problem was solved by Karl Sundman, a Swedish mathematician. http://en.wikipedia.org/wiki/Three-body_problem#King_Oscar_Prize Aug 06 06, 7:04 PM

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