King Oscar II Prize About The Solution For The n-body Problem
The problem of finding the general solution of the n-body problem was considered very important and challenging. Indeed in the late 19th century King Oscar II of Sweden, advised by Gösta Mittag-Leffler, established a prize for anyone who could find the solution to the problem. The announcement was quite specific:
Given a system of arbitrarily many mass points that attract each according to Newton's law, under the assumption that no two points ever collide, try to find a representation of the coordinates of each point as a series in a variable that is some known function of time and for all of whose values the series converges uniformly.
In case the problem could not be solved, any other important contribution to classical mechanics would then be considered to be prize-worthy. The prize was finally awarded to Poincaré, even though he did not solve the original problem. (The first version of his contribution even contained a serious error; for details see the article by Diacu). The version finally printed contained many important ideas which led to the development of chaos theory. The problem as stated originally was finally solved by Karl Fritiof Sundman for n = 3.
Read more about this topic: n-body Problem
Famous quotes containing the words king, prize, solution and/or problem:
“I know I have the body of a weak, feeble woman; but I have the heart and stomach of a king—and of a King of England too, and think foul scorn that Parma or Spain, or any prince of Europe, should dare to invade the borders of my realm; to which, rather than any dishonour should grow by me, I myself will take up arms—I myself will be your general, judge, and rewarder of every one of your virtues in the field.”
—Elizabeth I (1533–1603)
“Then, though I prize my friends, I cannot afford to talk with them and study their visions, lest I lose my own. It would indeed give me a certain household joy to quit this lofty seeking, this spiritual astronomy, or search of stars, and come down to warm sympathies with you; but then I know well I shall mourn always the vanishing of my mighty gods.”
—Ralph Waldo Emerson (1803–1882)
“All the followers of science are fully persuaded that the processes of investigation, if only pushed far enough, will give one certain solution to each question to which they can be applied.... This great law is embodied in the conception of truth and reality. The opinion which is fated to be ultimately agreed to by all who investigate is what we mean by the truth, and the object represented in this opinion is the real.”
—Charles Sanders Peirce (1839–1914)
“The problem for the King is just how strict
The lack of liberty, the squeeze of the law
And discipline should be in school and state....”
—Robert Frost (1874–1963)