In 1887 King Oscar II of Sweden and Norway offered a prize for the solution of an important maths problem. Suppose you have a number of celestial bodies (for example several planets and the Sun), and you know their masses and the speed and direction they are moving in at some given point in time. Their future motion is described by Newton’s laws of motion and, since the bodies exert a gravitational pull on each other, by his universal law of gravitation. Use those laws to calculate the trajectories of the bodies.
King Oscar’s prize was won three years after it was launched, in 1890, by the French mathematician Henri Poincaré (1854 – 1912), who restricted himself to the case in which there are just three bodies. After winning the prize Poincaré discovered a major flaw in his argument, putting him in a rather embarrassing situation since his manuscript was to be published for the King’s birthday within a few weeks’ time. Honourably, Poincaré admitted his mistake and a new manuscript was published a year later. … (+Plus Magazine)