A "vortex" is a point in the XY plane. It generates a vector field around it, which is (for a vortex located at the origin; for any other location please translate this field bodily) field = (-Y, X) * C / (X^2+Y^2) where the signed nonzero real number C is the "strength" of the vortex. The "laws of motion" of vortices are: Each vortex moves at a velocity which equals the sum of the fields generated by all the other vortices. Example: if there are exactly two vortices, they will move in two circular orbits about a common centerpoint located on the line segment between them, in such a way as to maintain fixed separation and fixed speeds. Why do we care? Because vortices that move according to the laws I just stated, generate a summed-field, which happens to be an exact solution of the "Euler equations" of inviscid, incompressible 2D fluid (except at the vortices themselves, where there are point singularities). QUESTION: Can vortices collide? I believe I can prove these theorems: 1. A 2-vortex collision is impossible; i.e. any collision must involve at least 3. 2. The collision must involve an infinite number of "circlings" as prologue. HOW TO SOLVE THE PROBLEM? You might be able to write down an exact solution. Or, you might be able to prove initial conditions yielding a collision, must exist, by using some topological argument.