An interesting way to formulate some problems that arise in science and industry is the following: given sets A and B (usually in a high dimensional Euclidean space), find a point in their intersection. This presentation of the problem would be empty (pun intended) if it were not for the fact that in many situations finding an element of A is easy, as is finding an element of B. Can this attribute of the sets A and B be exploited in solving the original problem, that is, finding an element in the intersection?
A few years ago I stumbled upon a general algorithm that solves the set intersection problem. The idea is to use projections onto the sets A and B as the basis of a dynamical system whose fixed points are associated with solutions. A special case of the algorithm had been used for decades in image reconstruction, without recognizing its generality. It now appears that the same algorithm is also effective in fields as diverse as Sudoku and protein folding.