Take a map of the world. Now put it down on the ground in Central Park, against a rock on Mount Everest, or on your kitchen table; there will always be a point on the map that sits exactly on the actual physical place it represents. Obvious? Not for mathematicians, who consider the question at its ultimate generality, and call it a general fixed point theorem. This theorem works for all kinds of maps, from a diagram of a metro route to a map of spaces used in quantum physics. But to prove it, a fixed point must be found for every possible case. Since the number of possible maps is infinite, the mathematicians were looking for a universal, purely mathematical method -- one that would work in any situation.
The challenge for the mathematicians was to find that fixed point. It was a bit like designing a method that could pinpoint the center of gravity of any object, real or purely mathematical. The problem has been opened since the 1960s and frustrated quite a few renowned Mathematicians.
The resulting proof, found in 2011 by a WIS mathematician and his collaborators, is relatively simple. By considering a space that is closely related to the original one, they were able to determine a fixed point, and then translate it back to the original space. In addition to the indisputable intellectual satisfaction that this elegant result represents, it also opens up long-term perspectives in other disciplines: For example, central theories in physics and economics make use of the idea of fixed points.