Mapping a fixed point

For fifty years, mathematicians have grappled with the so-called "fixed point" theorem. A team has now found an elegant, one-page solution that opens up new perspectives in physics and economics. 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. A more complex theorem, called the "fixed point theorem," has eluded them since 1963. "Some ideas seem evident to the human mind, but in reality involve complicated concepts that are difficult to demonstrate mathematically," says Nicolas Monod, researcher at EPFL.