#### Milestone Year

### 2011

#### A Fixed point theorem for all L1 Spaces

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.