Editing Brouwer fixed-point theorem (section)

===Explanations attributed to Brouwer===
The theorem is supposed to have originated from Brouwer's observation of a cup of gourmet coffee.<ref>The interest of this anecdote rests in its intuitive and didactic character, but its accuracy is dubious. As the history section shows, the origin of the theorem is not Brouwer's work. More than 20 years earlier [[Henri Poincaré]] had proved an equivalent result, and 5 years before Brouwer P.&nbsp;Bohl had proved the three-dimensional case.</ref>
If one stirs to dissolve a lump of sugar, it appears there is always a point without motion.
He drew the conclusion that at any moment, there is a point on the surface that is not moving.<ref name=Arte>This citation comes originally from a television broadcast: ''[https://archive.today/20130113210953/http://archives.arte.tv/hebdo/archimed/19990921/ftext/sujet5.html Archimède]'', [[Arte]], 21 septembre 1999</ref>
The fixed point is not necessarily the point that seems to be motionless, since the centre of the turbulence moves a little bit.
The result is not intuitive, since the original fixed point may become mobile when another fixed point appears.

Brouwer is said to have added: "I can formulate this splendid result different, I take a horizontal sheet, and another identical one which I crumple, flatten and place on the other. Then a point of the crumpled sheet is in the same place as on the other sheet."<ref name=Arte />
Brouwer "flattens" his sheet as with a flat iron, without removing the folds and wrinkles. Unlike the coffee cup example, the crumpled paper example also demonstrates that more than one fixed point may exist. This distinguishes Brouwer's result from other fixed-point theorems, such as [[Stefan Banach]]'s, that guarantee uniqueness.