
Introduction
Normal forms: a historical overview
One of the most common things to do in mathematics is solving equa-
tions. Since the introduction of the coordinate method for geometric problems
by Descartes, everyone knows that combining algebra and geometry leads to
mutual benefits: geometric problems may be approached in a uniform way
through solving algebraic equations, and algebraic equations may become eas-
ier to deal with if one tries to think in terms of geometric properties of solutions
to those equations. On the other hand, in the 20th century it became com-
mon to view geometric objects via algebras of functions on those objects. Once
this ...