Editing Theory of equations (section)

{{Short description|Study of polynomial equations}}
{{Distinguish|equational theory}}
{{inline|date=May 2014}}
{{onesource|date=June 2024}}
In [[algebra]], the '''theory of equations''' is the study of [[algebraic equation]]s (also called "polynomial equations"), which are [[equation (mathematics)|equation]]s defined by a [[polynomial]]. The main problem of the theory of equations was to know when an algebraic equation has an [[algebraic solution]]. This problem was completely solved in 1830 by [[Évariste Galois]], by introducing what is now called [[Galois theory]].

Before Galois, there was no clear distinction between the "theory of equations" and "algebra". Since then algebra has been dramatically enlarged to include many new subareas, and the theory of algebraic equations receives much less attention. Thus, the term "theory of equations" is mainly used in the context of the [[history of mathematics]], to avoid confusion between old and new meanings of "algebra".