Group theory has its origins in the 19th century and is part of the field of abstract algebra. It began as a way to understand polynomial equations that could not be solved through traditional algebraic methods.
The concept of a group came into being as mathematicians began to understand the symmetry and structural diversity in various mathematical objects and equations. A pivotal moment was Évariste Galois' use of groups to determine the solvability of polynomial equations, a foundation stone of what we now call Galois theory.
Today, group theory is applied in numerous fields such as physics, chemistry, and computer science. It helps illustrate and solve problems related to symmetry in molecules, crystal structures, and even algorithms.