The groups

Born at the beginning of the 19th century in the mind of the young brilliant mathematician Évariste Galois in the context of the solvability of a polynomial equation, the notion of group has literally invaded all domains of mathematics. Even though the group is an algebraic concept, several situations in geometry benefit from it. Many current problems in mathematics consist in determining a group, studying its properties, or finding an isomorphism between several of them. And this even goes beyond mathematics to reach other sciences: physics with fundamental particles or quantum mechanics, chemistry with the study of crystals. Other fields of human activity, such as social sciences, literature, games (including Rubik's Cube) or the arts can also rely on it. The famous Alexandre Grothendieck considered that the two greatest mathematical inventions of all time were zero and… the concept of group!
The files • The genesis of an innovative concept • Algebra revisited • Essential in geometry • Applications in multiple domains