Cohn's Conjecture

Cohn's Conjecture is a mathematical hypothesis proposed by Paul Cohn regarding the properties of certain algebraic structures called free associative algebras. It suggests that within these algebras, specific types of elements, known as "identities," which are equations valid for all elements, can be generated by a finite set of fundamental identities. In simpler terms, it proposes that a finite collection of basic rules or relations can explain all the possible equations that hold universally within these mathematical objects. The conjecture remains unproven, representing an important question in algebra and its understanding of structure and identity.