👉 Nonsolvability is a mathematical concept in number theory and algebraic geometry that refers to properties of a variety or ring which are preserved under certain operations but not by all other operations. It can be thought of as a property of the underlying structure, such as polynomial rings over a field, that cannot be uniquely determined by any finite set of operations. Here's an example: Let $R$ be a commutative ring with identity and let $L = R[x]/(x^2