Mathematics
The Ring Structure and Ideal Theory in Commutative Algebra
Quick fact
Ideals were invented by Dedekind in the 19th century to save unique factorization in rings of algebraic integers, a problem that arose from Fermat's Last Theorem.
Why this is interesting
You know how numbers can be divided, multiplied, and factored. But what if numbers could be replaced by more abstract objects, and 'divisibility' turned into something more general?