Mathematics
The Matroid Structure of Sets with Independent Subsets
Quick fact
Matroids were introduced in 1935 by Hassler Whitney to unify the notions of linear independence in vector spaces and acyclic sets of edges in graphs. They are precisely the structures for which the greedy algorithm is guaranteed to find a maximum-weight basis, a result known as the Matroid Greedy Theorem.
Why this is interesting
You've probably met independence before: linearly independent vectors, acyclic edge sets in graphs, or independent events in probability. But what if all these are the same thing? What structure lies beneath the surface, uniting them and even explaining the greedy algorithm's success?