Rota's conjecture

Rota's conjecture concerns a major question in combinatorics, specifically about matroids—an abstract way to capture the essence of independence, like in graphs or vectors. It states that for any given finite set, the ways to define independence (called matroids) can be classified into a finite number of fundamental types using specific properties called minors. Essentially, it suggests a finite list of "building blocks" from which all matroids of that size can be built or broken down. This conjecture, now proven, helps mathematicians understand the structure and classification of independence systems across a broad range of mathematical and applied fields.