Liam Schilling enhanced the mathematical foundation of multivariate polynomials in the leanprover-community/mathlib4 repository by developing features that relate the weighted total degree to existing degree notions. Using Lean and theorem proving techniques, Liam formalized the relationship between weightedTotalDegree, degrees, and degreeOf, ensuring consistency with the library’s weighting framework. This work enables more precise degree analysis in downstream proofs and theorems, supporting advanced reasoning about polynomial structures. Liam also updated documentation and laid the groundwork for future tests, demonstrating depth in both mathematical rigor and maintainability. The contribution deepened the library’s support for advanced polynomial theory in Lean.