Worked on core symbolic mathematics and algebraic structures, contributing to both the sympy/sympy and leanprover-community/mathlib4 repositories. In sympy, addressed correctness in symbolic computation by refining zero-product detection and improving non-commutative algebra simplification, using Python and algorithm refinement to reduce downstream errors and enhance maintainability. Also updated contributor attribution for better auditability. In mathlib4, refactored the primaryComponent function in group theory modules, generalizing its applicability over natural numbers without prime-factor constraints, leveraging Lean and type theory. The work demonstrated depth in formal verification, mathematical logic, and testing, resulting in more robust and broadly applicable mathematical libraries.