The document summarizes the work and contributions of four important mathematicians: Niels Henrik Abel proved the impossibility of solving the general quintic equation with radicals, an outstanding problem for 350 years. Évariste Galois determined the necessary and sufficient conditions for a polynomial to be solvable by radicals. Sir Isaac Newton worked on the properties of the quadratic equation. Their groundbreaking work laid the foundation for solving polynomial equations and shaped modern scientific progress.