What impact did Archimedes and Pythagoras have on the field on mathematics?

Archimedes and Pythagoras significantly shaped the foundations of mathematics through their pioneering work. Pythagoras is best known for his contributions to number theory and geometry, particularly the Pythagorean theorem, which established relationships in right triangles. Archimedes advanced mathematical methods, particularly in geometry, calculus, and the understanding of infinitesimals, laying groundwork for future mathematical analysis. Together, their insights and theories have influenced countless mathematical fields and concepts, forming the basis for much of modern mathematics.