Why did analysis become more central than classical Greek geometry in advanced mathematics after the 17th century?

After the 17th century, analysis replaced classical Greek geometry at the center of advanced mathematics primarily due to the development of powerful new algebraic methods and the evolving needs of science.1

While Greek geometry was a rigorous theoretical discipline, it was limited by its reliance on geometric figures and intuition. The 17th-century scientific revolution—driven by fields like astronomy, mechanics, and physics—required more flexible tools to study continuous change, motion, and complex curves.23415

Key factors in this shift included:

• Algebraic Power: The development of analytic geometry by René Descartes and Pierre de Fermat allowed mathematicians to use algebraic equations to represent and analyze curves, moving beyond the constraints of geometric construction.12
• Calculus: The invention of differential and integral calculus provided a systematic way to handle tangents, areas, and volumes, eventually leading to the fundamental theorem of calculus.12
• Generalization: Mathematicians like Leonhard Euler and Joseph-Louis Lagrange systematically separated calculus from geometry, establishing functions as the central organizing concept of analysis.5

This transition allowed mathematics to become a more unified, algebraic discipline, better suited for the demands of modern science than the traditional geometric approach.15