The Formation and Historical Development of Differential Geometry as a Science

Abstract

This paper presents a systematic account of the historical formation and development of differential geometry as a scientific discipline. The narrative spans from ancient Greek geometry through Descartes' coordinate system, Newton and Leibniz's differential calculus, Euler and Gauss's surface theory, Riemann's revolutionary generalization, and the tensor methods of Levi-Civita and Cartan. The interplay between twentieth-century global differential geometry and theoretical physics is also examined. The paper is intended as a supplementary reference for courses in the history of mathematics and differential geometry.