Hıstory of Modern Mathematics

David Eugene Smith's "History of Modern Mathematics" is a specialized work focusing on the developments in pure mathematics during the 19th and early 20th centuries. The author defines the "modern" era as the abstract and theoretical advancements beginning in the 19th century, explicitly distinguishing it from the 17th/18th-century work of figures like Newton, Laplace, and Lagrange (which he classifies as "applications" or mathematical physics). The book examines the various revolutionary fields of this period. These include advances in synthetic and projective geometry (Steiner, Poncelet, Von Staudt), the development of analytic geometry through the work of Plücker and Hesse, and the birth of non-Euclidean geometry (Lobatchewsky, Bolyai, Riemann). In algebra, it covers Galois's group theory and the theory of invariants by Cayley and Sylvester. In analysis, the emphasis is on the theory of functions and complex analysis, pioneered by Cauchy, Riemann, and Weierstrass. The work also encompasses the deepening of the theory of numbers through the contributions of Gauss, Kummer, and Dirichlet.