A History of Mathematics

Florian Cajori's A History of Mathematics (Second Edition) presents a comprehensive and detailed account of the subject's evolution, intended for both students and teachers of mathematics. The book meticulously traces the development of mathematical thought from antiquity through the modern era. It begins with the foundational contributions of the Babylonians and Egyptians, then moves to the "golden age" of Greek mathematics, detailing the work of figures such as Pythagoras, Euclid, Archimedes, and Diophantus. The narrative then bridges the "Middle Ages," highlighting the crucial contributions of Hindu and Arab scholars such as Brahmagupta and Al-Khwarizmi, who preserved and advanced Greek knowledge. The bulk of the work is dedicated to "Modern Europe," starting with the Renaissance (Copernicus, Vieta) and progressing through the 17th century's revolutionary developments by Descartes, Fermat, Newton, and Leibniz. The 18th century, dominated by Euler, Lagrange, and Laplace, is thoroughly examined. This "Revised and Enlarged" edition places special emphasis on the 19th and early 20th centuries, offering an expansive survey of the period's complex advancements in analysis, theory of functions, modern geometry, algebra, and applied mathematics, chronicling the work of pioneers like Gauss, Cauchy, Weierstrass, Riemann, and Poincaré. Cajori's history provides a "tolerably full history" of the entire discipline.