All change…the calculus of Fermat, Newton, and Leibniz

Abstract

Abstract Calculus is typically credited to the late 17th-century work of Isaac Newton and Gottfried Leibniz, though they built on earlier, pioneering work by many mathematicians, especially Pierre de Fermat. Calculus is usually broken down into differential calculus—the study of change—and integral calculus—the study of accumulated change. These two processes are essentially inverses of one another, something made explicit by the Fundamental Theorem of Calculus. ‘All change…the calculus of Fermat, Newton, and Leibniz’ gives a historical take on their work developing calculus, the change in emphasis from Ancient Greek geometric methods, and Newton’s work applying calculus to physics. But it also notes how calculus, in the 17th and 18th centuries, still lacked logically sound foundations: at this time calculus was ‘a collection of ingenious fallacies’.