Historians of mathematics have devoted considerable attention to Isaac Newton’s work on algebra, series, fluxions, quadratures, and geometry. This book examines a critical aspect of Newton’s work that has not been tightly connected to his actual practice: His philosophy of mathematics. Newton aimed to inject certainty into natural philosophy by deploying mathematical reasoning (titling his main work The Mathematical Principles of Natural Philosophy most probably to highlight a stark contrast to Descartes’ Principles of Philosophy). To that end he paid concerted attention to method, particularl ... More

Historians of mathematics have devoted considerable attention to Isaac Newton’s work on algebra, series, fluxions, quadratures, and geometry. This book examines a critical aspect of Newton’s work that has not been tightly connected to his actual practice: His philosophy of mathematics. Newton aimed to inject certainty into natural philosophy by deploying mathematical reasoning (titling his main work The Mathematical Principles of Natural Philosophy most probably to highlight a stark contrast to Descartes’ Principles of Philosophy). To that end he paid concerted attention to method, particularly in relation to the issue of certainty, participating in contemporary debates on the subject and elaborating his own answers. The author shows how Newton carefully positioned himself against two giants in the “common” and “new” analysis, Descartes and Leibniz. Although his work was in many ways disconnected from the traditions of Greek geometry, Newton portrayed himself as antiquity’s legitimate heir, thereby distancing himself from the moderns. The author reconstructs Newton’s own method by extracting it from his concrete practice and not solely by examining his broader statements about such matters. He examines the full range of Newton’s works, from his early treatises on series and fluxions to the late writings, which were produced in direct opposition to Leibniz. The complex interactions between Newton’s understanding of method and his mathematical work then reveal themselves through the author’s analysis of selected examples. The book uncovers what mathematics was for Newton, and what being a mathematician meant to him.