Isaac Newton on Mathematical Certainty and Method

Historians of mathematics have devoted considerable attention to Isaac Newton's workon algebra, series, fluxions, quadratures, and geometry. In Isaac Newton on Mathematical Certaintyand Method, Niccolo Guicciardini examines a critical aspect of Newton's work that has not beentightly connected to Newton's actual practice: his philosophy of mathematics. Newton aimed to injectcertainty into natural philosophy by deploying mathematical reasoning (titling his main work TheMathematical Principles of Natural Philosophy most probably to highlight a stark contrast toDescartes's 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 thesubject and elaborating his own answers. Guicciardini shows how Newton carefully positioned himselfagainst 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, Newtonportrayed himself as antiquity's legitimate heir, thereby distancing himself from the moderns.Guicciardini reconstructs Newton's own method by extracting it from his concrete practice and notsolely by examining his broader statements about such matters. He examines the full range ofNewton's works, from his early treatises on series and fluxions to the late writings, which wereproduced in direct opposition to Leibniz. The complex interactions between Newton's understanding ofmethod and his mathematical work then reveal themselves through Guicciardini's careful analysis ofselected examples. Isaac Newton on Mathematical Certainty and Method uncovers what mathematics wasfor Newton, and what being a mathematician meant to him.

Niccolo Guicciardini is Professor of the History of Science at the University of Bergamo, Italy. He is the author of The Development of Newtonian Calculus in Britain, 1700-1800 and Reading the Principia: The Debate on Newton's Mathematical Methods for Natural Philosophy from 1687 to 1736.