Isaac Newton on Mathematical Certainty and Method

Historians of mathematics have devoted considerable attention to IsaacNewton's work on algebra, series, fluxions, quadratures, and geometry. In IsaacNewton on Mathematical Certainty and Method, Niccol? Guicciardini examines acritical aspect of Newton's work that has not been tightly connected to Newton'sactual practice: his philosophy of mathematics. Newton aimed to inject

Historians of mathematics have devoted considerable attention to IsaacNewton's work on algebra, series, fluxions, quadratures, and geometry. In IsaacNewton on Mathematical Certainty and Method, Niccol? Guicciardini examines acritical aspect of Newton's work that has not been tightly connected to Newton'sactual practice: his philosophy of mathematics. Newton aimed to inject certaintyinto natural philosophy by deploying mathematical reasoning (titling his main workThe Mathematical Principles of Natural Philosophy most probably to highlight a starkcontrast to Descartes's Principles of Philosophy). To that end he paid concertedattention to method, particularly in relation to the issue of certainty, participating in contemporary debates on the subject and elaborating his ownanswers. Guicciardini shows how Newton carefully positioned himself against twogiants in the "common" and "new" analysis, Descartes andLeibniz. Although his work was in many ways disconnected from the traditions ofGreek geometry, Newton portrayed himself as antiquity's legitimate heir, therebydistancing himself from the moderns. Guicciardini reconstructs Newton's own methodby extracting it from his concrete practice and not solely by examining his broaderstatements about such matters. He examines the full range of Newton's works, fromhis early treatises on series and fluxions to the late writings, which were producedin direct opposition to Leibniz. The complex interactions between Newton'sunderstanding of method and his mathematical work then reveal themselves throughGuicciardini's careful analysis of selected examples. Isaac Newton on MathematicalCertainty and Method uncovers what mathematics was for Newton, and what being amathematician meant to him.