Isaac Newton on Mathematical Certainty and Method

Historians of mathematics have devoted considerable attention to Isaac
Newton's work on algebra, series, fluxions, quadratures, and geometry. In
Isaac Newton on Mathematical Certainty and Method, Niccolò
Guicciardini examines a critical aspect of Newton's work that has not been tightly
connected to Newton's 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'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 the subject and elaborating his own answers. Guicciardini 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.
Guicciardini 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 Guicciardini's careful analysis of
selected examples. Isaac Newton on Mathematical Certainty and
Method uncovers what mathematics was for Newton, and what being a
mathematician meant to him.