Hardcover | $55.00 Short | £37.95 | ISBN: 9780262013178 | 448 pp. | 7 x 9 in | 96 b&w illus., 9 tables| September 2009 Paperback |$20.00 Short | £13.95 | ISBN: 9780262516488 | 448 pp. | 7 x 9 in | 96 b&w illus., 9 tables| August 2011

# Isaac Newton on Mathematical Certainty and Method

## Overview

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.

Transformations: Studies in the History of Science and Technology

## About the Author

Niccolò 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. He is the recipient of the Sarton Medal for 2011-12 awarded by the University of Ghent, Belgium.

## Reviews

“This wonderful book is at once deeply informed and surpassingly lucid. I can find nothing in it to criticize.” — Katherine Dunlop, The Journal of the International Society for the History of Philosophy of Science

“This book offers a detailed and well-documented original view of Newton’s conceptions, strengths and weaknesses, clearly and vividly exposed.” — U. D’Ambrosio, Mathematical Review

“This book will become a classic. I recommend it very highly to any reader with interests in the history of mathematics, the history of science, or the philosophical issues emerging from mathematical and scientific practice.” — Paolo Mancosu, American Scientist

## Endorsements

"Guicciardini's book is a major contribution to Newtonian studies, documenting in authoritative detail Newton's views on the nature of mathematics and the place of mathematics in natural philosophy. Examining the different stages in the development of Sir Isaac's thought, Guicciardini analyzes Newton's conceptions in relation to those of such famous seventeenth-century philosophers as Descartes, Hobbes, and Leibniz. This penetrating study will be of interest to specialists in the history of exact science as well as to anyone interested in the intellectual context of seventeenth-century science."
Craig Fraser, Institute for the History and Philosophy of Science and Technology, University of Toronto

"This book not only gives a fresh and insightful analysis of the twisting evolution of Newton's thought, and of the rich historical context upon which Newton drew, it sheds new light on the role of mathematics in the creation of one of the founding documents of modern science."
Jeremy Gray, Professor of the History of Mathematics, Open University, UK

"This book takes up questions for which we have long awaited clearer answers: on the complex tensions between algebra and geometry in Newton's mathematical writings, on the methods that lay behind the Principia, and on the true nature of the priority dispute with Leibniz. In all these respects this is one of the most welcome additions of recent years to the literature on seventeenth-century mathematics."
Jacqueline Stedall, Queens College, Oxford University, co-editor of The Oxford Handbook of the History of Mathematics

"Isaac Newton on Mathematical Certainty and Method breaks important new ground in Newton scholarship by presenting, for the first time, a detailed and illuminating treatment of what Guicciardini calls Newton's philosophy of mathematics in the context of his scientific practice in both pure mathematics and natural philosophy. Brilliant new light is shed, in particular, on Newton's conception of the relationship between geometry and algebra (including the calculus), and the method of analysis and synthesis, as well as on Newton's break with Descartes (at the beginning of his career) and polemic with Leibniz (towards the end). Guicciardini has written an indispensable book for all those interested in the history of mathematics, the history of physics, and the history of philosophy in the early modern period."
Michael Friedman, Frederick P. Rehumus Family Professor of Humanities, Stanford University

## Awards

2011 Fernando Gil International Prize for the Philosophy of Science, presented by the Portuguese Foundation for Science and Technology and the Calouste Gulbenkian Foundation