Comprising fifteen essays by leading authorities in the history of mathematics, this volume aims to exemplify the richness, diversity, and breadth of mathematical practice from the seventeenth century through to the middle of the nineteenth century.

An analysis of Newton's mathematical work, from early discoveries to mature reflections, and a discussion of Newton's views on the role and nature of mathematics. 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.

This volume sheds new light on one of the most remarkable polymaths of the English Renaissance. It offers original perspectives not only on Harriot’s personal achievements in mathematics and natural philosophy but also on the wider realms of exploration, colonial ambition, and philosophical debate in which he earned the attention and respect of contemporaries in and far beyond the socially elevated circles of his two great patrons, first Walter Ralegh and then Henry Percy, the ninth Earl of Northumberland. Harriot’s sixteenth-century world was one of unprecedented expansion in both scientific understanding and the discovery of new lands and peoples. The essays gathered here bring out forcefully the effect of this expanding vision, encapsulated in Harriot’s Briefe and true report of the new found land of Virginia (1588), the first detailed description of America to be published in the English language. In addition to an essay by a recent biographer of Harriot, the volume contains reworked versions of seven Thomas Harriot Lectures, an annual lecture series inaugurated in 1990 in Oriel College, Oxford. It follows two earlier volumes of Harriot Lectures, also edited by Robert Fox, that appeared in 2000 and 2012.