On the invisibility and impact of Robert Hooke’s theory of gravitation

Robert Hooke\u2019s theory of gravitation is a promising case study for probing the fruitfulness of Menachem Fisch\u2019s insistence on the centrality of trading zone mediators for rational change in the history of science and mathematics. In 1679, Hooke proposed an innovative explanation of planetary motions to Newton\u2019s attention. Until the correspondence with Hooke, Newton had embraced planetary models, whereby planets move around the Sun because of the action of an ether filling the interplanetary space. Hooke\u2019s model, instead, consisted in the idea that planets move in the void space under the influence of a gravitational attraction directed toward the sun. There is no doubt that the correspondence with Hooke allowed Newton to conceive a new explanation for planetary motions. This explanation was proposed by Hooke as a hypothesis that needed mathematical development and experimental confirmation. Hooke formulated his new model in a mathematical language which overlapped but not coincided with Newton\u2019s who developed Hooke\u2019s hypothetical model into the theory of universal gravitation as published in the Mathematical Principles of Natural Philosophy (1687). The nature of Hooke\u2019s contributions to mathematized natural philosophy, however, was contested during his own lifetime and gave rise to negative evaluations until the last century. Hooke has been often contrasted to Newton as a practitioner rather than as a \u201cscientist\u201d and unfavorably compared to the eminent Lucasian Professor. Hooke\u2019s correspondence with Newton seems to me an example of the phenomenon, discussed by Fisch in his philosophical works, of the invisibility in official historiography of \u201ctrading zone mediators,\u201d namely, of those actors that play a role, crucial but not easily recognized, in promoting rational scientific framework change

The Newton–Leibniz Calculus Controversy, 1708-1730

This article examines the controversy between Isaac Newton and Gottfried Wilhelm Leibniz concerning the priority in the invention of the calculus. The dispute began in 1708, when John Keill accused Leibniz of having plagiarized Newton\u2019s method of fluxions. It will be shown that the mathematicians participating in the controversy in the period between 1708 and 1730\u2014most notably Newton, Leibniz, Keill, and Johann Bernoulli\u2014held different conceptions of mathematical method. The dispute began in a political climate agitated by the Hanoverian succession and was intertwined with tensions dividing the Royal Court. It developed into a discussion of technical issues concerning the relation between mathematics and natural philosophy and the methods of the integral calculus

Conceptulism and contextualism in the recent historiography of Newton’s Principia

Recently the Principia has been the object of renewed interest among mathematicians and physicists. This technical interpretative work has remained somewhat detached from the busy and fruitful Newtonian industry run by historians of science. In this paper will advocate an approach to the study of the mathematical methods of Newton's Principia in which both conceptual and contextual aspects are taken into consideration

In Memoriam: Derek Thomas Whiteside (1932–2008)

Derek Whiteside died in 2008. This is an overview of his contributio to Newtonian scholarship

Un Altro Presente : on the historical interpretation of mathematical texts

In this paper I discuss different approaches to past mathematical texts. The question I address is: should we stress the continuity of past mathematics with the mathematics practiced today, or should we emphasize its difference, namely what makes it a product of a distant mathematical culture

Specious algebra is fit enough to find out, but entirely unfit to consign to writing and commit to posterity : Newton’s publication strategies as a mathematical author

In my lecture I will be advocating an approach to the history of mathematics inspired by the method followed by intellectual historians. In the first part, I will recall some of the desiderata for intellectual history proposed long ago by Quentin Skinner. I take Skinner\u2019s rejection of what he called the \u201cmythologies\u201d of the history of ideas as a proposition that can still be inspirational for historians of mathematics. In the second part, which is devoted to Newton\u2019s publication and authorial strategies, I will show how a kind of humanistic historicism inspired by the work of intellectual historians can be pursued in writing, in an historically informed way, about one of the great giants of early modern mathematics. In the third part, I will attempt to draw some conclusions. First, I will state that I do not wish to downgrade, or reject, internalistic approaches to the history of mathematics, which indeed have been, and will continue to be, of central importance. Second, I will make clear that my talk is not meant to be a defence of Skinner\u2019s dense philosophical ideas on textual interpretation, which are inspired by Wittgenstein and Austin. My approach is much more philosophically naive, and should rather be taken as a methodological reflection on the craft of the history of mathematics, carried out by one of its practitioners