Séminaire – Doctoral Interdisciplinaire d’histoire et philosophie des Sciences (DISc )

Présentation de travaux de thèses

Clément BONVOISIN (SPHere, Université Paris Cité) – Go down in history ? How Magnus Hestenes became part of historical narratives on Pontryagin’s maximum principle (1948 – 1961)
In a paper published in 2009 in the scientific journal Control and Cybernetics, historian of mathematics Michael Plail and mathematician Hans-Josef Pesch summed up the history of Pontryagin’s maximum principle. This important result in nowadays optimisation (the search of best solutions to given problems) had been derived by a group of Soviet mathematicians gathered by Lev Pontryagin (1908 – 1988), in a series of works they published from 1955 to 1961. However, Plail and Pesch’s account of the history of Pontryagin’s maximum principle also mentions the research carried in the United States as early as 1950, by a mathematician called Magnus Hestenes (1906 – 1991). Back then, the latter was working for a think tank funded by the U.S. Army Air Forces called the RAND Corporation. There, he produced a couple of research memoranda that have hardly been distributed outside of the think tank.Commenting on one of these memoranda, the authors of the historical paper note that prior to the works of Pontryagin’s group, Hestenes had writtenan equation that was “a first formulation of a maximum principle.”This comment shows that from Plail and Pesch’s perpsective, Magnus Hestenes is a precursor in the history of Pontryagin’s maximum principle. As it happens, some scientists made similar claims before Plail and Pesch did. In this talk, I wish to question how scientists shape historical narratives and identify precursors, by describing how Magnus Hestenes came to be seen as such. Whofirst likenedPontryagin’s maximum principle to the equation written by Hestenes ? How did they know of Hestenes’ work in spite of its poor distribution ? In likening it to the maximum principle, how did they change its initial meaning ?

Jimmy Degroote (SPHere, Université Paris Cité) – How do you write the history of a philosophical abstraction ?
Even today, the history of philosophy is the main way of teaching and doing philosophy in France, at least on an academic level. As you may be aware, this contrasts with university practice in other Western countries, which is more concerned with the logical analysis of concepts and the scrupulous evaluation of the argumentative requirements. Although much has been written in the past about this difference in style between a philosophy ’à la française’, still called ’continental’, and an Anglo-Saxon philosophy – to the point, perhaps, of appearing a little hackneyed here – it is a reminder that the genetic apprehension of philosophical texts and theories is far from presenting the characteristics of obviousness and necessity that we often attribute to it. The historical method is not self-evident. One difficulty in particular needs our attention : if it is true that philosophy deals mainly with abstractions such as concepts and problems, how can we make the history of such objects ? Here, it is not a question of putting a piece back into the jukebox of realism and constructivism (are we dealing with ideal invariants that are independent of the contexts in which they are instantiated, or with human representations that are themselves subject to change and contingency ?), but rather to question the catch that the historical method can effectively exert on ’things’ that are not things in the ordinary sense of the term, but are content to find in matter a medium of expression or to leave evasive traces. So can we really do a history of abstractions ? We would like to study the difficulties associated with this question in the case of the problem of the applicability of mathematics, the origin of which several historians (such as Marco Panza) situate in the Pythagoreanism of Antiquity, while several philosophers (such as Mark Steiner) do not hesitate to maintain that it was not until the end of the 1990s that it clearly emerged. After briefly reviewing the reasons behind these contradictory judgements, we would like above all to explore the methodological difficulties underlying their expression : can we identify an ’ancient’ and a ’contemporary’ problem on the pretext that they find similar formulations ? Moreover, how can the similarity of these formulations be established beyond the differences in language and epistemological context ? Is it even possible to determine the date at which a problem appears in history ? Our aim is to contribute to the debates on the ’age’ of the problem of applicability, using a conceptual approach that is aware of the preceding difficulties.

Simon GENTIL (SPHere, Université Paris Cité) – Can we define what are curves ?
What is a curve ? At first sight, this question may seem naïve, reflecting a lack of knowledge of a primary mathematical object. However, if the idea of a curve is relatively intuitive, the desire for a mathematical discourse integrating this notion imposes the need for a rigorous definition of what a curve is. However, it appears that the concept of a curve as such does not have a fully satisfactory definition. The aim of this paper is to examine different definitions of a subclass of curves, whether current (algebraic curves, topological curves, etc.) or historical (geometric curves, interscendental curves, etc.), and to use examples to highlight the conflicts between the intuitive idea of what curves are and the rigorous definitions that can be proposed. The philosophical reflections proposed during this presentation will also be enriched by historical remarks. In particular, although the idea of a curved line has existed since antiquity, it would appear that the notion of a curve ’in general’ was not constructed until the early modern period and the introduction of an algebraic method in geometry, which on the one hand makes it possible to think of the curve in general and on the other hand makes it impossible to define such a notion. While this last observation may seem problematic, it also seems to us that it can be seen as a driving force in mathematical research, in particular by proposing counter-examples that encourage us to rethink established definitions. The presentation that we are proposing does not claim to be able to define what a curve is, but aims to suggest ways of thinking about the possibility of defining such an intuitive object in all its generality.

Lieu : salle 628 bâtiment Olympes de Gouges