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# Séminaire – Histoire et Philosophie des Mathématiques

## January 8 @ 9h00 - 17h30

**Séance des présentations**

**Frederike Lieven (Sorbonne Université)
**

*The « New Math » reform in France and in Germany: the challenges of a comparative analysis*

Abstract :

In the 1960s, the “New Math” was a movement that promoted deep changes in the teaching of mathematics. In many countries, it led to reforms of mathematical instruction, in its content and methods. In the 1970s, after a strong public contest, the reforms were gradually abandoned.

The reform movement was international, whereas the reforms took place in a national context. Indeed, in France and Germany, the curricula were elaborated on a national or regional level. This entanglement of international and national factors makes it interesting, but also challenging, to study the “New Math” reform in a comparative way.

First of all, what does the “New Math” stand for? Since the 1950s, the need for reform has become generally accepted among mathematics educators. At that time, the actors spoke about a modernisation of mathematics teaching. However, sources show that there was no consensus on the content of modernisation, and that the term was used with diverse meanings. International meetings and organisations contributed to shaping a more homogeneous understanding of the aims of the reform.

With regard to the institutional aspects, both in France and in Germany, the reform is carried out by a commission. However, there are important differences in the composition and the tasks of these commissions. Differences in the organisation between the two countries raise the question of the sources that the historian can use and of the possibility of making a comparison using different types of sources.

As a final point, I would like to analyse the public debate sparked by the reform, in order to show that the actors involved in the debate, as well as the issues mobilised for the contest, were by no means the same in France and in Germany. This raises the question of the interaction between an international movement and different national contexts.

**Elisa Dalgalarrondo (SPHERE, Université Paris Cité)
**

*Gendered representations in the mathematics of the Ladies’ Diary (1760-1784)*

Abstract :

The *Ladies’ Diary* is a British almanach published annually between 1704 and 1840. In this periodical, we can find different sections containing enigmas, charades, rebuses and mathematical questions to which members of the readership could directly participate by submitting their questions and solutions to the editor. Few of the contributors could read their own contributions with their name in the magazine issues, while the great majority of them could just see their names among lists of contributors following the published solutions. Initially adressed to « the Ladies », the *Diary* soon attracted a male readership. The period between around 1760 and 1790 tends to appear in the historiography as a time during which no women contributed to the mathematics of the *Ladies’ Diary*. Actually, two female names can be found among the frequent contributors of the mathematical questions. The first one is a man’s pseudonym from which we can find published participations. The second one is indeed a woman’s name, but just appeared among the unpublished contributors. In this talk, I will focus on these two cases in order to try to show how studying the mathematics of the *Ladies’ Diary* can raise some questions in terms of gendered representations.

**Clément Bonvoisin (SPHERE, Université Paris Cité)
**

*Failing to apply applied mathematics? On Donald Bushaw’s Ph.D. dissertation (1949 – 1955)*

Abstract :

In this talk, I will discuss issues pertaining to the application of mathematics. How are mathematical problems and results shaped by technical issues? Conversely, how do hypotheses made by mathematicians raise challenges for the design of instruments? And to what extent can this impede the application of mathematical knowledge, so to speak? In order to address these questions, I will build on the research carried out by US mathematician Donald Bushaw (1926 – 2012) for his Ph.D. thesis at Princeton University.

Back then, Bushaw worked as a consultant in a military-funded project. I will begin by discussing this broader project, what may be said of its practical aims, and the relations it had to the mathematical problem tackled by Bushaw. I will then turn to the mathematical content of the dissertation itself. Here, my focus will be on the differences between Bushaw’s work, and pre-existing research on similar practical problems by German engineer Irmgard Flügge-Lotz (1903–1974). I will show that these differences are threefold: in the relation between mathematics and technics; in the mathematical problem at hand; and in the generality of mathematical hypotheses made on solutions to the problem.

This last aspect will allow me to discuss the application of Bushaw’s results in the context of his project. As I will show, the mathematical generality of Bushaw’s work raised technical difficulties. In turn, these technical difficulties brought social and institutional issues, due to the military context in which Bushaw’s work was carried out. From this perspective, I will discuss intrications between mathematical, technical and social aspects in the application of mathematics, and how this may well cause failures in such applications.

Organization Clément BONVOISIN

**Salle** : 628 (6è étage, bâtiment Olympes de Gouges)

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