Table des matières

image/svg+xml Teaching

As part as my PhD contract, I carried out 2 teaching assignments of 32h "équivalent TD" inside the département histoire et philosophie des sciences of the Université Paris Cité, from 2024 to 2026. During this assignment, I got to take part into multiple teaching activities, including tutorial classes, or the organisation of the human sciences exam for the specific access pathway year for health training programs (PASS). But I mostly assumed full lectures for the master histoire et philosophie des sciencesmaster, on the following topics.

History of Algebra

(2025–2026, 2×3h CM, M1, SB) Introduction à lʼhistoire des mathématiques

These two sessions of introduction to the history of mathematics were part of a larger class for the first year of the master's program. The first of the two took dealt with a controversy around the interpretation of Old Babylonian tablets, and used this as an opportunity to present the problems related to the edition of the texts, and the importance of archaeological contexts to understand the mathematical content of the text. The following session took this as a starting point to explore further the reconstitution of mathematical practices from texts in Chinese and in Sanskrit.

(2024–2025, 7×3h CM, M2, SC) Histoire des mathématiques

This whole semester class dealt with the History of Algebra. I was in charge for the first half of the semester, which dealt with everything from Antiquity until the Modern Period (c. 17th century). My part of the class was organised around the reading of sources in their original language (Akkadian, Chinese, Sansirkt, Arabic, Latin, French and German). These texts were selected as an opportunity to talk about issues of method, regarding how to deal with the archaeological context of the sources, the stakes related to the methods of edition, the way texts are read, and so on.

History of Computations in Astronomy

(2025–2026, 1×3h CM, M2, SC) Histoire des mathématiques

This session was part of a larger class dedicated to the topic of "Numbers and Magnitudes". The goal for this session was to show how sources related to the History of Astronomy could be used to study such a theme. I composed the lesson around a collection of documents from different periods and in different languages, which constituded multiple case studies. Students could then choose to write their final essay on an article which allowed them to dive deeper into one of the topics explored in the class. (Documents présentés : 1–Chantilly, Bibliothèque et archives du château, Ms 65; 2–Istambul, Arkeoloji Müzeleri, Uruk 0126; 3–Brāhmasphutasiddhānta; 4–Paris, Bibliothèque nationale de France, Latin 7432; 5–Paris, Bibliothèque Sainte Geneviève, 1043; 6–Oxford, Bodleian Library, Ashmole 1796; 7–Oxford, Bodleian Library, Laud Misc 675; 8–Leiden, Universitätsbibliothek Leiden, Or. 8; 9–Paris, Bibliothèque nationale de France, Chinois 5015; 10–Oxford, Bodleian Library, Sinica 897/13; 11–Paris, bibliothèque nationale de France, Nouvelles acquisitions françaises 1844)

Sciences as seen from Asia

(2025–2026, 1×3h CM, M1, SA) History of mathematics in South Asia

I made this session in coordination with Haolin Wang 王浩霖 and Taro Tokutake 徳武 太郎. We presented an overview of multiple mathematical problems dealt in Sanskrit texts.

(2024–2025, 1×3h CM, M1, SA) Sciences in Mesopotamia

This class, made with Adeline Reynaud, was a general introduction to the history of sciences in the Ancient Middle East. It was composed around four themes: divination, medicine, mathematics and astronomy. These were used as case studies to explore the broader methodological question of characterising the role of "sciences" in ancient sources.

image/svg+xml Scientific animations

2024–2026: Palais de la découverte, Scientific popularization doctoral contract

Scientific popularization with the Mathematical unit of the Palais de la découverte, as part of my PhD contract

Savez-vous compter les jours… à la mode du xiiie siècle ?
Using manuscript 1043 from the bibliothèque Sainte Geneviève in Paris, this workshop explores how to compute the number of days elapsed from the beginning of a calendar, using texts taken from scholarly practice in late 13th-century Latin-speaking universities. This is a great opportunity to discover the methods of subtraction, multiplication and division by erasure that are given by John of Hollywood's Algorismus vulgaris, but also to learn how to read numerical tables with the canons to the Toledan Tables. To this end, I prepared a pedagogical tool available (in French) on the page dedicated to the workshop.
Fête de la Science 2026—« Comment calculait-on au xiiie siècle? »
During an event organized by the CNRS for the “Fête de la science” event in 2026, I collaborated with Clelia Crialesi to develop a workshop at the Exploradôme in Vitry-sur-Seine.
Mathematical recreations
The mathematical recreations proposed at the Palais de la découverte give the public an opportunity to discover games and puzzles to experiment with miscellaneous mathematical concepts, such as groups, graphs, recursion, algorithms, and so on.
Salon des mathématiques
During my work at the Palais de la découverte, I also took part in multiple stands during the Salon des mathématiques, which is organized every year in place Saint Sulpice in Paris.
2019-2023: Planète Sciences, Scientific animator

I helped children from 6 to 12 years old to perform experiments in extracurricular or leisure animations, or in public forums.

  • Building and programming robots and electronic circuits.
  • Experimenting around the notions of motion and mechanics.
  • Building rockets and performing games around space exploration.
2018-2019: Institut Henri Poincaré, Scientific animator
  • Guided visits for a temporary exposition in the Musée national des arts et métiers about mathematical surfaces, for classes from middle school to the master degree. These animations especially enabled the public to discover different fields of applied mathematics, and to answer students' questions about the prospects of mathematical studies.
  • Animation of augmented reality activities prepared by the company Holomath about Brownian motion during multiple events.

image/svg+xml Other dissemination activities

Publications

Clément Cartier, "Déchiffrez des tables du xiiie siècle !". Découverte n°452, 2026
Abstract

How many days are there between two given dates? To answer this question, Parisian scholars from the end of the 13th century used different numerical tables, for which multiple algorithms has been written down. By studying these texts, we learn more about the way computations were carried out at that time.

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Maxime Berger, Clément Cartier, Frédéric Jaëck, Bernard Lemaire, Édouard Thomas, "D'une forme à l'autre: jouer avec les polygones" in Marie José Pestel & Édouard Thomas (eds.), Maths en pleine forme. Express. Paris: Comité international de la culture et des jeux mathématiques. 2022
Abstract

This article presents the Wallace-Bolyai-Gerwein theorem, proving that if two polygons have the same surface, there is at least a finite collection of polygons that is a decomposition of both of them.

Lire
Maxime Berger, Clément Cartier, Frédéric Jaëck, Bernard Lemaire, Édouard Thomas, "Dissections de polygones avec Morceaux choisis de géométrie" in Marie José Pestel & Édouard Thomas (eds.), Maths en pleine forme. Express. Paris: Comité international de la culture et des jeux mathématiques. 2022
Abstract

This article presents the project of an application developed by the authors to explore different geometric activities related to polygons, especially by exploiting the Wallace-Bolyai-Gerwein theorem on equidecomposability of polygons of same area.

Lire
Clément Cartier, "Les mathématiques de l'apprentissage" in Marie José Pestel & Édouard Thomas (eds.), Les maths? Oui, ça sert! Express. Paris: Comité international de la culture et des jeux mathématiques. 2020
Abstract

This article is meant to be an introduction to statistical methods of automatic learning in artificial intelligence.

Lire

Talks

Isabelle Gallagher, Adrian Daerr, Turbulences. Entre Mathématiques et Physique: Conférence dans l'œil du cyclone. Paris: MathRix P7 et Phisis7, Thursday, January 26, 2017. Animation of a conference-duel between Mathematics and Physics about Navier-Stockes equations.