Karine Chemla | Université Paris Diderot (original) (raw)

Papers by Karine Chemla

Anachronisms in the History of Mathematics, 2021

European Congress of Mathematics

Studies in History of Mathematics Dedicated to A.P. Youschkevitch, 2002

Ses amis, ses collegues, se sont reunis autour d'Imre Toth, ce philosophe des sciences, philo... more Ses amis, ses collegues, se sont reunis autour d'Imre Toth, ce philosophe des sciences, philosophe artiste, engage dans tous les combats du XXe siecle, pour lui offrir ces essais reflets de sa pensee. Liberte, negation, c'est sur ces deux themes clefs de son oeuvre qu'ils ont, chacun selon son champ, compose des variations dans (presque !) toutes les langues dans lesquelles il a travaille. Le lecteur est donc emmene de la fleche de Zenon d'Elee a la logique contemporaine, en passant par l'universite de Kazan ou la Chine ancienne, les melancoliques nordiques ou Piero della Francesca. Un voyage a l'image de la recherche permanente qu'incarne celui que ces essais honorent. Le sommaire reproduit la table des matiere des volumes remis a Imre Toth le 29-12-1996, sous le titre Ceci N'EST PAS un festschrift pour Imre Toth. Certains articles du manuscrit d'origine ne sont pas reproduits ici. L'un d'entre eux a change de titre. Un autre n'est pa...

BJHS Themes, 2020

This essay approaches the knowledge required to write up and use instructions with a specific met... more This essay approaches the knowledge required to write up and use instructions with a specific method. It relies on specific procedures taken from the Chinese canon The Nine Chapters on Mathematical Procedures (九章算術), which, in the author's view, was completed in the first century CE. These procedures enabled readers to do things. To analyse the type of knowledge required to produce these texts of procedures and to use them, the essay puts into play two layers of commentary. The ancient layer was written between the third and the seventh centuries, whereas the later layer was composed between the eleventh and the thirteenth centuries. The author shows that these two layers of commentary read the same text of procedure differently, using different approaches and understanding it differently. The author also shows how the two layers of commentary use mathematical problems to approach a procedure, even though problems are used differently in the two contexts. This illustrates how, i...

Les themes des problemes que l'on trouve dans les manuscrits mathematiques recemment decouver... more Les themes des problemes que l'on trouve dans les manuscrits mathematiques recemment decouverts en Chine, dans des tombes datant des derniers siecles avant notre ere, presentent pour l'essentiel une grande continuite avec ceux qui nous sont parvenus dans Les Neuf Chapitres sur les procedures mathematiques (Ier siecle de notre ere), avec leur lot de commentaires indissociables du texte lui-meme. Ce fait suggere que ces ouvrages se rattachent a une meme tradition pour ce qui est de l'utilisation des problemes dans le contexte des demonstrations de la correction des algorithmes proposes. Alors que les historiens des mathematiques se sont davantage interesses a ces derniers, on defend ici l'hypothese que les problemes jouent un role clef dans la pratique ancienne des demonstrations. L'idee qu'un probleme et la procedure qui lui est associee forment une proposition generale, qu'ils soient formules de facon concrete ou abstraite, eclaire deux facettes de ce rol...

The article focuses on texts for algorithms found in the earliest extant mathematical sources in ... more The article focuses on texts for algorithms found in the earliest extant mathematical sources in Chinese. It brings to light that texts regularly make use of analogy. On the one hand, the author shows that the texts use several techniques to prescribe by analogy. On the other hand, she highlights that in addition to a prescriptive dimension, these algorithm texts regularly possess an assertive dimension, stating analogies by the way in which they are formulated. She analyses how analogies are thereby stated, proving that commentators on these texts interpreted this dimension of the text and read in it the assertion of an analogy at the level of the reasons underlying the correctness of the algorithm.

I sketch here a history of quadratic equation aiming at illustrating the potential fruitfulness o... more I sketch here a history of quadratic equation aiming at illustrating the potential fruitfulness of a non-linear history of algebraic equations. I show how a combination of three approaches is required to conduct such an inquiry in that particular case. Comparative history: in Babylonian, Chinese, and Greek sources, what we might recognize as quadratic equations manifests itself in very different ways depending on the corpus of texts considered. Conceptual history: this remark highlights that, in Antiquity, there were different concepts of equation available. We find respectively equation seen as problems (Mesopotamian sources), as operation depending on root extraction (Chinese sources), and as assertion of an equality (al-Khwarizmi). Historical documents show that, instead of one eliminating the other concepts, the history of algebraic equations evidences moments of synthesis between them. In particular, the work On equations by Sharaf al-Din al-Tusi at the end of the 12th century,...

East Asian Science, Technology, and Medicine, 2017

The two issues of EASTM that we have devoted to tables address the same set of basic questions. 1... more The two issues of EASTM that we have devoted to tables address the same set of basic questions. 1 They examine tables in a historical fashion, focusing 1 This issue (the second on the topic of numerical tables and tabular layouts published in this journal) also contains some of the papers presented during a twoday workshop I organized on March 22-23, 2012, on the topic of "Tables in scholarly Chinese sources" (http://www.sphere.univ-paris-diderot.fr/spip.php?article626).

East Asian Science, Technology, and Medicine, 2017

An introduction to volume 1 of Numerical Tables and Tabular Layouts in Chinese scholarly document... more An introduction to volume 1 of Numerical Tables and Tabular Layouts in Chinese scholarly documents, published as a special issue of East Asian Science, Technology and Medicine. The volume is devoted to the work to produce tables and the meaning of their format

Revue d Histoire des Mathematiques, 1998

Comment introduire de la generalite dans un monde geometrique ou une foule de verites particulier... more Comment introduire de la generalite dans un monde geometrique ou une foule de verites particulieres, etablies par des methodes ad hoc, restent sans liaison entre elles et forment donc un ensemble sans organisation ? En suivant les divers traitements d'un unique theoreme, appele aujourd'hui le theoreme de Menelaus, le present article vise a examiner comment les travaux geometriques de Lazare Carnot ont indique, aux geometres comme Poncelet ou Chasles qui posaient cette question, diverses pistes pour y repondre.

Cultures without Culturalism, 2017

HAU: Journal of Ethnographic Theory, 2019

Sources attesting to mathematical activities in ancient China form at least four distinct cluster... more Sources attesting to mathematical activities in ancient China form at least four distinct clusters of texts, bespeaking at least four different-though overlapping-ways of practicing mathematics. I will focus on two such sets of documents: the canons that in the seventh century constituted one of the two curricula taught in the Imperial "School of Mathematics," and manuscripts recently excavated from tombs sealed in the last centuries BCE. I will argue that these two sets of documents testify to two different ways of practicing mathematics, which related to different material practices. Accordingly, we can perceive that mathematical objects were shaped and explored in different ways, with significant consequences for the knowledge produced.

Bamboo and Silk, 2018

Refining our previous study in Jianbo 簡帛 12 (2016), this article examines the back-and-forth betw... more Refining our previous study in Jianbo 簡帛 12 (2016), this article examines the back-and-forth between scribal hands in the Suan shu shu 筭數書 from Zhangjiashan 張家山 M247 (sealed ≥186 b.c.e.). Introducing an improved methodology, we establish a link between one of the Suan shu shu’s scriptors and four other manuscripts in the same tomb, offering a hand-informed reading of the former to hypothesize what this means. 以《簡帛》第12輯（2016 年）的原作爲基礎，本文對張家山247號漢墓《筭數書》寫手輪流交替書寫的現象進行分析。在介紹我們對原有方法論的改進後，本文把《筭數書》的兩位寫手之一與隨葬的四種文本串聯，再由字跡、文意對讀解釋其意味。

East Asian Science, Technology and Society: An International Journal, 2017

Before becoming active in the history and philosophy of science, Evelyn Fox Keller had worked in ... more Before becoming active in the history and philosophy of science, Evelyn Fox Keller had worked in physics, in mathematical biology, and also in feminist theory. Many know about her publications in that last field. However, it is perhaps less known to historians and philosophers of science that her contributions to mathematical biology are still often quoted by practitioners of this field. In fact, as the article on which this issue comments and many others amply demonstrate, Keller never gave up participating actively in the reflection about life sciences, in particular genetics, and interacting with biologists. It is from this perspective that we can read her article about scientific cultures for what it reveals about scientific cultures. Keller’s starting point in this article is the conviction that the language currently used by biologists and primarily by geneticists might hinder due attention to temporality and to key phenomena that unfold in time. She argues that the overwhelming use of nouns in genetics—to begin with, the noun gene—meshes with an all too prominent emphasis placed on stable entities in the interpretation of phenomena. Keller attributes this feature to an entrenched and tacit commitment to what she calls an “entity real-

Centaurus, 2015

In this article I examine how mathematical procedures were written in ancient mathematical docume... more In this article I examine how mathematical procedures were written in ancient mathematical documents from China and elsewhere. Two key features are analyzed. Some of the texts for procedures require a 'circulation' (or movement) among the sentences that reveal competences that practitioners had to possess to use these texts in the contexts in which they worked. This feature of the text is correlated with the fact that the texts allow practitioners to derive different lists of actions for different cases. It thus discloses that generality was prized in this type of mathematical practice. The second feature noted is that some operations are prescribed using the reason why the operation should be carried out. This feature reveals how a text of procedure communicated not only actions, but also understanding of the actions. How the practitioner understood the operation to be executed requires examination. However, this feature undermines the widespread assumption that these texts were meant for practitioners who did not understand what they did and applied prescriptions blindly.

Extreme Orient Extreme Occident, 2007

Bretelle-Establet Florence, Chemla Karine. Qu'etait-ce qu'ecrire une encyclopedie en Chin... more Bretelle-Establet Florence, Chemla Karine. Qu'etait-ce qu'ecrire une encyclopedie en Chine ?. In: Extreme-Orient, Extreme-Occident, 2007, hors serie. Qu'etait-ce qu'ecrire une encyclopedie en Chine ? / What dit it mean to write an encyclopedia in China ? pp. 7-18.

Acta Historica Leopoldina, 2010

HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Archimedes, 2015

The texts of algorithms fall under the general rubric of instructional texts, discussed by J. Vir... more The texts of algorithms fall under the general rubric of instructional texts, discussed by J. Virbel in this book. An algorithm has two facets. It has a text—a written text—, which usually appears to be an enumerated list of operations. In addition, whenever an algorithm is applied to a specific set of numerical values, practitioners derive from its text a sequence of actions, or operations, to be carried out. In the execution of the algorithm, these actions generate events that constitute a flow of computations eventually yielding numerical results. This chapter aims mainly to develop some reflections on the relationship between these two facets: the text and the different sequences of actions that practitioners derive from it. I use two tools in my argumentation. Firstly, I use the description of textual enumerations, as developed by Jacques Virbel, to find out how enumerations of operations were carried out in the text of algorithms and how these enumerations were used. Then I focus on the language acts carried out in some of the sentences composing the texts, since, when prescribing operations, the texts of the algorithms differ in that they use distinct ways of carrying out directives. The conclusion highlights different ways in which the text of an algorithm can be general and convey meanings that go beyond simply prescribing operations.

Anachronisms in the History of Mathematics, 2021

European Congress of Mathematics

Studies in History of Mathematics Dedicated to A.P. Youschkevitch, 2002

BJHS Themes, 2020

East Asian Science, Technology, and Medicine, 2017

Revue d Histoire des Mathematiques, 1998

Cultures without Culturalism, 2017

HAU: Journal of Ethnographic Theory, 2019

Bamboo and Silk, 2018

East Asian Science, Technology and Society: An International Journal, 2017

Centaurus, 2015

Extreme Orient Extreme Occident, 2007

Acta Historica Leopoldina, 2010

Archimedes, 2015

Ses amis, ses collegues, se sont reunis autour d'Imre Toth, ce philosophe des sciences, philosoph... more Ses amis, ses collegues, se sont reunis autour d'Imre Toth, ce philosophe des sciences, philosophe artiste, engage dans tous les combats du XXe siecle, pour lui offrir ces essais reflets de sa pensee. Liberte, negation, c'est sur ces deux themes clefs de son oeuvre qu'ils ont, chacun selon son champ, compose des variations dans (presque !) toutes les langues dans lesquelles il a travaille. Le lecteur est donc emmene de la fleche de Zenon d'Elee a la logique contemporaine, en passant par l'universite de Kazan ou la Chine ancienne, les melancoliques nordiques ou Piero della Francesca. Un voyage a l'image de la recherche permanente qu'incarne celui que ces essais honorent. Le sommaire reproduit la table des matiere des volumes remis a Imre Toth le 29-12-1996, sous le titre Ceci N'EST PAS un festschrift pour Imre Toth. Certains articles du manuscrit d'origine ne sont pas reproduits ici. L'un d'entre eux a change de titre. Un autre n'est pas encore parvenu. Un, enfin, s'est ajouté par la suite. A l'ensemble, on joint ici une bibliographie des oeuvres de Imre Toth réalisée par M. Cattanei.
Die Freunde und Kollegen von Imre Toth, dem Philosophen der Wissenschaft, philosophischen Künstler und engagierten Teilnehmer an allen Kämpfen des XX. Jahrhunderts haben sich um ihn versammelt, um ihm diese Aufsätze - Widerspiegelungen seines Werks, die sie - jeder auf seinem Gebiet - in Variationen in (beinahe !) allen Sprachen komponiert haben, in denen er arbeitete. Der Leser wird so von Zenons Pfeil zur Logik der Gegenwart geführt, auf dem Umweg über die Universität von Kasan oder das antike China, die Melancholiker des Nordens oder Piero della Francesca. Eine Reise nach dem Bild der permanenten Forschung, die derjenige verkörpert, den diese Aufsätze ehren.
Das "Sommaire" gibt das Inhaltsverzeichnis der Bände wieder, die Imre Toth am 29.12.1996 unter dem Titel Ceci N'EST PAS un festschrift pour Imre Toth überreicht wurden. Einige Beiträge des Originalmanuskripts können hier nicht präsentiert werden, außerdem wurde ein Titel ausgetauscht, ein anderer ist noch nicht angelangt. Ein weiterer ist später hinzugekommen. Dem Ganzen wurde eine von Elisabetta Cattanei zusammengestellte Bibliographie der Schriften von Imre Toth hinzugefügt.

Monographs in Tang Official Historiography, 2019

This chapter develops a reading of the Sui shu 隋書 ‘Treatise on Economics’ (Shihuo zhi 食貨志) in the... more This chapter develops a reading of the Sui shu 隋書 ‘Treatise on Economics’ (Shihuo zhi 食貨志) in the light of a comparison with the equivalent treatise in the Han shu. Far from reducing the Sui shu treatise to an ideological piece following the intellectual and rhetorical thread of the Han shu model, such a reading allows us to better understand the questions raised by the author(s), which pervade not only the long introduction but also the body of the treatise. One of the more central questions will prove to be the paradoxical nature of imperial economic policy, especially as concerns the management of granaries and canals—the guarantors of sufficiency, circulation and, at the same time, the interests of the imperial clan and its display of power.