**Principal Investigator**

Karine Chemla SPHERE. She is a historian of mathematics and a sinologist, Senior Researcher (“Directrice de Recherche”) at the CNRS. Within the SAW project, her research concerns identification and description of mathematical cultures evidenced in ancient China. She pays special attention to the mathematical documents recently excavated or bought on the antiquities market and to the earliest documents handed down through the written tradition. She focuses on specific features through which mathematical cultures can be characterized, in particular: work with operations, number systems, textual organization and nature of these documents, epistemological goals and values they attest. Further, she examines how mathematical sources provide evidence of activities of officials in ancient China, and, vice versa, how connections between these sources and activities shed light on the nature of mathematical sources. She conducts theoretical work on the concept of mathematical culture and its uses, in particular through research in the historiography of science.

**Co-directors**

Agathe Keller SPHERE. She is a historian of mathematics working essentially on Sanskrit mathematical commentaries and a CNRS researcher. Within the SAW project, her intent is to to describe the cultures of computation of the 9th century commentator Caturveda Pṛthudakasvamin, as he glosses the mathematical chapter of Brahmagupta’s 7th century Brahmasphuṭasiddhānta. She is currently editing and translating this commentary, which presents both links to mathematical astronomy and to the mathematics that could have been used by merchant’s guilds or administrations. She is also investigating past and present political histories of mathematics in relation to the Indian subcontinent, and histories of how Sanskrit mathematical commentaries were read, edited, and translated in the past.

Christine Proust SPHERE. She is a historian of mathematics, working on cuneiform sources, Senior Researcher (“Directrice de Recherche”) at the CNRS, and member of the SPHERE team. Within the SAW project (first phase), she analyzes relations between computation, numbers, measures, and operations. In particular, she studies the context in which sexagesimal place value notation appeared in the 2nd half of the 3rd millennium BCE. She is also interested in different conceptions of numbers and operations developed in scribal schools and professional milieus of the Old-Babylonian period. For the second phase, she will focus on relations between mathematical and astronomical practices in the city of Uruk during the Seleucid period. She pays great attention to dissemination of history of ancient mathematics among non-specialists, especially secondary schools’ teachers and pupils.

**Coordinator** – Christine Mousset

**Financial officer** – Virginie Maouchi

**Team members**

Florence Bretelle-Establet, SPHERE

She is a sinologist and works in the field of history of medicine in China as a CNRS researcher in the SPHERE team (SPHERE, UMR 7219, Paris Diderot Université). She focuses on the medical writings produced in the most southern regions of the Qing empire (1644-1911) to examine what it meant to be a doctor, a medical author, in those regions which combined rural and urban configurations ; to what extent and along which channels medical doctrines and practices circulated in the empire; and how medical doctrines from central areas as well as medical doctrines from Europe were locally understood, tamed, and reconfigured. Within the SAW project, she particularly analyses the different ways of writing medical texts, on semantic, syntax and emotional levels, by focusing notably on the question of the practices of quotation, the significance of compilation, the role of paratextual elements such as prefaces and reading guidelines, the role of layout.

Martha Cecilia Bustamante , SPHERE

She is a historian of the theoretical physics in France (19th- 20 centuries). She is working on Paul Langevin’s teaching at the Collège de France on quantum physics, a field created in Germany in 1900, due to the work of Max Planck on the thermal radiation. Langevin taught at the Collège since 1902, but did not publish his classes. Therefore she is interested in the note-books produced by Langevin’ auditors. Within the SAW project, she analyses the relationship between note-books, as written scientific sources, and the “oral context” from which they are derived. She is concerned by questions such as what we can learn from that kind of documents, about Langevin’s method of teaching at the Collège de France ; what evidence the note-books can give us on how the lessons on theoretical physics were held. She tries to highlight the conditions in which the course was taught and the notes were taken. She is currently preparing a critical edition of notes which were written down in a notebook by the mathematician Emile Borel, who was one Langevin’s auditors during the course of 1912-1913. It was the first that Langevin devoted entirely to the subject of quantum physics.

Damien Chaussende, CRCAO – UMR 8155, CNRS & Université Paris Diderot

His research interests include political history and historiography of the Classical period in China, especially of the 3rd to 8th century Early Medieval China, as well as the 18th century, which was marked by an important philological movement among Chinese literati. He is currently preparing a translation from classical Chinese into French of the *Generalities on Historiography (Shitong),* a historiographical monograph written at the beginning of the 8th century by historian Liu Zhiji (661-721). Within the SAW project, he organised, together with Karine Chemla, a workshop on Li Chunfeng and historical treatises in early Tang China.

Matthieu Husson, SYRTE-Observatoire de Paris/ SAW ERC project

His research is devoted to the recovery and analysis of the mathematical practices found in connection with astral sciences in Europe, from the 13th to the 15th centuries. He is mainly working on the Alfonsine corpus, a group of astronomical tables which was the main computational tool in Europe for astronomical purposes in this period. He is also studying this topic in the broader epistemological context of the *scientiae mediae.* Therefore, he examines as well sources of musical theory and optic in order to contrast them with astral sciences sources.

Cécile Michel, HAROC – UMR 7041, CNRS & Université Paris Sorbonne

She is an assyriologist, Senior Researcher (“Directrice de Recherche”) at the CNRS in the laboratory “Archéologies et Sciences de l’Antiquité” (ArScAn, Maison de l’Archéologie et de l’Ethnologie, Nanterre). Her main research interests are decipherment of cuneiform texts from the first half of the 2nd millennium BC (private archives of merchants, state administrative archives), Mesopotamian trade, Upper Mesopotamian and Anatolian societies, gender studies, daily life and material culture (fauna, food, metals, textiles), calendars and chronology, history of sciences, education, writing and computing. Within the SAW project, her research concerns the writing of numbers and computing methods used in cuneiform practice documentation of the 2nd millennium BC; the aim is to evaluate the merchants’ knowledge in mathematics and to discover how they were computing.

Stéphane Schmitt, SPHERE

He is a historian of life sciences (18th-19th centuries), researcher at the CNRS. He works on the history of embryology, comparative anatomy, and the emergence of evolutionary theories, especially in France and Germany. He is the editor of Georges-Louis Leclerc de Buffon’s *Œuvres complètes* (Honoré Champion, 2007-, 7 volumes published so far). Within the SAW project, his research concerns issues such as the genesis and composition of Buffon’s *Histoire naturelle*: he is particularly interested in the sources, their mobilization (e.g. practices of quotation), and the use by Buffon and his collaborators; the significance of compilation, intertextuality and polygraphy in such a work; the role of paratextual elements as well as illustration; the relationship of text, image and objects of collection, and he tries to connect such approaches with the history of concept. He is currently working on the importance of “ancient” knowledge in the *Histoire naturelle* and more generally on the meaning of the notion of “ancient knowledge”.

Catherine Singh, Université Paris Diderot

Along with her teaching activities, she is pursuing a PhD at the Université Paris 3 Sorbonne Nouvelle under the supervision of Nalini Balbir (Paris 3) and Karine Chemla (Paris 7). She is working on Sanskrit and Prakrit texts, dealing with Mathematics and Cosmology from the Jain tradition (~ 9th century). Within the SAW project, her research is mainly related to the computational and algorithmic aspects of the fundamental operations, their illustration in manuscripts and commentaries, and, jointly with Agathe Keller, the exploration of similarities/differences between different indian texts belonging to the same time period.

Ivahn Smadja, Université Paris Diderot

His research interests within the SAW project relate to the historiography of mathematical proof in ancient traditions. He investigates the ways nineteenth-century European mathematicians and historians of mathematics took into account the Sanskrit mathematical sources previously made available by Henry Thomas Colebrooke. He studies, in particular, how a contrast between Sanskrit and Greek ‘proofs’ came to be shaped and meant in different ways by different actors, in different contexts. He focuses on the various interpretations of Brahmagupta’s rules on cyclic quadrilaterals produced by Michel Chasles, Ernst Kummer and Hermann Hankel. More broadly, part of his work aims at contributing to a *histoire croisée* of philology and mathematics in nineteenth-century Europe.

**Post-docs**

CHEN Zhihui, SPHERE

He is a historian of the astronomy and relevant academics in ancient China, in he is particularly interested in the astral-mathematical speciality under the contexts of Han School’s prosperity in the late 18th and early 19th century. He obtained his PhD in 2013 from Shanghai Jiao Tong Université, with a dissertation entitled “Combining Western Learning for Inheriting the Lost Confucian Knowledge: The Astral-mathematical Speciality in Qianlong and Jiaqing Reign Periods in the Horizon of Transformation of Knowledge in Modern China”. Within the SAW project, Chen Zhihui is working with Karine Chemla on the historiography of mathematical sciences in China in the 18th and 19th century, and the further comparison of historiography between China and the West.

Daniel Morgan, SPHERE

Historian of the astral sciences in China, particularly the 3rd century BCE to the 8th century CE. He obtained his PhD in East Asian languages and civilizations in 2013, from the University of Chicago. Research interests include plurality in astral and mathematical traditions, manuscript culture and textual transmission, the historiography of technical knowledge in antiquity, and discrepancies between normative/prescriptive accounts and the products of practice. Within the SAW project, Daniel is working with Karine Chemla on questions concerning the transmission of mathematical texts in a manuscript culture and the relationship between developments in mathematics and mathematical astronomy in the first millennium CE.

Martina Schneider, SPHERE

Historian of mathematics concerning the 19th and 20th centuries. Martina, who studied mathematics, did her PhD, supervised by Erhard Scholz (Wuppertal universität), focusing on the use and acceptance of group-theoretical methods in early quantum mechanics. Her research interests include the mathematization of science (in particular the interrelationship between mathematics and physics), of nature and of society, as well as the study of interdisciplinary configurations (involving mathematics), historical epistemology, and the historiography of mathematics in particular. In the SAW project she will work with Karine Chemla, Agathe Keller and Ivahn Smadja on historiography. She will compare the German contributions to history of mathematics by mathematicians during the second half of 19^{th} century. The focus will be on ways to construct “national” styles and the co-creation of “Western” and “non-Western” mathematics. Special attention will be given to the rising nationalism throughout Europe, and to on-going processes of professionalization (of both mathematics and the history of mathematics) as well as the emergence of “modern” mathematics.

ZHU Yiwen, SPHERE

Historian of mathematics and sinologist, he gained his PhD in 2011 from the Institute of the History of Natural Science in Beijing, with a thesis on counting rods and transition from rods to paper in the 13th century China. His research interests are history of ancient Chinese mathematics, uses of counting rods and transition from rods to paper in the Song period, treatises on harmonics and calendars, relations between the study of Confucianism and mathematics in the Tang period. Within the SAW project, he is working with Karine Chemla on history of mathematics in the 7th century China.

**PhD students**

Pierre Chaigneau, SPHERE

He studied mathematics at the Université de Tours before completing the Master LoPHiSS-SC2 in history and philosophy of mathematics at the Université Paris Diderot. His master’s dissertation was on “control and structure in complex systems”, a quite contemporary subject, but also related to ancient sciences. He had joined the SAW project as a PhD student and is currently working under the supervision of Christine Proust, on the historiography of cuneiform mathematics seen through the monumental editions of cuneiform texts by Thureau-Dangin and Neugebauer in the 1930-1940’s.

Magali Dessagnes, SPHERE

She studied history and archaeology at the Université Paris Panthéon-Sorbonne and École du Louvre, and completed a Master’s degree in the history of science, with a thesis on creation and development of the Louvre Museum in 1847-1880. Her PhD research, under the joint supervision of Christine Proust and Bruno Belhoste, is on the collections of cuneiform tablets assembled at the end of the 19th – beginning of the 20th century

HIROSE Sho, SPHERE

He is a historian of astral sciences in Sanskrit texts. After studying astrophysics at Tokyo University, he worked for a while as an editor and writer in a company aimed at popularizing astronomy. He discovered there his interest in the history of astronomy and subsequently went to study under Michio Yano’s supervision at Kyoto Sangyo University. He wrote his master thesis on a 7th century astronomical commentary. Within the SAW project, he will work under the supervision of Agathe Keller to examine how observations and mathematics were linked in Sanskrit texts. His dissertation will include a revised critical edition of the “Goladipika”, a 15th century text, using Sanskrit manuscripts written in Malayalam script. HIROSE Sho has succefully defend his PhD dissertation “*Critical edition of the Goladīpikā (Illumination of the Sphere) by Parameśvara, with translation and commentaries” *last March 17th at Université Paris Diderot. From April 1st 2017, he will hold a post-doctorate position at ETH Zürich in the History and Philosophy of Mathematical Sciences Laboratory (Department of Humanities, Social and Political Sciences).

Robert Middeke-Conlin, SPHERE

He is an Assyriologist currently pursuing his PhD at the Université Paris Diderot. His dissertation, supervised by Christine Proust and Cécile Michel, explores the use of approximations in the Old Babylonian period southern Mesopotamia (Babylonia). His prior education include a BA in Ancient Mediterranean studies at the University of Minnesota, Twin Cities campus with an emphasis on the Eastern Mediterranean, and a MA in Assyriology at Yale University. His main research interests concern the society and economy of Old Babylonian southern Mesopotamia, cuneiform mathematics, calculation practices, the technical language used in administrative and economic texts, as well as craft industries and archives. Within the SAW project, his research concerns the writing of numbers and quantities as well as computational techniques and mathematical practices exhibited by the administrative/economic texts and corpuses of the Old Babylonian period.

Charlotte de Varent, SPHERE

She is a PHD student in History of Ancient Mathematics and Didactics at the Université Paris Diderot. Her dissertation, supervised by Christine Proust and Nicolas Decamp, is entitled: “Ancient Mathematics in secondary schools: issues, current practices and perspectives”. Her prior education includes a Master in History of Sciences and Techniques from the Université de Nantes and a Master in Mathematics from the Université de Rennes-Nantes. Her research interests are related to the integration of mathematical practices from Ancient History of Mathematics and the issues at stake for mathematical education, society’s understanding of educational practices as well as the use of the Didactic of Mathematics and Physics. Within the SAW project, her research concerns mainly the integration of ancient practices in schools: the introduction of different number practices for multiplications and measuring units, the issues at stake for students, the study of current practices as well as the perspectives. She also focuses on the issues linked to the diffusion of History and Epistemology of non occidental Ancient Mathematics in their complexity and plurality to students.

ZHOU Xiaohan, SPHERE

After studying theoretical physics at the undergraduate level, his interests shifted to the history of science. He studied history of Chinese mathematics at Shanghai Jiaotong University, China, and completed his Master’s degree with a thesis on comparative study of two Bamboo strips, Shu (Mathematics）, Suanshushu (Writing on Mathematical Procedures), and The Nine Chapters in Han Dynasty (202B.C.-220). He is currently working under the supervision of Karine Chemla, on the continuity of Chinese mathematics to examine how the questions and procedures are maintained, changed and developed in the long history of Chinese mathematics. Ming Dynasty’s(1568-1644) mathematics will be his entry point to this rich topic.

**Associated members**

**CRCAO – UMR 8155, CNRS & Université Paris Diderot**

Jean-Pierre Drège -EPHE

Dimitri Drettas – Post-doc

Matthias Hayek – Université Paris Diderot

Marc Kalinowski – EPHE

François Martin – EPHE

Emmanuel Poisson – Université Paris Diderot & SPHERE

**Universities and research centres in France**

Philippe Clancier – HAROC – UMR 7041, CNRS & Université Paris 1

Nalini Balbir – Université Paris 3

Pierre-Sylvain Filliozat – EPHE

François Patte – Université Paris 5

Grégory Chambon – Université de Bretagne Occidentale

**International**

Antoine Cavigneaux – University of Geneva

Laurent Colonna d’Istria

Grégoire Nicolet

Irfan Habib – National University of Educational Planning and Administration, New Delhi

Han Qi – Institute for the History of Natural Sciences, China

Hayashi Takao – Doshisha University, Kyoto

Christoph Harbsmeier – University of Oslo

Jens Høyrup – Roskilde University, Denmark

Ikeyama Setsuro – Kyoto

Alexander Jones – ISAW, NYU

Geoffrey Lloyd – University of Cambridge & NRI

Michael Loewe – University of Cambridge

Ma Biao – Yamaguchi University, Japan

Christopher Minkowski – University of Oxford

Reviel Netz – Stanford University

Ouyang Xiaoli – USA

Mathieu Ossendrijver – Topoi, Berlin

Peng Hao – Jingzhou Museum & Wuhan University, China

Qu Anjing – Northwest University, China

Dhruv Raina – Jawaharlal Nehru University, New Delhi

Ken Saito – Osaka Prefecture University

Sreeramula Raja Sarma – Duesseldorf

Martina Schneider – Mainz Universität

Nathan Sidoli – Waseda University, Japan

John Steele – Brown University

Donald B. Wagner – Nordic Institute of Asian Studies, Denmark

Yano Michio – Kyoto Sangyo University