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Home > Archives > Previous years: Seminars > Seminars 2020-2021: archives > Reading Mathematical Texts 2020–2021

Axis History and philosophy of mathematics

Reading Mathematical Texts 2020–2021

This seminar is organized around a presentation of a primary source and the issues it raises, followed by a reading of this edited and translated source. A session can last up to 3 hours, and is conducted by experienced researchers, doctoral students, or even Master’s students. The working language is French or English depending on the case.

This seminar has a variation in the form of a cuneiform text reading seminar for those interested in cuneiform writing (in this case contact C. Proust christine.proust ( (at) )

The assessment for students of the Lophiis Master may consist of a written analysis of one of the texts presented at the seminar.

Organisers : Agathe Keller, Karine Chemla, (CNRS, CHSA, SPHere), and the associated group: H. Amini, F. Cornu, Christine Proust (CNRS, CHSA, SPHere), C. Singh, G. Toucas, A. Trouillot, A. Reynaud

SCHEDULE 2020-2021

On Mondays, 2pm – 5pm, Room Gris, 734A,
University of Paris, ampus Diderot, Building Condorcet, 4, rue Elsa Morante, 75013 Paris *

Dates 2020/10/19/ 11/23 12/14 2021/1/25 02/15 postponed! 03/1 03/29 05/03 06/14
Monday October 19 !! 2pm–3:30pm !!
  • Hasan Amini (University of Teheran) [online]
    A delicate method for the calculation of π in an anonymous 15th century text in Arabic
    In the history of mathematics, π as a special number and an important ratio has been calculated by various mathematical methods, invented to produce a better approximation. Al-Kāshī, a Persian astronomer and mathematician of the 14-15th century, is mostly known for his calculation of π correctly to 9 sexagesimal digits. In this reading/seminar,, we will decipher and study an abridged Arabic mathematical text, which is devoted to a different method to compute π. This anonymous text from the 15th century, referring to al-Kāshī, evidently is supplementary to his work, presenting a method with two different approximations for the computation of π.

Monday November 23 !! 2pm–3:30pm !!

  • Alexei Volkov (National Tsing-Hua University, Hsinchu, Taiwan)
    Analogical reasoning in traditional Chinese mathematics: Calculation of areas and volumes in the ’Mathematical procedures of Nine Categories’ (Jiu zhang suan shu 九章算術)
    The analogical argument in pre-modern (and, especially, pre-Buddhist) Chinese thought has been discussed by a number of authors; their discussions provided a variety of interpretations of the phenomenon of analogical reasoning in China. While the authors almost unanimously stressed the importance of analogy and analogical argument in traditional China, they made – in formal or informal way – no attempts to provide a unified interpretation of Chinese analogical reasoning. Instead, they offered a number of case studies, most often dealing with excerpts from philosophical texts, while numerous cases of analogical reasoning found in scientific (or “proto-scientific”, or “pseudo-scientific”) texts have remained untreated, if not unnoticed. This lack of interest to the use of analogy in scientific texts is regrettable, especially because the logic of their authors can be, at least in some cases, reconstructed with some degree of certainty on the basis of understanding of the subject matter these texts contain in terms of respective modern disciplines, while the original meaning of the authors of philosophical texts still remains a matter of debate.
    My presentation will focus on the cases of “analogical reasoning” found in ancient Chinese mathematical treatises, in particular, in the Jiu zhang suan shu 九章算術 (Computational Procedures of Nine Categories, known in French translation as Les Neuf Chapitres sur les Procédures Mathématiques). In earlier publications I argued that some methods of calculation of volumes of solid figures featured in the treatise were three-dimensional analogs of two-dimensional cases. In the present talk I will especially focus on the process of “generation” of solid objects and on the relationships between them. In the last section of my presentation I will discuss one particular case that illustrates how a family of “similar” solid objects may have been obtained via the variation of parameters of their prototype.

Monday December 14 !! 2pm–3:30pm !! webconference

  • Jean-Claude Penin (Dishas)
    Un artisan, astronome et mathématicien du 15e siècle : Jean Fusoris
    Pour construire ses instruments d’astronomie et calculer des tables planétaires, Jean Fusoris avait besoin de tables trigonométriques précises donnant les valeurs des cordes sur des fractions de degré. N’ayant pas accès aux tables qu’ils désiraient, il construisit une table des cordes sur des intervalles de 15 min à une précision supérieure à celles qui existaient. Après avoir donné une courte biographie de Fusoris et un bref inventaire de ses travaux, j’examinerai sa méthode, assez originale semble-t-il, pour construire ses tables et situerai ce travail dans le contexte de l’époque.

Monday February 15 !! session postponed to March 1st !!

Monday March 1st, 2pm–5pm

  • Catherine Morice-Singh (SPHere)
    Quelques considérations autour du kuṭṭīkāra de Mahāvīra
  • Alexis Trouillot (University of Paris–ED 623, SPHere)
    Nuzhat al-ʿalbāb, a treatise on calculations by ʾUmar al-Walātī (d. 1836-7)

Monday March 29, 2pm–3:30pm

  • Guillaume Loizelet (University of Paris–ED 623, SPHere, & University of Toulouse)
    Treatise on the magnitudes of distances and volumes according to Ptolemy’s measures and on the method to obtain them by Kūshyār ibn Labbān

Monday May 3, 2pm–5pm

  • Adeline Reynaud (University of Paris–ED 623, SPHere)
    Variations entre les procédures, variations entre les formulations, variations entre les diagrammes dans la collection de problèmes paléo-babylonienne MS 3052
  • C. Yifu (Institute of Modern History, Academic Sinica, Taiwan)
    Paroles et Actes - accord inexact entre des comptines et les mouvements des boules dans le boulier chinois

June 14, 2pm–5pm, face-to-face and/or webconference

IMPORTANT: Due to the current health situation, the sessions will take place by webconference only. To participate via Zoom_University of Paris, please contact Agathe Keller
kellera ( (at) ) for a virtual connection
  • AJ Misra (University of Copenhangen)
    On the first two proofs of Euclid’s Proposition I.47 in Jagannātha’s Rekhāgaṇita
    and Nasīr al-dīn al-Ṭūsī’s
    Taḥrīr-i Uqlīdis: a comparative examination
  • X. Wang (Institute for the History of Natural Sciences, Chinese Academy of Sciences, Beijing)
    The texts resulting from teaching analysis at the end of the 18th century

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Map of campus with metro and buses stops.
Access: Metro line 14 / RER C / Station: Bibliothèque François Mitterrand
Metro line 6 / Station: Quai de la Gare
Bus 64 / stop: Tolbiac-Bibliothèque François Mitterrand
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Bus 325 / stop: Watt