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Home page > Archives > Previous years: Seminars > Seminars 2013–2014: archives > Reading Mathematical Texts 2013–2014

Axis History and philosophy of mathematics

Reading Mathematical Texts 2013–2014


Organiser : Agathe Keller - CNRS, REHSEIS–SPHERE



We read original sources and their translations, presented by their translator.
Texts this year will deal on the one hand on cultures of computations and on the other on the relations between mathematical texts and «texts of the practice» in commercial and administrative contexts.


Archives :
2015-2016, 2014-2015, 2012-2013, 2011-2012, 2008-2009




PROGRAM 2013-2014
: on Wednesdays, 10:00–13:00, Building Condorcet, University Paris Diderot, 75013.
Interactive campus map showing metro and RER station and buses stops.




3 December, !! 13:00 – 17:00 !!, Room Gris, 734 A

  • Krishnamurthi Ramasubramanian (IIT Mumbai)
    Extracts of the Karaṇapaddhati.

11 December, 10:00 – 13:00, Room Malevitch, 483A

  • Pascal Crozet (SPHERE)
    Les opérations arithmétiques chez Abū Kāmil.

18 December, 10:00 – 13:00, Room Rothko, 412B

  • Matthieu Husson (SPHERE)
    Division of algebraic expressions in the Quadripartitum numerorum of John of Murs (14th c. France).
    In his Quadripartitum numerorum John of Murs progressively shaped mathematical procedures for the division of algebraic expressions using a specific division table as well as a “denominatio” for algebraic expressions with quotients. During the seminar we will examine the portions of texts where this procedure is described and look at the impact of this procedure on the solving of equations.

15 January, 10:00 – 13:00, Room Malevitch, 483A

  • Agathe Keller (SPHERE, CNRS & SAW)
    Bhāskara I (629) ’s table of solutions of linear indeterminate equations with astral parameters.

29 January, 10:00 – 13:00, Room Mondrian, 646A

  • Daniel P. Morgan (SAW)
    Introduction to the Procedures of Early Chinese Mathematical Astronomy: The Luminous Inception system of 237 CE.
    In this text-reading, we will attempt to make our way through the first half (or so) of the Luminous Inception system (Jingchu li 景初曆), a manual of li mathematical astronomy from 237 CE. The Luminous Inception system saw use from the third to fifth centuries CE; the concepts and mathematics involved are very simple; and, in as much as the Chinese li manual genre changed very little from the first to sixteenth centuries CE, this manual serves as an excellent entrée into the greater genre. This session is intended as an introduction to reading key materials in the Chinese astral sciences through which we may begin to discuss how and what mathematics were deployed for astronomical purposes.

5 February, 10:00 – 13:00, Room Klein, 612 B

  • Charles Burnett (Warburg Institute)
    Computing with the Gerbertian Abacus.

12 February, 10:00 – 13:00/17:00, Room Mondrian, 646A

  • Matthieu Ossendrijver (Humboldt University)
    Two challenging Late Babylonian procedure texts for constructing a gnomon.

19 February, 10:00 – 13:00, Room Mondrian, 646A

  • Hermann Hunger (Univ. of Vienna)
    Mesopotamian astronomical diary.

12 March, 10:00 – 13:00, Room Rothko, 412B

  • QU Anjing (Northwest University, Xi’an)
    The shape of earth and algorithm of lunar eclipse.
    Several pieces of original texts related to the lunar eclipse in calendar-making systems in dynasties of Tang, Song and Yuan will be read. We will come to the conclusion that those Chinese mathematicians would have to make use of the assumption that the earth is round to construction their algorithm although they never mentioned such a fact.
  • Lis Brack-Bernsen (Univ. Regensburg)
    Texts testifying of numerical functions describing periodic astronomical phenomena in Mesopotamia.

19 March , 10:00 – 17:00, Room Mondrian, 646A

  • Steve Schnider (Bar Ilan Univ., Israel)
    The Saros Text and the secret of Column Φ.
    The astronomical cuneiform tablet BM 36705 was published by Neugebauer in 1957. An additional corner fragment was found and published by Aaboe in 1968. The tablet revealed the special meaning of the sexagesimal number 17,46,40, familiar from other texts, and provided the first big step in the understanding Column Φ developed by Aaboe and Britton. We will read and discuss some of the text with the help of commentary by Neugebauer, Aaboe and Ossendrijver.
  • Clemence Montelle (Univ. of Canterbury)
    Āmarāja’s commentary on the Khaṇḍakhākdyaka of Brahmagupta.

2 avril, 10:00 – 13:00, Room 612B

  • Marc Kalinowski (EPHE)
    The preface to the Yisizhan.

9 April, 10:00 – 17:00, Room Mondrian, 646 A

  • Zhu Yiwen (SAW)
    Qin Jiushao on the Chinese remainder theorem.
  • Krishnamurthi Ramasubramanian (IIT Mumbai)
    Extracts of the Karaṇapaddhati.

30 April, 10:00 – 13:00, Room Mondrian, 646 A

  • Sho Hirose (SAW)
    Extracts from Parameśvara’s Goladīpika.

21 May, 10:00 – 17:00, Room Mondrian, 646 A

  • Michio Yano (Kyoto Sangyo University)
    Extracts of the Siddhāntaśiromaṇi of Bhāskara II.
  • Li Liang (IHNS, Chinese Academy of Science, Beijing and ex-HTN)
    Huihui lifa (Muslim cadendrical astronomy in China).

4 June, 10:00 – 13:00, salle Mondrian, 646 A

  • S. R. Sarma
    Magic Squares in Sanskrit texts.
    Magic squares have long been used in diverse contexts and cultures and are interesting combinatorial objects. We shall discuss some methods of their construction as found in Chapter XIV of Nārāyaṇa Paṇḍita’s Gaṇitakaumudi (1356).

18 June, 10:00 – 17:00, Room Mondrian, 646 A

  • Kim Plofker (Union College)
    The Sūryagrahana of Muhammad Shah.


Glen van Brummelen (Quest Univ., Canada)
Precision and Approximation in Trigonometric Tables: Ancient Greece and Medieval Islam
Ptolemy’s chord table, the earliest trigonometric table and the ancestor of all that followed, nevertheless contained a flaw inherent in its structure: with the circle divided into 360 parts, only 1/3 of the entries can be computed relying on geometric methods. Ptolemy was therefore forced into approximation. Discomfort with Ptolemy on this point (among others) spread to medieval Islam, with Ibn al-Haytham expounding a criticism, and al-Samaw’al offering an unusual solution. We shall read texts from all three authors.

25 June, 10:00 – 13:00, Room Klein, 612B

  • Willis Monroe (Brown University)
    Micro-Zodiac Schemes in Late-Babylonian Astrology and Astronomy.





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
Bus 62 & 89 / stop: Avenue de France or Bibliothèque François Mitterrand (terminus)
Bus 325 / stop: Watt