**textual sources**. Speakers are encouraged to make their sources available to the participants.

Coordination: Simon Decaens (Univ. Paris Diderot & SPHERE), Emmylou Haffner (Centre A. Koyré, Univ. de Lorraine, & SPHERE), Eleonora Sammarchi (Univ. Paris Diderot & SPHERE)

Archives:

2016-2017, 2015-2016,

2014-2015, 2013-2014,

2012-2013, 2011-2012,

2010-2011, 2009-2010

**SCHEDULE 2017-2018** : Details and abstracts soon online

Sessions as usual on Mondays, 9:30–17:00, in Room Klimt (366A), 3rd floor,

Building Condorcet, Paris Diderot University, 4 rue Elsa Morante, 75013 Paris. Campus map with access.

Date | Thema | Organisation |

9/10/2017 | Trigonometry and maths related to astronomy | K. Chemla & A. Keller |

13/11 | Algebra and geometry. Guests: J. Gray, P. Nabonnand, A. Brigaglia | E. Haffner & N. Michel |

4 to 7/12 | Practices of Mathematical Reasoning | C. Proust & al. |

15/01/2018 | Teaching Contexts and Mathematical Demonstration | C. Proust |

12/02/2018 | Duality | S.Decaens |

19/03 | On the works of Legendre | K. Chemla |

9/04 | Algebra and arithmetics | M. Houg |

14/05 | Proportions and Reports | S. Rommevaux-Tani, A. Malet |

4/06 | Geometry and computation | N. Michel |

October 9
**Mathematical Practices in Astronomy**

9:30-10:45,

- A. J. Misra (Tamas, Observatoire de Paris)
*The computational procedures in reconstructing the Sine tables of Amṛtalaharī of Nityānanda*.

The Amṛtalaharī (or perhaps, the Kheṭakṛti) of Nityānanda is an undated Sanskrit manuscript found in the collection of the University of Tokyo discovered by Prof. Pingree. This manuscript contains astronomical tables for computing calendrical elements (like tithis, nakṣatras, yogas), right and oblique ascensions tables of the zodiacal signs, the planetary equation tables and mean motion tables. In addition to this, it also includes a Sine table (sinus totus of 60), solar declination table (maximum obliquity of 24;0,0), lunar latitude table, and three shadow-length tables for gnomons of height 7, 12, and 60 digits. This last set of tables are collectively presented for arguments one to ninety degrees or arc over three folia. In this talk, I discuss the mathematical techniques and generative algorithms in recomputing the Sine table within the context of its relation with the other tables in this collection. .

10:45-11:00 Break

11:00-12:15

- Jiang-Ping “Jeff” Chen (StCloud State University)
*The “First” Chinese Treatise in Trigonometry, Its Latin Sources, and the Algebraic Techniques*.

The calendar reform at the end of Ming China (1368-1644) produced many “firsts” in the efforts. The Jesuits involved and their Chinese collaborators faced many challenges to adapt/collate/translate certain existing European treatises into Chinese: coining new terms, introducing foreign concepts, and working with extreme time constraints, to name a few. Included among the products is the “first” trigonometric treatise in China, 大測 Dace (Grand Measure), which was presented to the court in 1631. This work establishes the paradigm of the principles for constructing trigonometric tables in China and inspires many Chinese trigonometric treatises in the centuries that followed.

12:15-13:30 Lunch Break

13:30-14:45

- Yiwen Zhu (Zongshan Univ.)
*Writing Mathematics in Thirteenth Century China——The Case Study of Qin Jiushao’s Writing on*the Procedure for great inference.

By contrast with early mathematical documents, a conspicuous feature of writing mathematics in thirteenth century China was the use of diagrams, in which mathematical procedures carried out with counting rods were written down. However, the reasons behind this historical phenomenon are still not clear. This talk aims at shedding light on this issue based on the case study of Qin Jiushao’s秦九韶(1208-1261) writing on the*Procedure for great inference with all numbers*大衍總數術, i.e. the so-called Chinese Remainder Theorem.

In Qin Jiushao’s famous monograph,*Mathematical Book in Nine Chapters (Shushu jiuzhang*, 數書九章, completed in 1247), the*Procedure for great inference with all numbers*was used in the first nine problems. But among them only the first problem about*Book of Changes*contained the graphic explanation of the*Procedure for great inference looking for one*大衍求一術, i.e a method for solving linear congruences, that is the core of*Procedure for great inference with all numbers*. On the other hand, in the twelfth problem about calendric calculations there was no*Procedure for great inference with all numbers*, but the*Procedure for great inference looking for one*was written down with diagrams. Hence, I will focus on the first and the twelfth problems. By analyzing these two problems, I find that their modes of using diagrams to write the procedure*Procedure for great inference looking for one*are different: in the first problem, diagrams are written being intertwined with texts, and in the twelfth problem diagrams are written with lines. Relying on the study of modern historian of mathematics Li Jimin李繼閔(1938-1993), we know the twelfth problem could be real, and the first problem was artificial. Therefore, the writing mode in the twelfth problem could imply Qin Jiushao borrowed the procedure from others, and the writing mode in the first problem implies it was Qin’s own procedure.

In Qin Jiushao’s preface and the twelfth problem, he stated the*Procedure for great inference looking for one*came from calendric calculations, but astronomers used it as Fangcheng procedure, i.e. a method for solving liner equations. We know that a*Fangcheng*procedure was recorded in mathematical books as early as in the*Nine Chapters on Mathematical Procedures*(Jiuzhang suanshu九章筭術). In order to reveal how*Procedure for great inference looking for one*and*Fangcheng*procedure are connected, I make an assumption about the astronomical*Fangcheng*procedure. From this point of view, we will see how Qin Jiushao improved this old*Fangcheng*and made it into*Procedure for great inference looking for one*.

The necessity of using diagrams could be understood in Qin Jiushao’s classification of mathematical knowledge. According to this classification, mathematics was divided into two parts: inner procedures and outer procedures. Outer procedures, like in the*Nine Chapters on Mathematical Procedures*, were written down in Chinese characters, and carried out with counting rods. Inner procedures were not recorded. Therefore, when an inner procedure was written, the best way was to use counting diagrams and present the whole process using counting rods. This was exactly what happened in*Procedure for great inference*as presented in the second problem.

13 novembre 2017
**Algèbre et Géométrie**

- Jeremy Gray (Open University & Warwick University)
*Brill and Noether: Cayley—Bacharach, Riemann—Roch*.

In the second half of the 19th century mathematicians began to look for theorems about algebraic curves with complicated singularities. Part of this activity was intended to extend the work of Plücker, part of it was meant to rederive Riemann’s ideas in the setting of plane algebraic curves. As this talk will explain: what is geometry, what is algebra, what is assumed, and what is proved was never fully agreed.

- Philippe Nabonnand (LHSP - AHP, Univ. de Lorraine)

Titre et abstract à venir

- Aldo Brigaglia
*The young Segre and the introduction of hyperspatial geometry in Italian algebraic geometry*.

Thanks to Klein and Lie, the concept of abstract (i. e. multidimensional) geometry made great progress, and (after Segre) it became an ordinary tool for the contemporary Italian geometers. Indeed nothing is more fertile than the multiplication of our intuitive powers operated by this principle: it is as if besides the mortal eyes with which we examine a figure, we have thousands of spiritual eyes to observe its manifold transfigurations; all this while the unity of the object shines in our enriched reason, and it enables us to easily go from one form to another. These words of Federigo Enriques (written in 1922, only two years before Segre’s death) are important to understand the role played by Segre in introducing a more abstract (but not less intuitive) point of view in algebraic geometry. In my talk I will try to give an overview of Segre’s first papers and how, starting with his dissertation, he faced the problem of developing a complete theory of the projective geometry of hyperspaces by using some of the most important algebraic results that Weierstrass, Kronecker and Frobenius had obtained and applying them to the purely geometric interests favoured by the Italian school.

December 4 -> 7 2017
**Practices of Mathematical Reasoning**

January 15, 2018 – 9:30–15:00
**Teaching Contexts and Mathematical Demonstration**

- Sabine Rommevaux-Tani (CNRS, SPHERE)
*Quelques exemples de l’influence du mode d’enseignement dans les universités médiévales sur le style des démonstrations mathématiques.*

- Jeff Chen (Saint-Cloud State University, SPHERE)
*Mathematical Rigor in certain English textbooks in trigonometry in the 19th century, its Chinese translations, and model examination answers by Chinese students.*

- Marion Cousin (Institut d’Asie Orientale de Lyon) - tbc
*Le rôle des manuels de l’ère Meiji dans la formalisation des démonstrations géométriques au Japon.*

Guests: Ralf Krömer (Bergische Universität Wuppertal), Emmylou Haffner (Bergische Universität Wuppertal & SPHERE) - tbc

March 19 2018
**Autour des travaux de Legendre**

April 9 2018
**Algèbre et arithmétique**

Invités : Kenneth Manders (University of Pittsburgh), Sébastien Maronne (IMT, Toulouse), Erwan Penchèvre (SPHERE)

May 14 2018
**Proportions et rapports**

June 4 2018
**Géométrie et calcul**

Building Condorcet, University Paris Diderot, 4 rue Elsa Morante, 75013 - Paris*.Map

Calculate your itinerary with the public transport website RATP

Metro: lines 14 and RER C, stop: Bibliothèque François Mitterrand or line 6, stop: Quai de la gare. Bus: 62 and 89 (stop: Bibliothèque rue Mann), 325 (stop: Watt), 64 (stop: Tolbiac-Bibliothèque François Mitterrand)

In the same section :

- Science and Philosophy from Ancient to Modern Age
- Powers of Imagination. Historical Approach.
- History Review of the technical modernity in France (the twentieth century to the present)
- Meetings HPS of Paris Diderot
- AXIS HISTORY AND PHILOSOPHY OF MATHEMATICS
- Mathematics from Ancient to Modern Age
- "Arabic" Mathematics
- Seminar Riemann
- Seminar PhilMath Intersem 8. 2017
- AXIS HISTORY AND PHILOSOPHY OF SCIENCE OF NATURE
- History and Philosophy of Physics
- Averroes’s Cosmology: The
*Middle Commentary*on the*De Caelo*of Aristotle - History and Philosophy of Chemistry
- Psychophysical entanglement
- AXIS HISTORY AND PHILOSOPHY OF MEDECINE
- Medical humanities
- Global Health: Knowledge, devices, policies
- AXIS HISTORY OF PHILOSOPHY FROM ANCIENT TO MODERN AGE
- The Aristotle Metaphysics of Alexander of Aphrodisias
- Ethics in Aristotle (text and contexts)