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Accueil > Axes de recherche > Histoire et philosophie des mathématiques 2018-2022 > Workshop Mathesis

History and Philosophy of Mathematics, sous-axe Mathématiques et Philosophie de l’Antiquité à l’Age Classique

Workshop Mathesis

Since September 2017, the workshop "Mathesis" is developing in the form of an ANR project of the same name.

- Argument
- Members
- Activities


The aim of the Mathesis project is to promote the study of the unpublished mathematical manuscripts of the philosopher and mathematician Gottfried Wilhelm Leibniz (1646-1716), by means of a work of editing and commentary. We plan to publish nearly 800 pages of printed texts, as well as two volumes of translations and comments.

The idea of a European collaboration in this field is already old since it was proposed since 1901, when the launch of the edition of the complete works of Leibniz. The First World War unfortunately prevented this collaboration from succeeding, with regrettable effects on the one hand a considerable delay in the work of Leibniz-Archiv, and on the other hand an obvious obstacle to research.

To date, more than a century after the launch of the idea, nearly three quarters of Leibniz’s mathematical work during the period of interest in this project (1677-1716) remains unpublished. It is not necessary to insist on the obstacle this situation imposes on the research of one of the greatest mathematicians and philosophers of Europe of his time. According to the projections of the Leibniz Archives (based in Hanover as regards the edition of the mathematical texts), it will be necessary to wait until 2022 at the earliest so that this corpus can be simply approached, and 2053 at the earliest for the company can hope to succeed.

Our ambition is to initiate a dynamic remedying this very unsatisfactory situation for researchers, but also, more generally, for all those who are interested in the work of Leibniz.

Our work revolves around six major themes :

  • Perspective geometry (V. Debuiche, V. De Risi, M. Brancato)
  • Curve Geometry and Traction Movement (S. Bella, D. Crippa, A. Michel-Pajus, D. Rabouin, C. Schwartz)
  • Ars combinatoria (A. Costa, A. Remaki, D. Rabouin, Post-doc3)
  • Game theory (V. Leroux, D. Rabouin)
  • Logic and geometric analysis (J-P. Alcantara, V. Debuiche, V. De Risi, D. Rabouin)
  • Epistemology of algebra, foundation of calculation (J.-P. Alcantara, M. Houg, A. Michel-Pajus, D. Rabouin)


Researchers Jean-Pascal Alcantara (ESPE/Université de Bourgogne), Andrea Costa (Centre Jean Pépin-UMR 8230), Valérie Debuiche (AMU, Centre Granger-UMR 7304, investigator for Aix-Marseille), Vincenzo De Risi (CNRS, SPHERE-UMR 7219), Baptiste Mélès (Archives Poincaré-UMR 7117), Anne Michel-Pajus (IREM, Paris Diderot), David Rabouin (CNRS, SPHERE-UMR 7219, principal investigator) & Claire Schwartz (University Paris Ouest, Nanterre).
Post-docs ANR Mattia Brancato, Davide Crippa
Associate PhDs Students Sandra Bella, Morgan Houg, Vincent Leroux, Arilès Remaki.
Foreign partners M. Kempe et S. Probst (Leibniz-Archiv Hanovre), R. Arthur (Mc Master, Canada), E. Grosholz (Penn State, USA), A. Pelletier (ULB, Belgique), J. Echeverria (Universidad del País Vasco, Consejo Superior de Investigaciones Científicas).

ACTIVITIES 2011 2012 2013–2014 2014–2015 2015–2016 2016–2017 2017–2018


Wednesday September 25, 13:30–16:30, Room tba

  • 10:00–12:30 meeting of beginning of semester
    Richard Arthur & David Rabouin
    Le statut des infinitésimaux chez Leibniz
    Presentation of texts on which Sandra Bella will work
  • 14:00–17:30 session together woth Colleagues in Liège, Brussells and the ENS
    On the recent publication of Richard Arthur : Monads, Composition, and Force : Ariadnean Threads through Leibniz’s Labyrinth, Oxford University Press, 2018. One chapter, one talk , then general discussion

Wed. October 16 & 31st, !! Institut Henri Poincaré !!
Tribute to Michel Serfati

co-organisation with IREM & SELLF

October 16 :

  • Claire Schwartz & Davide Crippa on Leibniz
  • Siegmund Probst on copies of Descartes’ youth work done by Leibniz

October 31st :
Precisions tba

Wed. November 20

  • Discussion on translation of texts

Wed. December 18, and later 2020

Precisions tba


Wednesday May 16, 13:30–16:30, Room 888C, Grands Moulins

  • Mattia Brancato (post-doc MATHESIS)
    Présentation du programme de recherche sur l’édition des textes concernant l’arithmétique binaire

Wed. & Th. April 10–11 avril, !!! University of Aix-Marseille (AMU) !!!

: : Workshop : The manuscripts on perspective of Leibniz

Wed. March 6, 13:30–16:30, Room 888C, Grands Moulins

  • Emily Grosholz (Penn State Univ)
    Leibnizian Analysis in Metaphysics, Mathematics, Physics, Geology : From Leibniz to Darwin

Wednesday February13, 13:30–16:30, Room 888C, Grands Moulins

  • Discussion on translating manuscripts on perspective

Wednesday January 9, 2019, 13:30–16:30, Room 888C, Grands Moulins

  • Vincent Leroux (University Paris Diderot, SPHERE)
    La classification des jeux selon Leibniz)
  • Miguel Palomo (University of Sevilla)
    Huygens and Leibniz : The Thin Line Between the Master and the Student

Wednesday December 12, 13:30–16:30, Room 888C, Grands Moulins

  • Julio Vasconcelos (UEFS, Brasil)
    Aspects structurels de la science galiléenne du mouvement (abstract in English, slides in French)
  • Adwait A. Parker (Stanford University)
    Newton’s Mathematical Concept of Force : composition of active quantity of matter

Wednesday November 7, 10:30, Room 888C, Grands Moulins

  • Ric Arthur (McMaster University)
    Monadic states : Leibniz’s Law of continuity and the discreteness of change

Monday October 22,
14:30–17:00, session together with the seminar "Mathematics from Ancient to Modern Age"

  • Arilès Remaki (Univ. Paris Diderot, SPHERE)
    La place de l’Algèbre et le rôle des fonctions symétriques dans la pensée combinatoire de Leibniz à la fin du séjour parisien.
  • Eberhard Knobloch (Technische Universität Berlin)
    Le concept leibnizien d’un art caractéristique général ou d’un art combinatoire : quelques exemples.

Friday September 21, 14:30,
Room Dali, 240A, Building Condorcet, University Paris Diderot

  • Marko Malink (Pr, New York University) and Anubav Vasudevan –videoconf.– (Pr, University of Chicago)
    The Peripatetic Program in Categorical Logic : Leibniz on Propositional Terms


Wednesday June 18, 09:30–17:00, Grands Moulins, Room 888C

Study day "Invention of transcendence and reception of differential calculus" ANR "Mathesis" - Edition of Leibniz Mathematical Manuscripts

  • 9:30 : Davide Crippa (SPHERE, project Mathesis)
    The impossibility of squaring the circle : James Gregory and the idea of transcendence
  • 11:00 : Sandra Bella (Laboratoire Jean Leray, Nantes/SPHERE)
    Définir différentielle, le récit de Varignon
  • 12:30 : Lunch Break
  • 14h : Viktor Blåsjö (Utrecht University)
    The goal of doing calculus : a taxonomy of motivations among early practitioners
  • 15:30 : Claire Schwartz (University Paris Ouest)
    Malebranche & la réception du calcul infinitésimal

Wednesday May 18, 09:30–17:00, Grands Moulins, Room 888C

  • Massimo Mugnai (Scuola Normale superiore, Pisa)
    Leibniz begins : the dissertation on combinatorial art
  • Arilès Remaki (Mathesis, post-doc)
    Le rôle des tables et de leurs structures dans l’évolution de la pensée combinatoire de Leibniz au cours de son séjour parisien

lMonday April 16, 10:00–17:30, Room Mondrian, 646A, Building Condorcet

Study day in the framework of the ANR project "Mathesis. Edition and commentary of unpublished manuscripts of Leibniz » (ANR-17-CE27-0018-01) Autour de la Dynamica de Leibniz

Organization : David Rabouin & Vincenzo de Risi, (CNRS, SPHERE)

  • 10:00 : Dan Garber (Princeton University/IEA Paris)
    Is Leibniz’s dynamics consistent with his monadology ?
  • 11:30 : Mathieu Gibier (CPGE, Amiens)
    Dynamique & Pneumatique chez Leibniz, de la période parisienne au traité florentin.
  • 14:30 : Andrea Costa (Centre Jean Pépin)/Enrico Pasini (Università di Studi di Torino)
    Le travail d’édition sur la Dynamica de potentia de Leibniz.
  • 16:00 : François Duchesneau (University of Montréal)
    Le recours aux principes architectoniques dans la Dynamica.

March 21, 10:00–17:30,Room 888C, Building

  • V. Debuiche et M. Brancato (Mathesis)
    Présentation des manuscrits leibniziens sur la perspective
  • Javier Echeverria (Université du Pays basque)
    Sur la perspective chez Leibniz

February 22 , 14:00-17:00, Room 888C, Building Grands Moulins

  • D. Rabouin (Mathesis, CNRS, SPHERE)
    Sur les axiomatisations leibniziennes de l’algèbre

January 24 , 14:00-17:00, Room 888C, Building C Grands Moulins

  • D. Crippa (Mathesis, post-doc)
    Exactitude dans la géométrie de Leibniz : instruments pour construire des courbes transcendantes

December 19–21, 2017, Leibniz Archiv, Hanovre

Launch of the project in the presence of German colleagues. Initiation to the techniques of publishing the complete works of Leibniz


Room 888C, Building C, Grands Moulins

Tuesday 14 March, 14:00-17:00

  • Finalization of the project ANR
  • Final reviewing text [5]

Thursday 5 January 2016 (joint session with the seminar « âge classique »), 14:00-17:00

  • D. Rabouin & M. Gibier : Autour de la Dynamica de Leibniz

Wednesday 14 December, 10:00-13:00, !! Room 512A-Kupka, Condorcet !!

  • Annexe 2 & texte [4]

Tuesday 22 November, 14:00-17:00

  • Fin de [2] & début du [3].

Tuesday 25 octobre 2016, 10:30-13 :30

  • Overview on project ANR
  • Relecture texte [1]


Room 888C, Building Grands Moulins

Friday 20 April (tbc), 10:30-17 :30
Study Day with Richard Arthur (Mc Master University), invited Professor at University Paris Diderot.

  • Morning : presentation of the edition on Mathématique universelle
  • Afternoon : Richard Arthur : Espace physique & analysis situs chez Leibniz

Friday 20 April (tbc), 10:30-13:30

  • Relecture de LH XXXV I, 9, fol. 8 & 9-14.

Friday 11 March, 10:30-13:30

  • Relecture de la « Praefatio ».

Friday 12 February, 10:30-13:30

  • Finalization on LH XXXV I, 9 fol. 1-4. Reviewing from folio 2 verso.

Friday 15 January 2016, 10:30-13:30

  • Presentation of all texts in pre-final version. Work on Annex 3.

Friday 18 December, 10:30-13:30

  • Finalization on Elementa nova. If time permits, correction on De Ortu

Friday 13 November, 14-17, !! Room Rothko 412B, Condorcet !!

  • Relecture LH XXXV I, 9, fol. 1-4. Suite & fin.

Friday 16 octobre, 10:30-13:30

  • Proofreading of the translation of LH XXXV I, 9 1-4
  • Afternoon : meeting of Centre d’Etudes Leibniziennes

Friday 18 September 2015, 10:30-13:30

  • Organization of the year’s work
  • Revision of the translation of LH XXXV, I, 9 fol. 1-4


Room 888C, Building C Grands Moulins

Friday 29 mai, 10:30–13:30,

  • Session n°16 : Reading & discussion of the translation De Ortu, progressu & natura algebrae (GM VII, 203 sq)

Friday 10 April
  • 10:30–13:30, presentation by Siegmund Probst of the diagrams editing software used by the Akademie Edition, as well as the digital catalog of the Hannover Library.
  • 14:00–17:00, reading with S. Probst on Historia & Origo

Friday 20 March, 10:30-13:30

  • Session n°15
    – Overview of ANR/editorial projects
    – Discussion translation Praefatio (GM VII, 49-53)

Friday 20 February, 10:30-13:30

  • Synthesis of results (D. Rabouin) & study of manuscripts

Thursday 15 January 2015, 10:30-13:30

  • Presentation LH XXXV 1, 9, fol. 7-14 (transcription & translation) by Anne Michel-Pajus

Friday 19 December, 10h-13h, !! Room Rothko, 412B, Building Condorcet !!

  • Session n°14 : Discussion of the translation of Elementa Nova

28-29 November

Annual Congress of SELLF (Société d’Etudes Leibniziennes de Langue Française)

  • Intervention of the group (D. Rabouin & V. Debuiche) : Unité & pluralité de l’espace chez Leibniz

Friday 17 octobre, 10:00–13:00, !! Room 437A-Alechinsky, Building Condorcet !!

  • Session n°13 :
    – overview on ANR (the procedures have changed for this year)
    – review of our exchanges for publication at Vrin
    – resumption of our translation of Elementa Nova

Friday 11 September, 10:30-13:30, Room 888C, Building C des Grands Moulins

  • Session n°12 : Discussion of the translation of the Elementa Nova Matheseos Universalis.


Room 888C, Building C Grands Moulins

Wednesday 18 juin, 10:30-13:30

  • Session n°11
    10:30-13:30, Discussion of the translation of the Elementa Nova Matheseos Universalis.
    Afternoon, annual meeting of CEL (Centre d’Etudes Leibniziennes) at Sorbonne

Friday 23 mai 2014, 10:30-13:30

  • Siegmund Probst (Leibniz Archiv, Hanovre)
    Leibniz as reader and second inventor

Thursday 22 mai, 10:30-13:30
joint session with Seminar « Mathematics at Modern Age »

  • Work Session with Siegmund Probst (Leibniz Archiv, Hanovre).
    Autour de la méthode des coefficients indéterminés.

Friday 18 April , 10:30-13:30

  • Session n°10 : Proofreading of the translation of Elementa Nova Matheseos Universalis.

Friday 21 March, 10:30-13:30,
  • Session n°9 : Final proofreading of the translation of Mathesis Universalis & début de traduction des Elementa Nova Matheseos Universalis

mardi 25 February, 14:00–17:00, ! Room Alechinsky, 437A, Building Condorcet !

  • Session n°8 : End of text translation Mathesis Universalis (GM VII, 53-76)

Friday 10 January 2014, 14:30–17:30, ! Room Alechinsky, 437A, Building Condorcet !
  • Session n°7 : text translation Mathesis Universalis (GM VII, 53-76)

Monday 9 December, 14:00–17:00, ! Room Alechinsky, 437A, Building Condorcet !
  • Session n°6 : text translation Mathesis Universalis (GM VII, 53-76).

Monday 4 November, 14:00–17:00, ! Room Alechinsky, 437A, Building Condorcet !
  • Session n° 5 : text translation Mathesis Universalis (GM VII, 53-76).


Room Rothko, 412B, Building Condorcet

Wednesday 26 juin, 10:00–13:00

  • Session n° 4 : text translation Mathesis Universalis (GM VII, 53-76).

Friday 19 April , 10:00–13:00
  • Session n° 3 : text translation Mathesis Universalis (GM VII, 53-76).

Friday 22 February, 10:00–13:00
  • Session n° 2 : text translation Mathesis Universalis (GM VII, 53-76).

Friday 21 December 2012, 15:00–17:00
  • Session n°1 : animated by David Rabouin, around Leibniz’s project of transcription, translation & editing devoted to Mathesis Universalis.


Room Rothko, 412B, Building Condorcet

Monday 4 juin 2012, 10:00–13:00

  • Tzuchien Tho
    What is expressed in motion

Wednesday 23 mai, 14:30–17:30, Room Klimt, 366A
Joint Session with seminar Mathematics at Modern Age (Laboratoire SPHERE, UMR 7219) & du Centre d’Études Leibniziennes.
  • David Rabouin (Laboratoire SPHERE, UMR 7219)
    Imagination & mathématiques chez Leibniz.

Friday 13 April , 15:30–17:30
  • Davide Crippa (Doctorant, Laboratoire SPHERE, UMR 7219)
    La notion de tractus chez Leibniz.


Tuesday 18 juin, 10:00–13:00, Room Rothko, 412B, Building Condorcet
Joint Session with seminar Mathematics at Modern Age (Laboratoire SPHERE, UMR 7219) & du Centre d’Études Leibniziennes.

  • Valérie Debuiche
    Lecture des travaux géométriques de Desargues & de Pascal pour une compréhension de leur influence sur l’invention par Leibniz de son calcul des situations.

Monday 30 mai, 14:30–18:30, Room Mondrian, 646A
Joint Session with seminar Mathematics at Modern Age (Laboratoire SPHERE, UMR 7219) & du Centre d’Études Leibniziennes.
  • Presentation of the book by Vincenzo De Risi, Geometry and Monadology (Birkhauser, 2007), with the author.
  • Jean-Pascal Alcantara (IUFM, Mâcon), Valérie Debuiche (Amiens) & Jean-Pascal Anfray (ENS, Paris) respectively on chapters 2 (« Geometry »), 3 (« Phenomenology ») & 4 (« Metaphysics »).
    Discussant : Sébastien Maronne (University Toulouse, IMT, SPHERE).

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