Leibniz's Unpublished Geometrical Manuscripts. Edition and Commentary – MATHESIS

The aim of the MATHESIS project is to promote, through an edition and a commentary, the study of Gottfried Wilhelm Leibniz’s (1646-1716) unpublished mathematical manuscripts and to launch a dynamic of research on a European level. We plan to edit more than 800 printed pages of texts and two volume of translations with commentary.
To develop a European collaboration in this respect is not a new idea since it was proposed in 1901, when an edition of Leibniz’s complete works was first planned. First World War unfortunately put a dramatic end to this collaboration. The negative effects of this interruption are now clear: a considerable delay in the work of the Leibniz Archiv and an obvious obstacle to the research. To these days, more than one century after the launching of the enterprise, almost 75 % of Leibniz’s mathematical texts in the period 1677-1716, which will interest us in this project, is still unpublished. It won’t be necessary to insist on the barrier that this situation imposes on the study of one of the most prominent mathematicians and philosophers of his time. According to the prospective drawn by the Leibniz Archiv (located in Hanover as regards the editing of the mathematical texts), one will have to wait, in the best case scenario, until 2022 for this corpus to be reached by the editors and 2053 for the whole enterprise to be achieved. Our main ambition is to initiate a dynamic which would remediate this unfortunate situation. With the help of young researchers recruited in the project and thanks to new research dynamics, we propose to work on an edition and a commentary of Leibniz’s work in geometry – here understood in its various Leibnizian forms: analysis situs, work on perspective and projections, geometry of curves, “universal mathematics”, axiomatization and conceptualization of the continuum. But we also conceive this project as a first step toward the launching of larger-scale projects, in particular at the European level.
The project can benefit of a particularly favorable situation due to the development in recent years of the research in the history and philosophy of Leibnizian mathematics. In 2010, two important programs were started: on the one hand, the launching of a research group (head : D. Rabouin and V. Debuiche) gathering the French researchers working on Leibniz mathematics, in the newly created framework of the Centre d’Etudes Leibniziennes ; on the other hand, the launching under the supervision of V. De Risi of the program “Modern Geometry and the concept of Space” program at the Max-Planck-Institut für Wissenschaftsgeschichte. Not long before, an international conference organized in Nancy by Ralf Krömer on Leibniz’s scientific reception in the XXth Century had already testified for the renewal of the studies on Leibniz’s mathematics and for the fecundity of a French-German collaboration on these issues. It is naturally toward these various partners that the Leibniz Archiv turned when it was envisaged to attack a corpus for which a scientific expertise was a necessary condition for the advancement of the editorial work. The present project details the modalities of this collaboration, already initiated through many punctual collaborations, and also describes its possible impacts on a larger audience through the creation of a website dedicated to a public presentation of Leibniz’s mathematical manuscripts.