Marouane Ben Miled

Research project

Mathematical traditions in the Mediterranean region.

Project summary

My research project has four complementary aspects:

1/ Editing, translating and commenting mathematically and historically on al-Ahwazi’s Commentary on Book X of Euclid’s Elements;

2/ To finish writing a general course on the history of mathematics (collective work);

3/ Draw up a detailed plan for an exhibition on the history of mathematics, organized by conceptual tradition;

4/ Organize a working group (seminar) on the question of mathematicians’ own justifications for mathematical proofs.

To be more precise:

1/ Book X is the chapter of Euclid’s Elements in which the theory of irrationals is presented as an answer to the problem posed by the discovery of incommensurability. The advent of al-Khawarizmi’s algebra made it possible to give an algebraic translation of this work (part of a body of work on the algebraization of geometry). There are numerous commentaries on Book X of the Elements, which I described and analyzed in Opérer sur le Continu, (Carthage, 2005); I also edited al-Mahani’s commentary. Here, I propose to edit al-Ahwazi’s 10th-century commentary, based on the fifteen or so manuscript copies that have come down to us. This is a scientific edition with critical apparatus, accompanied by historical and mathematical commentaries.

2/ In 2004, we organized an international course on the history of mathematics in Tunis. The writing and publication of this course has begun, and I intend to complete this work.

3/ Knowledge of the history of mathematics has advanced considerably in recent decades. This progress has made it possible to give a new reading of this history, organized by conceptual and universal traditions, which combines history and epistemology, as proposed by Roshdi Rashed. This knowledge, in its new organization, can now be passed on to the general public, and is made necessary by current events and identity references. I propose to popularize them in an exhibition that would materialize the path of thought along axes, crossroads and arteries of various importance, forming a city that could be explored both chronologically and logically.

4/ Having been asked by Robert Ilbert to organize a project around “the proof of proof”, I initiated contacts with logicians and epistemologists-historians. The first step was to organize a seminar on a text by al-Karaji (10th-11th c.), to be translated and edited, on the justification of algebraic proofs, independent of geometry, in a context where the only axiomatic references are geometrical. A doctoral student, Foued Nafti (Ecole nationale d’Ingénieurs de Tunis) is working on the project.