ABSTRACT
The relations between theoretical philosophy and mathematics are established in four types of works, whose authors are: philosophers; philosopher-mathematicians such as al-Kindi, Muhammad ibn al-Haytham; mathematician-philosophers such as Nasir al-Din al-Tusi and mathematicians such as Thabit ibn Qurra, his grandson Ibrahim ibn Sinan, al-Quhi, Ibn al-Haytham. The links between philosophy and mathematics are essential to the reconstitution of al-Kindi's system. Finally, al-Kindi proceeds by reductio ad absurdum, by adopting a hypothesis: the part of an infinite magnitude is necessarily finite. The general approach of Maimonides consists in borrowing concepts from the Aristotelian philosophy of his predecessors, and proof and exposition techniques from mathematics. Just like his predecessors since al-Kind, Maimonides has found in mathematics both a model for architectonics, demonstration procedures, and means of argumentation. A genuine philosophy of mathematics is developed. Indeed one witnesses in succession is the elaboration of a philosophical logic of mathematics, then a project of ars inveniendi and finally of an ars analytica.
