We'll present some examples of new traditions in Arabic mathematics, as they were thought by their founders, according to their metamathematical writings, specially in the prefaces of their books. We'll compare these new traditions with the Greek and the classical ones opening the door to an alternative periodization of the mathematical thoughts.

We'll study some of the texts of al-Khawarizmi and Thabit ibn Qurra concerning the algebra as a Theory of the equations and its foundations; of al-Mahani, al-Khazin and al-Ahwazi concerning the algebraic theory of irrationality; of al-Karaji and al-Samaw'al concerning polynomial algebra and its foundations; of al-Khayyam concerning the geometrical algebra; of al-Quhi and Ibn al-Haytham concerning geometry ...