The mathematical cultures of Medieval Europe

International audienceWhen one thinks of medieval mathematics in Europe, the first ideas that come to mind are the introduction of the Hindu-Arabic number system with its algorithms as well as the first beginnings of algebra based on Latin translations from the Arabic. But there was far more mathematics developed and discussed in the European Middle Ages, not only in Latin but also in Arabic and Hebrew. In particular, there were three different mathematical cultures in medieval Europe, the dominant Latin Catholic culture, the Hebrew culture found mostly in Spain, southern France, and parts of Italy, and the Islamic culture that was dominant in Spain through the thirteenth century. We will compare and contrast these three mathematical cultures and consider how they interacted with each other in the pre-modern period, laying the groundwork for the explosion of mathematical knowledge in Europe beginning in the Renaissance..