Practicing History of Mathematics in Islamicate Societies in 19th-Century Germany and France

This paper discusses methodological and interpretive aspects of practices in the history of the mathematical sciences in Islamicate societies as they emerged in Germany and France during the nineteenth century. It argues that in the nineteenth century, those who practiced history of mathematics in Islamicate societies had a strong methodological commitment. They formulated three main research lines with clear methodological claims. Two of these approaches (a scientific history of mathematics and a serious investigation of primary sources) found general approval in history of mathematics at large. Thus, they continued to be followed in the historiographical and methodical practices during the twentieth century. The third (the integration of progress and source studies into a cultural and biographical narrative) was discarded as a methodological principle. Only under the impact of discussions in history of science and the humanities since the 1980/90s did approaches similar to, and at the same time more sophisticated than, this forgotten third way practiced in the late nineteenth century find new practitioners with a new methodological consciousness.