From Alexandria, through Baghdad: Surveys and studies in the Ancient Greek and medieval Islamic mathematical sciences in honor of J.L. Berggren

The practice of the history of mathematics is in flux. This statement may seem ironic or even paradoxical, for a discipline that relies seemingly on logic and precision. However, trends in the scholarly practice of history are gradually causing substantial changes in the questions raised by practitioners of the discipline, and the methods used to try to arrive at answers. Fifty years ago the discipline was populated mostly by mathematicians, emphasizing logical reconstructions and explanations; today, the concerns of the historian are being heard. Surprisingly, nowhere are these changes more true than in the study of ancient Greek mathematics, which has seen precious little genuinely new source material come to light in the past decades. Debates concerning, for instance, how to consider the Greek notion of geometric algebra led to an increasing realization that even mathematical structures can be shaped by cultural perspective; therefore, modern reconstructions of ancient concepts contain the hidden danger of saying as much about the historian as about the history.