The summer school was the second edition of a series of summer schools that we planned to organize in the following years. The aim of the summer school in the history of ancient mathematics remained to give post-graduate students and early-career scholars in the domain an overview of a global history of ancient mathematics (that was, in our definition, a history ranging from the third millennium BCE till the fourteenth century).
Our intention was to enable scholars involved in teaching the history of mathematics or likely to be involved in the future to include a world-wide perspective in how they teach the history of ancient mathematical sciences. The novelty of our summer school further lied in the fact that we also aimed to train the participants with new methods that were developed specifically to read ancient sources, and more widely to present perspectives and questions that had deeply revitalized this field, opening fresh venues for research in general. This summer school took a global perspective and involved researchers working on cuneiform, Greek, Sanskrit, Chinese, Arabic and Latin sources. It presented case studies that illustrated how new questions and methods could reopen what may have seemed finalised in standard historiographies of ancient mathematics. For this, we adopted a perspective that examines in a critical way the kinds of sources with which standard historiographies have been written, and we suggested considering new sets of sources, or using sources that were long used in different ways. We also examined the kinds of questions standard historiographies pursued, and how new questions opened new perspectives for research. In particular, we discussed in which respects historians should take into account the contexts in which mathematical texts were composed, used and stored.
The coherence of the classes about Arabic, Chinese, cuneiform, Greek, Latin and Sanskrit documents derived from the fact that they would all deal with the following issues:
– The history of number systems and arithmetical operations;
– The basic types of sentences and texts with which practitioners of mathematics worked, and how they worked with them. In particular, we payed special attention to how algorithms were worked with;
– Reasonings, proofs and theories;
– The different forms of algebraic knowledge and practices that could be perceived in ancient texts;
– The different types of work with geometric figures and diagrams;
– Definitions and organisations of mathematics.
