About:

This summer school will be the second edition of a series of summer schools that we plan to organize in the following years. The aim of this summer school in the history of ancient mathematics remains to give post-graduate students and early-career scholars in the domain an overview of a global history of ancient mathematics (that is, in our definition, a history ranging from the third millennium BCE till the fourteenth century). Our intention is 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 lies in the fact that we also aim to train the participants with new methods that were developed specifically to read ancient sources, and more widely to present perspectives and questions that have deeply revitalized this field, opening fresh venues for research in general. This summer school will take a global perspective and involve researchers working on cuneiform, Greek, Sanskrit, Chinese, Arabic and Latin sources. It will present case studies that illustrate how new questions and methods can reopen what may have seemed finalised in standard historiographies of ancient mathematics. For this, we will adopt a perspective that examines in a critical way the kinds of sources with which standard historiographies have been written, and we will suggest considering new sets of sources, or using sources that were long used in different ways. We will also examine the kinds of questions standard historiographies pursued, and how new questions can open new perspectives for research. In particular, we will discuss 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 will derive from the fact that they will 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 will pay special attention to how algorithms were worked with;
- Reasonings, proofs and theories;
- The different forms of algebraic knowledge and practices that can be perceived in ancient texts;
- The different types of work with geometric figures and diagrams;
- Definitions and organisations of mathematics.