Preliminary issues are to understand how the social and political context is a determinant of the development of knowledge and scientific ideas; and to explain why and how different individuals reveal different interests and preferences, talents, abilities and specificities in generating, organizing and sharing knowledge.

What does it mean, in different cultural settings, mathematics or philosophy or natural philosophy or religion? Disciplines are the result of the dynamic of a complex of strategies generated in response to the pulsions of survival and transcendence, both by individuals and by groups.

Although we recognize societies that were absolutely isolated – such as, for example, the Amazonian Pirahãs – we may say that, since prehistoric times, cultural encounters have always played a major role in the evolution of strategies to survive and to transcend. In every cultural encounter, we note either total acceptance or total rejection or, what is more common, syncretism. But, in any case, extant strategies to survive and to transcend play a conscious and unconsciousness role in further generation of knowledge.

With respect to Mathematics, the aim is to identify conceptualizations of space and time, spirituality, number, dimension, shape, symmetry and the like in many aspects of ancient and modern life, not restricted to an elite, particularly academics. A major research area is to recognize the contributions, in generating and organizing knowledge, of what is generally called invisible society. Many of these contributions are appropriated by the elite and shaped as disciplines.

A major theme in History is to understand how elites were formed in different cultural settings. A focus of this Symposium is how small elites of scholars organized themselves as National Societies, which are intellectual circles and associations, aiming at the enhancement of their common intellectual interests as individuals. This occurred all over the World and the Symposium shall address specificities of the process in different cultural environments.

The institutionalization of an informal group as a National Society helped to overcome the geographical, linguistic and cultural barriers, thus paving the way for identifying mathematics as a discipline, that is a corpus of knowledge with international agreement on beliefs, values and behaviors.