The goal of the Mathemagix project is to develop a new and free software for computer algebra and computer analysis, based on a strongly typed and compiled language. In this paper, we focus on the underlying type system of this language, which allows for heavy overloading, including parameterized overloading with parameters in so called "categories". The exposition is informal and aims at giving the reader an overview of the main concepts, ideas and differences with existing languages. In a forthcoming paper, we intend to describe the formal semantics of the type system in more details.
