Essays on SIGMA: Simulation and Implementation of General Mathematical Activity

These Essays embody a comprehensive scheme for the development of a database for research in all areas of Mathematics. The underlying mathematical computer processor proposed, called SIGMA, is seen as providing an interactive research environment. The application of arbitrary theorems to well-formed expressions constitutes the basic activity within this environment and the goal is to produce theorems which are formulated in maximally operational and constructive modes. This presents a huge challenge to mathematical ingenuity and technique and it is proposed that it is pursued internationally through a dedicated Institute. The Essays on SIGMA furnish a substantial foundation for this crucially important enterprise.