Thesis proposal Scheme-based Theorem Discovery and Concept Invention

This thesis proposal outlines an automated reasoning system for helping a user to navigate through a theory and discover theorems that mathematicians generally find to be interesting. The project focuses on the processes of invention of mathematical concepts, and invention (and verification) of conjectures about concepts by using a scheme-based approach. Mathematical theories usually have infinitely many theorems (and concepts), and an Automatic Theorem Discovery (ATM) system is expected to address the generation and identification of the interesting ones. Regarding the generation process, we believe that there exists a small number of schemes that consistently instantiate to a large number of theorems and/or concepts that mathematicians generally find to be interesting, while generating a relatively small quantity of non-interesting theorems/concepts. Concerning the evaluation we think that it is possible to estimate the quality of invented concepts by observing what theorems (if any) can be discovered and proved concerning the concepts.