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Research Interests

Broadly speaking, my research concerns logic and automated reasoning. My PhD focuses on inventing and identifying high quality mathematical concepts and conjectures about concepts, and proving those conjectures which are valid. The goal is to build an automated reasoning system to assist a user with the invention process.

This research is part of a dream of automating all mechanizable processes of mathematical theory formation. The tasks involved in these processes include the formation of concepts and definitions, making of conjectures about these concepts, proving theorems, finding examples and counterexamples and inventing algorithms for solving problems.

The main motivation for our project is to explore the capabilities and limitations of the scheme-based approach applied to the problem of theorem discovery and concept invention. Our aim is to investigate the approach across a number of mathematical theories including number theory, set theory and others.