Learning Intelligent Theorem Proving from Large Formal Corpora

The talk will discuss several AI methods used to learn proving of conjectures over large formal mathematical corpora. This includes (i) machine-learning methods that learn from previous proofs how to suggest the most relevant lemmas for proving the next conjectures, (ii) methods that guide low-level proof-search algorithms based on previous proof traces, and (iii) methods that automatically invent suitable theorem-proving strategies on classes of problems. We will show examples of AI systems implementing positive feedback loops between induction and deduction, show the performance of the current methods over the Flyspeck, Isabelle, and Mizar libraries, and also mention emerging AI systems that combine statistical parsing of informal mathematics with such strong theorem proving methods.