An automatic theorem proving project
This is the opposite direction to what I expected to see for new theorem proving efforts: "Good old fashioned AI" vs leveraging advances of deep learning for natural language.I think the direction that is ripe for advance is a two-part process: (1) translating from human-language mathematics proof to computer-verifiable formal proof language combine with (2) GPT3-style automated generation of plausible next-steps in human language proofs.Gowers emphasizes the success of humans at "pruning" to only consider potentially useful next steps in a proof.  I think GPT3 demonstrates such pruning in generating plausible natural language text continuations.And the success of natural language translation between natural languages suggests natural->formal language translation may also be ripe.Combined with the success of formal language automated theorem provers, it seems plausible to build on current technologies a stack that produces formally verified natural language proofs.