The Second Machine Turn: From Checking Proofs to Creating Concepts
This addresses the challenge of advancing mathematical discovery through AI, potentially reshaping the field, but it appears incremental as it builds on existing automation of proof-checking.
The paper tackles the problem of automating the creation of mathematical concepts, identifying a shift from proof-checking to concept generation, and discusses current progress, obstacles, and potential impacts on mathematics and human-machine collaboration.
We identify a second machine turn in the process of mathematical discovery: after automating proof-checking, AI is now poised to automate the *creation* of mathematical concepts themselves. We discuss the current state of the art, obstacles and potential solutions as well as a preliminary attempt at mathematizing the creation of concepts itself. The paper ends with an assessment of how these capabilities could reshape mathematics and human-machine collaboration, and a few different futures we might find ourselves in.