We report on the Equational Theories Project (ETP), an online collaborative pilot project to explore new ways to collaborate in mathematics with machine assistance. The project successfully determined all 22 028 942 edges of the implication graph between the 4694 simplest equational laws on magmas, by a combination of human-generated and automated proofs, all validated by the formal proof assistant language Lean. As a result of this project, several new constructions of magmas satisfying specific laws were discovered, and several auxiliary questions were also addressed, such as the effect of restricting attention to finite magmas.

Every major technical invention resurfaces the dual-use dilemma—the new technology has the potential to be used for good as well as for harm. Generative AI (GenAI) techniques, such as large language models (LLMs) and diffusion models, have shown remarkable capabilities (e.g., in-context learning, code-completion, and text-to-image generation and editing). However, GenAI can be used just as well by attackers to generate new attacks and increase the velocity and efficacy of existing attacks. This monograph reports the findings of a workshop held at Google (co-organized by Stanford University and the University of Wisconsin-Madison) on the dual-use dilemma posed by GenAI. This work is not meant to be comprehensive, but is rather an attempt to synthesize some of the interesting findings from the workshop. We discuss short-term and long-term goals for the community on this topic. We hope this work provides both a launching point for a discussion on this important topic as well as interesting problems that the research community can work to address.