The need for ethical guidelines in mathematical research in the time of generative AI

Generative artificial intelligence (AI) applications based on large language models have not enjoyed much success in symbolic processing and reasoning tasks, thus making them of little use in mathematical research. However, recently DeepMind’s AlphaProof and AlphaGeometry 2 applications have been reported to perform well in mathematical problem solving. These applications are hybrid systems combining large language models with rule-based systems, an approach sometimes called neuro-symbolic AI. In this paper, I present a scenario in which such systems are used in research mathematics, more precisely in theorem proving. In the most extreme case, such a system could be an autonomous automated theorem prover (AATP), with the potential of proving new humanly interesting theorems and even presenting them in research papers. The use of such AI applications would be transformative to mathematical practice and demand clear ethical guidelines. In addition to that scenario, I identify other, less radical, uses of generative AI in mathematical research. I analyse how guidelines set for ethical AI use in scientific research can be applied in the case of mathematics, arguing that while there are many similarities, there is also a need for mathematics-specific guidelines.