Reacción a "OpenAI announces the results of ten mathematical research problems using its Astra artificial intelligence model"

In recent times, we have witnessed a growing presence of artificial intelligence in mathematical research. It has recently been announced that well-known problems in various fields of mathematics have been solved, or substantial progress has been made towards their solution, both by researchers using AI tools and directly by companies in the sector. In many cases, the validity of the proofs is guaranteed by their formalisation in Lean, a proof assistant that enables the automatic verification of arguments.

Combined with formal verification, these tools will enable us to tackle more ambitious problems, explore ideas more quickly and detect structures and patterns that were previously beyond our reach. It is, without doubt, a promising prospect: they have the potential to raise the already excellent standard of current mathematical research even further.

At the same time, these advances raise questions that directly challenge the mathematical community: how to evaluate and attribute results obtained with the aid of AI, how to adapt publication models, or how to train the next generations in this context. Answering these questions will require an active and measured dialogue, which we must undertake with a broad perspective, steering clear of both fatalism and triumphalist proclamations. The community has already begun to organise itself in this regard: the recent Leiden Declaration on Artificial Intelligence and Mathematics, endorsed by the International Mathematical Union, proposes precisely such shared standards for the use of these tools.

It is worth remembering, in any case, that mathematics goes far beyond the solving of specific problems, however interesting and difficult they may be. There is a profound interplay between problem-solving, the development of theories and the formulation of conjectures, which in turn drives — and sometimes creates — entire fields of mathematics. Deciding which questions are worth asking, and understanding what their answers tell us, will remain essentially human tasks.