Again, a week full of developments around AI and math. More than 700 papers have been published on more than 300 open math problems. The good news first: AI seems to make sign mistakes as well, resulting in a withdrawal of three papers . Nevertheless, the problems that have been ‘resolved’ have stirred mathematics in each corner, some people quickly checking the outcomes in relation to their (sometimes lifetime) work.. Now, I may be witnessing this from a relatively comfortable position, but this may not be the case for younger researchers, our PhD students and postdocs, who find it hard to see how the mathematical landscape is evolving, even where this is going in a few months, or even weeks from now. So here are some thoughts, in an attempt to shed some light on this.

First of all, my own experience with the students that I encounter in my department and around. They actually seem very hesitant to use genAI, for several reasons: ethical, environmental, but also because they don’t want to deprive themselves of the pleasure of discovery. On the other hand, they are also aware of the necessity to use it, driven by the competition they are in. Clearly, for the careers and promotion of our young researchers, in the past decade the focus was put heavily on brilliance and excellence, based on number of publications, proposals, etc. Again, and this I am also witnessing myself: many (many!) more publications are submitted to journals, which are generated by AI, and also research proposals overload the funding system, as it is very easy to write these with AI-assistance.

My glimpse into the future is that we, mathematicians, should adopt a different style of working. Concerning publishing papers: maybe similar to our colleagues in physics, after a quick pen-and-paper creative exploration, we may have to stir ‘the machine’ in the search for the right Lemmas and Theorems. And, in the other direction, we may have to identify the ‘data’ worth further research, among a ‘zoo’ of genAI-generated Lemmas and Theorems.

Our publication practice should then also become more hybrid in nature, where we may strive for a combination of ‘human’-written or -stirred research, showing the skills of the authors, and AI-assisted parts, speeding up the research. This may be realized by a non-linear publication style, where one ideally zooms into different levels of details of the manuscript. This may be realized by the type of publications we see in other fields, such as physics, biology or chemistry: a short letter highlighting the main theorems and conceptual insights, which is then followed by additional material including more details; the latter possibly contains AI-generated material, for which the authors at all times keep their responsibility of course.

For our next generation, the challenge is to explore the balance between their own, and the AI-generated ideas. Excellence will then get a different meaning, precisely in this two-faceted combination. For publishers of mathematics journals, one should facilitate the exposition of these two levels, allowing editors and referees to judge articles based on both of these quality criteria. And, in line with this, for national science foundations the challenge will then be to quantify excellence based on both of these quality criteria, while being extremely careful to distinguish the two facets!

Remains that also I am curious to see where all of this is going, what the landscape will be in a year from now, or even months, or weeks. Most importantly is that we keep discussing this together!