Recent advances in the application of artificial intelligence to mathematical research have made the rapid pace of change clear: systems that until recently played mainly a supporting role can now contribute to solving mathematical problems of considerable difficulty. Regardless of how individual results are assessed, this evolution raises important questions for research, education and, more generally, for the relationship between human knowledge and artificial intelligence. From this perspective, mathematics offers a particularly interesting vantage point. Today’s artificial intelligence rests on decades of advances in mathematics, computer science and technology; at the same time, mathematics makes a fundamental distinction particularly clear: obtaining an answer does not necessarily mean understanding it; verifying the correctness of a line of reasoning is not the same as grasping the ideas behind it; having a very powerful tool at one’s disposal does not mean knowing how to use it judiciously.
These distinctions extend far beyond mathematics. In public debate, artificial intelligence is still often viewed as an undifferentiated whole. For example, people speak of the “algorithm” almost as though it were an entity with a will of its own, and attitudes easily swing between excessive distrust and excessive confidence. As increasingly capable systems become more widespread, however, it will be necessary to gain a better understanding of their potential and limitations and, above all, to learn to distinguish between what can be entrusted to these tools and what requires human judgement, responsibility and autonomy.
Education is, in our view, one of the crucial areas. Students will have access to tools capable of solving problems, writing texts, programming and contributing, in different ways, to the production of knowledge. The task of schools and universities will be to integrate these tools into the educational process without sacrificing what education must above all foster: understanding, intellectual autonomy, critical thinking and personal responsibility. It will therefore be necessary to rethink both how we teach and how we assess the knowledge and abilities students have actually acquired.
The same is true of research and its evaluation: if a growing share of scientific activity is carried out with the assistance of artificial intelligence, it will become even more important to distinguish between the result produced and the researcher’s understanding of it; between the volume of research output and its quality and originality; and between the effective use of a tool and the scientific autonomy of the person using it. The criteria we use to train, select and evaluate researchers will also need to take this transformation into account.
More generally, the development of artificial intelligence also calls for reflection from a humanistic perspective. This is not a matter of setting scientific culture against humanistic culture, but of recognising that the availability of increasingly powerful tools makes the ability to interpret, choose, form judgements and take responsibility for one’s decisions even more important.