Recent advances in artificial intelligence have shaken the world of mathematics: systems are now announcing solutions to problems that have remained open for a long time. But this acceleration does not make researchers unnecessary. Instead, it raises new questions about the verification of proofs, the organization of research, education and the role of human reasoning in a discipline that cannot be reduced to calculation.
Announcements that are shaking the community
For several months, announcements of mathematical results produced with the help of AI have been arriving at an unusual pace. For specialists, some have the impact of a shock: they concern problems considered particularly difficult, sometimes open for a long time, and seem to call into question research avenues pursued for years.
This unease also reflects a deeper concern about the future of the profession. Mathematician Hugo Duminil-Copin, who was awarded the Fields Medal in 2022, has expressed the feeling that several of his areas of work have suddenly been overtaken by these advances. The recent publication of hundreds of documents claiming solutions to open problems has further reinforced this sense of acceleration.
These announcements must nevertheless be examined with caution. A result presented as a solution is not automatically a correct, complete proof that the community can understand. Mathematicians must be able to check every step, identify any errors and determine whether the result precisely answers the question posed.
A proof alone does not define research
The validity of a proof is essential, but it does not sum up the entire mathematical process. Researchers are also interested in the ideas that lead to a result, the connections it reveals with other fields and the methods it makes possible. Understanding why a proof works can be just as important as knowing its conclusion.
Stéphane Mallat, the 2025 CNRS Gold Medalist, points out that mathematics is much more than an activity involving calculation. It is a way of structuring thought, clarifying a problem and understanding complex phenomena. Even if an AI can produce proofs, the need to interpret, assess and contextualize results therefore remains central.
This distinction helps explain why automating part of the work does not mean the discipline will disappear. A system can suggest an avenue or quickly process a large number of possibilities; it is still necessary to decide which questions are worth asking, assess the significance of a result and explain how it changes existing knowledge.
Verifying results: a new challenge
Assessing proofs produced by systems
As the volume of results generated or assisted by AI grows, one task is becoming increasingly important: establishing reliable methods for examining them. This means distinguishing sound proofs from incomplete results, documenting the tools used and establishing shared rules for presenting a proof obtained with the help of a model.
In the United States, the Simons Foundation has announced a $15 million program, co-funded by OpenAI and Anthropic. It will support workshops devoted to assessing mathematical results produced by AI and developing standards for its use. This initiative illustrates the emergence of new needs: specialists are not only called upon to create knowledge, but also to organize its validation in the age of automated tools.
The question is also linked to the trust placed in these systems. This trust should not be based on how convincing an answer seems or on the number of results announced. The standards of precision in mathematics are high: every step must be verifiable, and the conditions under which a result applies must be explicit.
Mathematical research can also open up new avenues
Moving beyond certain obstacles
Researchers do not all see current advances as a threat to science. François Charles, director of the Department of Mathematics and Applications at the École normale supérieure, distinguishes between the uncertainties surrounding how professions are organized and the scientific possibilities opened up by these tools. Problems that have so far been difficult to tackle could become more accessible, while new questions could emerge from collaboration between humans and machines.
AI can help explore hypotheses, identify structures or speed up certain computational steps. The challenge is to use it to broaden the scope of investigation without confusing speed of output with understanding. If obstacles are overcome, mathematicians may also be led to take on more ambitious problems and explore fields that have so far been neglected.
This shift is part of a broader transformation of professional activities. Debates about AI affect financial markets, as shown by this article on concerns about artificial intelligence on Wall Street, as well as the allocation of public funds, discussed in this analysis of the 2027 budget and its new trade-offs around AI.
Teaching mathematics in the age of AI
Preserving the desire to learn
Education presents a challenge distinct from that of research. If students feel that machines can solve problems for them, they may doubt the value of learning mathematics. This perception would be reductive: the ability to reason, understand a proof and formulate a question correctly are skills that cannot be equated with obtaining an automated answer.
School curricula could therefore place greater emphasis on the role of reasoning, problem formulation and the interpretation of results. AI can become a subject of study and a teaching tool, provided students learn to examine its outputs rather than accept them uncritically. The ability to spot an error or explain an approach remains an essential component of mathematical literacy.
This reflection echoes questions raised by AI in other areas of education and work. The debate over how to redefine skills and the value of human work is notably present in discussions about the added value of legal professionals in the face of artificial intelligence.
Professions in transition, not facing imminent extinction
Mechanization as a point of comparison
To shed light on the current upheaval, Stéphane Mallat compares the arrival of AI in mathematics with the changes brought about by agricultural mechanization. The introduction of new machines profoundly changed professions and ways of life, forcing some people to retrain. This comparison reminds us that innovations can transform employment and the skills required without making all the knowledge in a field obsolete.
Mathematicians also have transferable skills: abstraction, logic, modeling and the analysis of complex problems. These can be applied in many fields, including those where AI systems are developed or assessed. The evolution of tools could therefore change day-to-day tasks, training paths or the early stages of a scientific career without eliminating the need for specialists who can understand the foundations of the methods being used.
However, uncertainties remain about how the community is organized. The way people enter the profession, pursue a doctorate or gain recognition for a contribution may change as automated tools take over certain tasks. Research institutions will in particular have to determine how to distinguish researchers’ own contributions from those of systems and from the collective work needed to validate results.
A transformation that extends beyond laboratories
Economic, political and environmental questions
The role of AI in mathematics cannot be considered in isolation from its broader consequences. Developing and using advanced systems requires infrastructure, budgets and material resources. Questions about their environmental cost are addressed in this article on the potential growth of artificial intelligence’s ecological footprint.
Technological choices also influence collective decisions and the distribution of power. Debates about the governance of these tools echo discussions about how AI is transforming political issues. For mathematical research, these questions lead to further questions about who develops the tools, the conditions for accessing their capabilities and the principles according to which their results will be checked.
As systems become more capable, the challenge is therefore not limited to determining whether they can solve a problem. It is also about deciding which questions to assign to them, how to make their approaches verifiable and what place to give to intuition, explanation and understanding. From this perspective, the final result is only one part of mathematical activity: the path leading to it remains an object of research and instruction in its own right.
