Two days to examine how artificial intelligence – especially large language models – is already reshaping mathematical work, from proof-oriented reasoning to writing, idea exploration, and bibliographic research. 

This two-day meeting aims to encourage discussion and exchange on the current use of artificial intelligence — in particular large language models (LLMs) — in mathematical practice. It will examine concretely what these tools can already contribute to mathematics: first, within mathematical reasoning itself, especially through the (semi-)automatic construction of proofs; and second, within the working environment of mathematicians, through tools for exploring ideas, sketching arguments, drafting text, and conducting bibliographic research.

The workshop will also analyze the structural limitations of these technologies — errors, fragile chains of reasoning, and the absence of guarantees — together with the conditions for their responsible and informed use. Particular attention will be given to formalization with proof assistants, viewed both as a scientific practice fostering rigor, explicitness, and reproducibility, and as a possible semi-automatic verification layer within AI-assisted proof generation.

More broadly, these two days are intended to open a space for reflection on the evolution of mathematics in the age of generative tools.

Program

16th of June

• Use of LLMs for mathematical reasoning, including the (semi-)automatic construction of proofs.
• Impact on the mathematical working environment: idea exploration, argument sketches, writing support, and bibliographic research.
• Critical assessment of structural limits: hallucinations, fragile reasoning, and lack of formal guarantees.

17th of June

• Formalization with proof assistants and its relation to trustworthy mathematical workflows.

Scientific committee

• Frédéric Déglise (UMPA)
• Stéphane Gaussent (ICJ)
• Philippe Malbos (ICJ)
• Véronique Maume-Deschamps (ICJ)
• Sophie Morel (UMPA)
• Filippo Nuccio (ICJ-LIP)

An event organized in the context of the Lyon Saint-Étienne scientific strategy

The workshop is part of the scientific strategy currently being developed around artificial intelligence on the Lyon Saint-Étienne academic site. Late 2025, a Thematic Institute in Artificial Intelligence: uses, concepts and challenges was launched to bring together research on AI and research about AI across exact sciences, experimental sciences, social sciences, and humanities carried out by all members and associated members of Université de Lyon (ComUE).

It aims to make visible, deepen, and strengthen AI-related activities across Lyon Saint-Étienne, from the foundational core of AI to its many applications, uses, and broader implications. It also promotes collaborative dynamics between academic stakeholders and with the socio-economic world.

This initiative relies in particular on AILyS, a consortium currently bringing together 11 higher education, research, and health institutions in Lyon Saint-Étienne around AI.