From June 30 to July 4 2025, the University of Luxembourg welcomed the 33rd edition of Journées Arithmétiques (JA25). For the first time in its history, the world’s largest number theory conference was held in Luxembourg, and it did not disappoint. With record-breaking attendance, JA25 became the largest mathematics conference the country has hosted over the past 20 years. This marks a milestone for both the University of Luxembourg and the global mathematics community.
Bringing together world-class mathematicians
Researchers from around the globe gathered to share breakthroughs and forge new collaborations. At the heart of the programme were ten plenary lectures delivered by some of the most respected figures in number theory. Among them was Fields Medalist Peter Scholze, along with several other laureates of international scientific honors.
Yet JA2025 also celebrated emerging voices in the field. Staying true to its inclusive format, the conference also welcomed researchers at all stages of their careers. This year’s edition featured almost 250 contributed talks, held across ten parallel thematic sessions, showcasing the diversity of current research in number theory.
‟ These Journées Arithmétiques will go down in history as a landmark edition.”
Highlighting emerging talent
This spirit of inclusivity extended to the next generation of mathematicians. Among the youngest contributors was Emma Pěchoučková, a Master’s student at Charles University, who has already coauthored two research papers. Another standout was Bogdan Jones, a high school student, conducting original research with support from mentors at the University of Chicago.
Beyond the formal sessions, it was during informal conversations that ideas truly took shape. These moments sparked fresh questions and often planted the seeds for future research projects, reflecting the collaborative spirit that has long defined Journées Arithmétiques.
With nearly a third of participants being PhD students, the event offered an important platform for the next generation of number theorists to present their work and connect with others in the field.
‟ I felt that the conference was inclusive, and I personally didn’t feel as impacted by the gender imbalance that I often experience at conferences.”
Open lecture: bringing mathematics to the public
A new and exciting feature of this year’s programme was a public lecture aiming to share scientific trends with a broader audience. The guest speaker was Dr. Kristin Lauter, Senior Director at Meta AI Research and Affiliate Professor at the University of Washington. A leading expert in number theory and cryptography, Dr. Lauter discussed in particular the growing impact of AI on cryptographic security.
‟ AI is just mathematics making high probability predictions.”
Senior Director at Meta AI Research and Affiliate Professor at the University of Washington
She highlighted the emerging need for cryptosystems that are robust against AI-driven attacks, even though artificial intelligence still struggles with some fundamentals of modular arithmetic. A central message of her talk was the importance of openness: open models, open data, open code. Drawing on her experience at FAIR, Dr. Lauter emphasised the importance of full transparency in research, stating that true openness involves releasing not just the code, but the trained models and the data as well. This, she argues, is essential to ensuring reproducibility, driving innovation, and democratising access to powerful tools.
With the successful hosting of JA25, the University of Luxembourg firmly places itself on the map of global mathematical excellence. Bringing together some of the world’s leading experts alongside emerging talent, the event highlighted the university’s commitment to strengthening the global number theory community.
Several key sponsors supported the conference, most notably the Luxembourg National Research Fund (FNR). The organisers used most funding to support the stay of young participants and offered lunches to facilitate exchanges among all participants.