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Arithmetic, the common denominator of the Alpine countries

Italian, Swiss and Austrian mathematicians gathered at the UniDistance Suisse campus in Brig to present their research in number theory. Arithmetica Transalpina is the name given to this meeting, which was held on 17 October 2025 and organised by Professor David Loeffler. He revealed the benefits of this conference and its everyday applications.

Arithmetica Transalpina: a name with southern accents for a conference on number theory. Indeed, the Italian, Swiss and Austrian scientific communities are demonstrating unrivalled dynamism in the field of mathematics. And the city of Brig, in the heart of the Alps, was particularly well suited to such a conference. This was highlighted by David Loeffler, Professor of mathematics at UniDistance Suisse: ‘Switzerland, like its neighbouring countries, has particularly flourishing research groups in this field. The choice of Brig as a venue for exchanges was therefore made quickly and naturally.’

The participation of Wieslawa Niziol and Pierre Colmez from the French National Centre for Scientific Research (CNRS), Andrew Graham from the University of Oxford and Andreas Langer from the University of Exeter gave the meeting significant visibility. This was a great opportunity for the brand new Faculty of Mathematics at UniDistance Suisse, which collaborated on this occasion with ETH Zurich and the Universities of Milan, Padua, Genoa and Vienna. ‘Thanks to Arithmetica Transalpina, we hope to have found ways for our new research group to make itself known and showcase its work,’ explains David Loeffler. 

At the heart of the discussions in Brig: p-adic number theory, a branch of mathematics that focuses on the properties of prime numbers. In short, it is an unfamiliar numbering system in which the concept of ‘size’ is defined differently, so that some numbers that were previously “large” become “small’. According to mathematician David Loeffler, this mirrored arithmetic world has consistent rules and can provide us with new insights into familiar arithmetic problems that are difficult to solve in other ways. 

"While these abstract theories may seem incredibly deep and sophisticated at first glance, number theory is used in many everyday applications, such as cryptography, the science of sending messages securely. Cryptocurrencies, such as Bitcoin, are perhaps the most famous example, but every time you make a credit card payment or check your email on a public wireless network, you are using number theory," concludes the professor at UniDistance Suisse. 

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