In this workshop we proposed an exchange of ideas about the role of history and epistemology of mathematics in perspective teachers training. We have made reference to some historical references, in order to celebrate the third centenary of Leonhard Euler’s birth (1707). Both the authors have been in the situation of giving a 20 hours teachers training course for the « Scuola di Specializzazione per l’Insegnamento Secondario » at the University of Udine (Italy), so they have moved from their own experience. They considered some pages from Euler’s treatise entitled Vollstandige Anleitung zur Algebra (proposed both in the English 1828 edition, and in the French 1807 edition) about Diophantine equations as starting material to plan a lesson for perspective teachers. Then, another issue has been submitted to participants: the discussion about the opportunity to provide a socio-cultural analysis of different proofs of a « same theorem » produced in different times and situations.

The case analysed concerned the infinity of prime numbers, namely Euclid’s, Kummer’s, Euler’s classical proofs, and the recent Seidak’s proof.