Résumé
This chapter collects the contributions discussed during the working sessions by the thirty-one participants from fourteen countries of the WG1 "Argumentation and proof" at CERME7 in Rzeszow (Poland). Eighteen papers from eleven countries have been presented and discussed. Each presentation was followed by a reaction from a participant presenting the key issues and posing questions to the author(s). The papers are presented under five themes: epistemological and cognitive issues, means for analysing proving activities, transparency, educational implication of views on mathematics, on the relevance of proof on teaching mathematics.. We will conclude this introduction by some challenging perspectives emerging from our discussion.