The article discusses questions as follow: What do mathematicians do?; What way do people understand mathematics?; How can understanding of mathematics be communicated? What is a proof?; What does people motivate to do mathematics? The arguments relate to a text of Jaffé and Quinn in which these authors compare different forms of communication: oral (in a seminar or a colloquium), and written (e.g. in a special journal). Concerning the status of the written text – conjectures, tasks, proofs – they rely implicitly to a philosophy of mathematics which lines up on a single axe speculation – rigour. Thus, in Thurston’s opinion, they leave out essential points he describes in his text, above all the point of understanding proofs, and communicative aspects of mathematics. He exemplifies his position with personal experiences about reception of proofs and theories developed by him within the mathematical community. (ZDM/Mathdi)