How do students in the beginning of their undergraduate studies cope with the requirement for rigour? Why do they so often resort to the familiarity of number? Why do they have problems with constructing examples and with identifying and accepting counterexamples? How do they manage to express in symbols their thoughts about the convergence of a sequence? Why is reference to the domain of a function so conspicuously absent in their writing? How do their teachers at university help them acquire the 'genre speech' of university mathematics and the athematician's 'toolbox' of useful images, theorems and techniques? Do these teachers pursue the help of mathematics education researchers in these complex tasks? If at all, how? If not, why not?... Amongst Mathematicians, a 2007/8 Springer monograph which I will use as the basis for this lecture, discusses these and other similar questions through offering a perspective on how mathematicians perceive student learning, teach and reflect on their own teaching practice. Based on interviews with mathematicians from across the UK (in which they discussed thematically-focused samples of students' mathematical writing and episodes from tutorials) it describes mathematicians' perspectives on: students' encounter with formal mathematical reasoning and with concepts such as function and limit; students' attempts to mediate mathematical meaning (through verbalisation, symbolisation and visualisation); undergraduate mathematics pedagogy; and, the relationship between mathematicians and researchers in mathematics education. Through the narrative method of re-storying its analyses are presented in the form of a dialogue between two fictional, yet entirely data-grounded characters, M and RME, mathematician and researcher in mathematics education respectively. The book, and the research on which it draws, are amongst the first contributions to the systematic study of mathematicians' pedagogical perspectives and in this lecture I will introduce recent and crucial theoretical developments in this growing and exciting area of mathematics education research.