We introduce "virtual duoethnography" as a novel research approach in mathematics education, in which researchers produce a text of a dialogic format in the voices of fictional characters, who present and contrast different perspectives on the nature of a particular mathematical phenomenon. We use fiction as a form of research linked to narrative inquiry and exemplify our approach in a dialogue related to various proofs of infinitude of primes. We view Lakatos' (1976) dialogue in the seminal "Proofs and Refutations" as an example of virtual duoethnography. We discuss the affordances of this approach as an alternative to the formal ways of presenting research in mathematics education.