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In this article, we discuss the centrality of improvisation for teaching, based particularly on readings of Cassin (2014, 2020), Ranciere (1991, 1999, 2020), and Bailey (1992). Our starting point is that there simply can be no teaching without improvisation, i.e., the delicate practice of responding to, situating, and attuning to events within educational encounters that cannot be foreseen, but constantly call for attention and action through the finest virtue of our intellect at play. In the article, we go along with the early Sophists for whom improvisation meant to be able to speak about everything by allowing oneself to be led by opportunity (Cassin, 2014). We will be claiming that improvisation of the Sophist teacher is both an intellectual and bodily virtue, requiring discipline as well as poesis and techne as well as praxis. In short, improvisation as a specific form of educational performativity. Together with Ranciere (1991, 2020), DiPiero (2020), and Bailey (1992) we intend to show how improvisation in teaching speaks to our senses and sets into motion simultaneously the sharing and uniqueness of sensing as such, captured by Ranciere's understand-ing of le partage du sensible. Improvisation, we conclude, can be understood as the product of contingent encounters between subjects, objects, and environments, where it emerges in the rupture between form and content (DiPiero, 2020). As such, it allows for other ways of speaking and being in the world than those desired by the institu-tionalisation of a certain police order (fixing a particular and non-negotiable partage du sensible) and therefore becomes, we suggest, a central element in a democratic realization of teaching practice.