This article is a celebration of the pleasure inherent in the teaching of mathematics, with a particular focus on a university undergraduate context, and a taught course in the Theory of Numbers. The paper describes a conscious effort by one lecturer to respect the ‘genetic sequence’, whereby students are encouraged and enabled to investigate the subject matter, to make conjectures, and to construct generic examples and formal proofs. It considers whether, and if so how, this joyful experience of teaching and learning might be sustained in the absence of face-to face classroom teaching.