For mathematicians, a monad is an endofunctor derived from an adjunction that is useful for describing a diverse class phenomena in fields such as algebra and topology.

In computer science, monads have arguably proved most useful in giving a semantics for effects (such as input-output or mutable state) in an otherwise pure (effect-free) programming language.

Interestingly, the mathematical and computer science literature on monads tends to describe them rather differently, so that someone familiar with one perspective may not immediately recognize the equivalence of the other.

In this very general talk we will briefly present both perspectives, explain their equivalence and use them to describe several examples of monads from mathematics and computer science, including the monad of terms in a language, an elegant folklore example, not often encountered in print.