In this talk, we bring into perspective the famous Riemann zeta function and its natural generalization, the multiple zeta functions. We focus more on the evaluations of such objects at positive integers. The techniques used in these evaluations rely on the properties of some special functions.

Although they look rather simple, it turns out that the single and multiple zeta values play a very important role at the interface of analysis, number theory, geometry and physics with applications ranging from periods of mixed Tate motives to evaluating Feynman integrals in quantum field theory.

The talk should be accessible to non specialists and graduate students.