The problem of proving a particular binomial identity is taken as an opportunity to discuss various aspects of this eld and to discuss various proof techniques in an examplary way. In particular, the unifying r^ ole of the hypergeometric nature of binomial identities is underlined. This aspect is also basic for combinatorial models and techniques, developed during the last decade, and for the recent algorithmic proof procedures. Much of mathematics comes from looking at very simple examples from a more general perspective. Hypergeo-metric functions are a good example of this.