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The formal verification of concurrent systems is usually seen as an example par excellence of the application of mathematical methods to computer science. Although the practical application of such verification methods will always be limited by the underlying forms of combinatorial explosion, recent years have shown remarkable progress in computer aided formal verification. They are making formal verification a practical proposition for a growing class of real-life applications, and have put formal methods on the agenda of industry, in particular in the areas where correctness is critical in one sense or another. Paradoxically, the results of this progress provide evidence that successful applications of formal verification have significant elements that do not fit the paradigm of pure mathematical reasoning. In this essay we argue that verification is part of an experimental paradigm in at least two senses. We submit that this observation has consequences for the ways in which we should research and apply formal methods.