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In this talk, Imbert shall argue that constraint-based reasoning provides a useful framework for understanding what scientific practices are adopted and how progress sometimes occurs in science. This approach has been developed by Humphreys in his analysis of how tractable mathematics influences progress in the physical sciences and the selection of physical models. Imbert shall investigate whether this pattern of reasoning can be extended beyond tractability constraints: to other kinds of constraints, other scientific practices, and other stages of inquiry. Imbert shall illustrate this extension with several plausible cases in which constraints of different kinds appear to play a prominent role in shaping scientific practices and development. Imbert shall then turn to challenges raised by this approach, concerning how constraints should be conceptualized, under what conditions constraint-based reasoning can be legitimately applied, and the heterogeneous pathways along which constraints can shape scientific activity and development.

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