This may be a stretch, in that it is not really about "solving math problems", but according to Amir Aczel's book on the subject, the Bourbaki collective (and in particular its emphasis on structure as an organizing principle in mathematics) was heavily influenced by the ideas of Structuralism that were current among philosophers (e.g. Saussure), anthropologists (e.g. Lévi-Strauss) and psychologists (e.g. Piaget) of the day.