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][1], 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.  


  [1]: http://www.goodreads.com/book/show/208933.The_Artist_and_the_Mathematician