On the Aims and Norms of Inquiry in Mathematics

I examine inquiry in mathematics and suggest that its consideration supports either an account of inquiry as aimed at epistemic improvement rather than knowledge of the answers to questions. In supporting this claim, I further argue that three norms of question-directed inquiry; (i) that we should not stop inquiring before we reach knowledge, (ii) that we should not inquire into what we know, and (iii) that we should regard the questions we inquire into as sound, are incorrect (at least for some kinds of inquiry). I suggest a norm of my own and suggest that it may lead to a more pluralistic view of inquiry.