Mathematical practice

Mathematical practice comprises the working practices of professional mathematicians: selecting theorems to prove, using informal notations to persuade themselves and others that various steps in the final proof are convincing, and seeking peer review and publication, as opposed to the end result of proven and published theorems. Mathematical practice comprises the working practices of professional mathematicians: selecting theorems to prove, using informal notations to persuade themselves and others that various steps in the final proof are convincing, and seeking peer review and publication, as opposed to the end result of proven and published theorems. Philip Kitcher has proposed a more formal definition of a mathematical practice, as a quintuple. His intention was primarily to document mathematical practice through its historical changes. The evolution of mathematical practice was slow, and some contributors to modern mathematics did not follow even the practice of their time. For example, Pierre de Fermat was infamous for withholding his proofs, but nonetheless had a vast reputation for correct assertions of results. One motivation to study mathematical practice is that, despite much work in the 20th century, some still feel that the foundations of mathematics remain unclear and ambiguous. One proposed remedy is to shift focus to some degree onto 'what is meant by a proof', and other such questions of method.