Statistics and mathematics: the appropriate use of mathematics within statistics

Mathematics uses precise language and precise statements. Those statements are justified by logically argued proofs. Mathematics unifies examples and generalizes them to a broader theory. I argue that statistics can and should use these approaches to become more relevant to the problems that it tackles, not less. Moreover, where a corpus of mathematical theory is available which solves the statistical problem at hand, it should be used. Finally, some statistical communication could benefit from the clear labelling used by mathematicians.