Conceptual engineering is a booming topic in the philosophy of language and metaphilosophy today. Arguably, mathematics is a prime example of a discipline where conceptual engineering takes place and is successful. In the talk I’ll propose to view mathematical definitions and axioms as tools for conceptual engineering. I’ll raise two issues that have been broached in discussions of conceptual engineering: the implementation problem and topic continuity. I’ll focus on the first. I’ll provide a novel account of mathematical language which explains the increased control afforded when engineering mathematical concepts.