  Engineering needs mathematics, but the converse is also increasingly evident.
Indeed, mathematics is still recovering from the drawbacks of several
"reforms". Encouraging is the revived interest in proofs indicated by various
recent "introduction to proof"-type textbooks. Yet, many of these texts defeat
their own purpose by self-conflicting definitions. Most affected are
fundamental concepts such as relations and functions, despite flawless accounts
50 years ago. We take the viewpoint that definitions and theorems are tools for
capturing, analyzing and understanding mathematical concepts and hence, like
any tools, require diligent engineering. This is illustrated for relations and
functions, their algebraic properties and their relation to category theory,
with the "Halmos principle" for definitions and the "Arnold principle" for
axiomatization as design guidelines.
