  A recent trend in mathematical modeling is to publish the computer code
together with the research findings. Here we explore the formal question,
whether and in which sense a computer implementation is distinct from the
mathematical model. We argue that, despite the convenience of implemented
models, a set of implicit assumptions is perpetuated with the implementation to
the extent that even in widely used models the causal link between the (formal)
mathematical model and the set of results is no longer certain. Moreover, code
publication is often seen as an important contributor to reproducible research,
we suggest that in some cases the opposite may be true. A new perspective on
this topic stems from the accelerating trend that in some branches of research
only implemented models are used, e.g., in artificial intelligence (AI). With
the advent of quantum computers we argue that completely novel challenges arise
in the distinction between models and implementations.
