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.

翻译：数理建模领域近期的趋势之一是将计算机代码与研究结果一同发布。本文探讨一个形式化问题：计算机实现在何种意义上有别于数学模型。我们认为，尽管已实现的模型带来便利，但实现过程中会隐含一组特定假设，以至于即使在广泛使用的模型中，（形式化）数学模型与结果集之间的因果联系已不再确定。此外，代码发布常被视为可重复研究的重要推手，但我们提出在某些情况下可能适得其反。随着人工智能等研究分支中仅使用已实现模型的趋势加速，这一话题催生了全新视角。我们进一步论证，量子计算机的出现将为模型与实现的区分带来前所未有的挑战。