Digital transformation has made possible the implementation of environments in which mathematics can be experienced in interplay with the computer. Examples are dynamic geometry environments or interactive computational environments, for example GeoGebra or Jupyter Notebook, respectively. We argue that a new possibility to construct and experience proofs arises alongside this development, as it enables the construction of environments capable of not only showing predefined animations, but actually allowing user interaction with mathematical objects and in this way supporting the construction of proofs. We precisely define such environments and call them “mathematical simulations.” Following a theoretical dissection of possible user interaction with these mathematical simulations, we categorize them in relation to other environments supporting the construction of mathematical proofs along the dimensions of “interactivity” and “formality.” Furthermore, we give an analysis of the functions of proofs that can be satisfied by simulation-based proofs. Finally, we provide examples of simulation-based proofs in Ariadne, a mathematical simulation for topology. The results of the analysis show that simulation-based proofs can in theory yield most functions of traditional symbolic proofs, showing promise for the consideration of simulation-based proofs as an alternative form of proof, as well as their use in this regard in education as well as in research. While a theoretical analysis can provide arguments for the possible functions of proof, they can fulfil their actual use and, in particular, their acceptance is of course subject to the sociomathematical norms of the respective communities and will be decided in the future.

数字转换使实现与计算机相互作用的数学体验的环境成为可能。示例是动态几何环境或交互式计算环境，例如GeoGebra或Jupyter Notebook， 分别。我们认为，随着这种发展，构造和体验证明的新可能性出现了，因为它使环境的构建不仅能够显示预定义的动画，而且实际上允许用户与数学对象进行交互，并以此方式支持证明的构建。我们精确定义了此类环境，并将其称为“数学模拟”。在理论上剖析了可能与这些数学模拟进行的用户交互之后，我们将其与其他沿“交互性”和“形式性”维度支持数学证明构建的环境进行了分类。此外，我们对基于模拟的证明可以满足的证明功能进行了分析。最后，我们在Ariadne，拓扑的数学模拟。分析结果表明，基于模拟的证明在理论上可以发挥传统符号证明的大部分功能，显示出有望将基于模拟的证明作为另一种证明形式的考虑，以及将其用于教育实践中。以及在研究中。尽管理论分析可以为证明的可能功能提供依据，但它们可以实现其实际使用，特别是，它们的接受当然取决于各个社区的社会数学规范，并将在将来决定。