According to the parsimony principle, what is advised when modeling in mathematics?

The parsimony principle, often summarized as "keep it simple," suggests that when modeling in mathematics, one should prefer the simplest model that adequately describes the situation at hand. This principle is based on the idea that simpler models are easier to interpret, require fewer assumptions, and are less likely to overfit the data compared to more complex models. By eliminating unnecessary complexity, the simplest model can effectively capture the essential features of the underlying phenomenon while remaining robust and manageable.

In practical applications, a simpler model allows for clearer insights and predictions and makes it easier to communicate findings. Moreover, if a simpler model performs just as well as a complex one, it is usually favored because it is more efficient and easier to develop. Overall, the advice to use the simplest model aligns with the overarching goal of obtaining a functional and comprehensible representation of data or scenarios in mathematical modeling.