In scientific practice, what do mathematical models serve to do?

Mathematical models play a critical role in scientific practice by providing frameworks to propose relationships that are consistent with observed data. These models are constructed based on established theories and empirical observations, allowing scientists to represent complex systems and phenomena in a simplified, quantifiable manner. This capability enables researchers to make predictions, test hypotheses, and analyze the underlying structure of relationships within the data.

When scientists utilize mathematical models, they do not aim to prove abstract concepts outright but rather to explain and interpret the data. Through the use of equations, simulations, and statistical methods, these models can reflect how different variables interact with each other and how they behave under various conditions, ensuring that the proposed relationships are aligned with empirical findings.

Mathematical modeling is essential for iteratively refining theories and enhancing the scientific understanding of specific phenomena, often leading to new insights and guiding further research. Overall, they serve as powerful tools for understanding and exploring the scientific aspects of the world, reinforcing empirical observation with quantitative analysis.