Now an important question is what is the tool used by physicists to express their findings and what features does this tool have?
A great physicist such as Galileo correctly understood the importance of this question. According to Galileo, “The philosophy of nature […] is written in mathematical language...”
Generally, science tools should, in the first place, be protected from any human errors that threatens the authenticity of the findings or reduces their accuracy. Then, it should make it possible to discover newer findings that are explicitly in agreement or in conflict with the previous findings and allow the comparison of findings and empirical data. In fact, science tools must be able to advance science.
But especially in physics, the tools must be based on a consistent and accurate logical system. In fact, the propositions derived from these tools must be valid in nature as the field of study of physics.
Mathematics can be defined as the study of objects, for example quantities, and their relations. But the feature that turned mathematics into a powerful tool for developing the cognitive foundations of different fields of knowledge is the solid and precise structure of its explicit and unambiguous reasoning and logic. Therefore, propositions derived from mathematics in the boundaries of physical observation are always consistent. Also, the results of mathematical propositions are comparable to empirical data.