A matemática como linguagem estruturante do conhecimento físico: abordagens históricas

In the current scenario of physical knowledge, it is practically impossible to develop a theoretical model with a phenomenological focus without using a mathematical language. This indicates that there have been transformations that have elevated Mathematics to the position of a language that structures thinking about physical phenomena. To this end, it is crucial to investigate the progress of physical thought through historical records that allow us to identify evidence of these transformative events, which not only made Mathematics a language, but also led to the mathematization of Physics. In this regard, the objective of the work was to highlight these transformational events and, in addition, to extract the progression of the function of Mathematics in Physics, in which the quantitative and enigmatic role is replaced by the role of modeling and structuring. The methodological aspect was based on bibliographic research of texts that explored and described the evolution of physical thought and, above all, the evolution of the relationship between Physics and Mathematics, focusing on the process of insertion and adaptability of Mathematics as a structuring language of physical knowledge. In this way, it was possible to outline lines of analysis, albeit simplified, on the factors that contributed to this transformation. The analysis indicated that the practice of mathematizing began with Pythagorean ideas, in which Mathematics was seen as more of an enigmatic aspect than a language. Even in Greece, it is possible to highlight the figure of Archimedes, as someone who used mathematical language, much closer to the idea of a structuring language for Physics, than other thinkers. However, it was with Galileo, when he presented a method of doing Science, that Mathematics is certifying and has the capacity to describe physical phenomena. Newton increased this aspect when he developed specific mathematical concepts to explain natural phenomena. However, electrodynamic phenomena, and part of thermodynamic phenomena, demanded a new focus, and the result of this was the increase in the mathematization of Physics, mainly after the development of Analytical Mechanics. The beginning of the mathematization of matter, which culminated in highly mathematized Modern Physics, made mathematical modeling assume an importance as important as empirical observation for the description of natural phenomena. Mathematics seems to have the ability to describe and symbolize physical phenomena, as well as being a path that bridges the boundary between the real and the abstract. However, this does not mean that mathematical rationalism is capable of directly describing a phenomenon, but rather that mathematical language has a structuring character based on a reasoning that underlies it.