The Role of Mathematics in Physical Sciences And Dirac's Methodological Revolution

In our paper, avoiding any strong metaphysical commitment on the world, we face the topic of the interplay between mathematics and physics by starting from a semiotic approach. It will be shown that it allows us to insert in a unitary and coherent framework answers to questions such as: Why mathematics is physics? What is the role of mathematics in physics? Why is mathematics effective in physical sciences? In the second part of the paper, and by utilizing what discussed in the first one, we analyse what we call Dirac’s methodological revolution, according to which to do good and new physics we must first work on good and promising mathematics. Finally, we exemplify Dirac’s methodological revolution by recalling the role of the mathematical theory of simple spinors in constructing new perspectives for theoretical physics.