This essay explores the intersection between Mathematics and Physics, proposing a reflection on possible conceptual connections between elegant mathematical structures and fundamental constants of nature. Starting from Euler’s identity, renowned for its beauty and synthesis of different branches of Mathematics, the study examines relationships involving the speed of light and the gravitational coupling constant between electrons. The approach adopts a physico-philosophical perspective, suggesting that the microscopic scale can serve as a convergence point between mathematical idealization and the imprecision of the physical world. Drawing on Platonic and Kantian ideas, the essay emphasizes that knowledge of the universe is not merely a passive discovery but also a construction of the human mind: the representation of space, time, and physical constants depends on conceptual structures that shape our experience. In this sense, Mathematics provides symbolic and metaphorical tools to understand fundamental aspects of reality, while Physics offers empirical data that guide and constrain these abstractions. The article does not propose a new physical theory but encourages reflection on the role of scientific imagination, mathematical abstraction, and empirical observation in building models that articulate the ideal world and the sensible world.
Falsetti et al. (Fri,) studied this question.