Abstract
The history of mathematics shows that its foundation, as well as its development, were given slowly, at first without much rigor, but always with creativity. The axiomatic method, theorems, propositions and rational concepts, logically arranged, were the greatest successes achieved by this science. However, mathematics is also characterized by a singular elegance, not always obvious and little explored. Considering that it is one of the bases of scientific spread and it is part of the historical and cultural structure of society, it is necessary to further deepen this characteristic. In this context, in order to prove the existence of this elegance, or rather, of the beautiful in mathematics, is used the works of philosophers and mathematicians who stood out during the elaboration of this science. The focus is on Descartes’ work The Geometry, composed of three parts. In one of them the philosopher affirms that a certain theorem is very beautiful. Thus, the starting point will be to explore the concept of beauty in Plato, towards the beautiful in mathematics.