"No entre nadie que no conozca la geometría"

The Academy was the philosophical school founded by Plato around 387 a. C. in the gardens of Academos in Athens. In this, almost all the mathematical work of the time was developed, besides teaching medicine, rhetoric and astronomy. It can be considered as an antecedent of the universities. Geometry was considered a science of flat figures and proportions that, apart from its practical utility for the art of war, also elevates the mind towards the contemplation of the intelligible world.

Until the process of idealization was converted at once into something without dimension, to the line in length without width, to the flat surface without thickness and to the solid in an ideal spatial volume, they were considered real figures existing in things. However, Plato will refuse to grant real existence to the point, defining it simply as the name given to the ends of a line. On the other hand, the lines, the surfaces and the solids do give them a real existence because they have magnitude.

Plato states that mathematics is in the human soul, because in this is present the logos that governs the material world through arithmetical and geometric proportions. In some of his dialogues some sophists appear, whom the author will condemn accusing them of confusing the abstract numbers or the ideal geometrical figures with the sensible physical appearances.

La Escuela de Atenas. Rafael (1509 - 1510)

At the center of the composition is Plato, founder of the Academy. In the first plane, on the left: Grammar, Arithmetic and Music, on the right: Geometry and Astronomy and at the top of the Rhetoric and Dialectic staircase.