Plato was a Greek philosopher (427 BC? - 347 BC?), one of the most important of all time. His theories, called Platonism, focus on the distinction of two worlds: the visible, sensible or world of reflexes, and the invisible, intelligible or world of ideas. Socrates' disciple, develops the theory of method (or dialectic) and the theory of reminiscence, according to which man lives in the world of ideas before his incarnation and contemplates them in their pure state.
After Socrates' death in 399 BC, he leaves Athens and travels for many years, passing through Egypt and Italy. In Sicily, he is charged with teaching Philosophy to King Dionysus, who later expels him from his court, selling him as a slave. He returns to Athens in 387 BC and founds the Academy, seeking to rehabilitate Socrates' philosophy. There is no consensus on the chronology of Plato's work. His best known books are Socrates' Apology, in which he takes up the philosopher's theories about the idea, giving them new meaning. The Banquet, which exposes in a poetic way the dialectic of love; and The Republic, which summarizes all its philosophy and addresses theories about the immortality of the soul, politics and dialectics.
Plato was a mathematical enthusiast. The great mathematicians of his time were either his students or his friends. In this sense, one cannot fail to mention that, at the entrance of the Academy, according to later sources, the maxim read: "That not among those who do not know geometry."
For Plato Mathematics is primarily the key to understanding the universe. Asked once about the demiurge's activity, he replied, "He geometrizes eternally."
Moreover, mathematics is the model of the whole process of comprehension. If the mission of philosophy is to discover the truth beyond the opinion and appearance, the changes and illusions of the temporal world, mathematics is a remarkable example of knowledge of eternal and necessary truths independent of sense experience. As Plato argues in the Republic, the philosopher must know mathematics because "it has a very large effect on the elevation of the mind compelling it to reason about abstract entities."
Plato has always held that the science of numbers or arithmetic is above many others that were regarded as essential to the professional arts. The legend attributes the fatherhood of arithmetic to the hero Palamedes who fought in front of Troy and who is said to have taught the supreme chief Agamemnon the use of new art for strategic and tactical purposes. Plato laughs at those who think so because, according to him, Agamemnon would not have been able to count his fingers, much less the contingents of his army and his fleet.
For Plato, arithmetic is much more than just an auxiliary science for combat. Its value does not lie in its practical applications. Without it man would not be man. It is with an astonishing wealth of analysis that Plato determines the cultural value of mathematics as something that purifies and stimulates the soul, a knowledge that pushes thought to the most sublime objects, which drags the soul into the Self. facilitate those who have talent for it the ability to understand the whole class of sciences.
As for the lazy, when they are initiated and trained, while mathematics does not bring them other usefulness, at least it stimulates their sharpness of mind. For, as Plato says in the Republic, mathematics is "more important than ten thousand eyes."