Is God a Mathematician? by Mario Livio Read Free Book Online

establishment of the Academy and the first description of the inscription, we cannot be absolutely certain that such an inscription indeed existed. There is no doubt, however, that the sentiment expressed by this demanding requirement reflected Plato’s personal opinion. In one of his famous dialogues, Gorgias , Plato writes: “Geometric equality is of great importance among gods and men.”
    The “students” in the Academy were generally self-supporting, and some of them—the great Aristotle for one—stayed there for as long as twenty years. Plato considered this long-term contact of creative minds to be the best vehicle for the production of new ideas, in topics ranging from abstract metaphysics and mathematics to ethics and politics. The purity and almost divine attributes of Plato’s disciples were captured beautifully in a painting entitled The School of Plato by the Belgian symbolist painter Jean Delville (1867–1953). To emphasize the spiritual qualities of the students, Delville painted them in the nude, and they appear to be androgynous, because that was supposed to be the state of primordial humans.
    I was disappointed to discover that archaeologists were never able to find the remains of Plato’s Academy. On a trip to Greece in the summer of 2007, I looked for the next best thing. Plato mentions the Stoa of Zeus (a covered walkway built in the fifth century BC) as a favorite place to talk to friends. I found the ruins of this stoa in the northwest part of the ancient agora in Athens (which was the civic center in Plato’s time; figure 8). I must say that even though the temperature reached 115 °F that day, I felt something like a shiver as Iwalked along the same path that must have been traversed hundreds, if not thousands of times by the great man.

    Figure 8
    The legendary inscription above the Academy’s door speaks loudly about Plato’s attitude toward mathematics. In fact, most of the significant mathematical research of the fourth century BC was carried out by people associated in one way or another with the Academy. Yet Plato himself was not a mathematician of great technical dexterity, and his direct contributions to mathematical knowledge were probably minimal. Rather, he was an enthusiastic spectator, a motivating source of challenge, an intelligent critic, and an inspiring guide. The first century philosopher and historian Philodemus paints a clear picture: “At that time great progress was seen in mathematics, with Plato serving as the general architect setting out problems, and the mathematicians investigating them earnestly.” To which the Neoplatonic philosopher and mathematician Proclus adds: “Plato…greatly advanced mathematics in general and geometry in particular because of his zeal for these studies. It is well known that his writings are thickly sprinkled with mathematical terms and that he everywhere tries to arouse admiration for mathematics among students of philosophy.” In other words, Plato, whose mathematical knowledge was broadly up to date, could converse with the mathematicians as an equal and as a problem presenter, even though his personal mathematical achievements were not significant.
    Another striking demonstration of Plato’s appreciation of mathematics comes in what is perhaps his most accomplished book, The Republic, a mind-boggling fusion of aesthetics, ethics, metaphysics, and politics. There, in book VII, Plato (through the central figure of Socrates) outlined an ambitious plan of education designed to create utopian state rulers. This rigorous if idealized curriculum envisaged an early training in childhood imparted through play, travel, and gymnastics. After the selection of those who showed promise, the program continued with no fewer than ten years of mathematics, five years of dialectic, and fifteen years of practical experience, which included holding commands in time of war and other offices “suitable to youth.” Plato gave clear explanations as