The relationship between the expressive richness of natural language and the rigor of mathematics has been explored by poets and writers over the centuries with surprising results. Mathematics has been used by artists to define strict Boundaries within which to express their creativity as well as to build bold metaphors. Among the many, we remember Borges, who in numerous works is seduced by the vertigo of mathematical thought. An example is the Aleph point of infinite dimensions: “An Aleph is one of the points of space that contain all the points […] the place where they are found without confusion, all the places of the earth, seen from all angles”.
Among the poets of the past, Dante Alighieri built his masterpiece, the Divine Comedy, making full use of mathematics. For instance, Dante assigns a special value to the number 3 and makes it the structural foundation of the poem. The poem is an immense construction of 14233 verses, divided into 3 parts, each made up by 33 songs, plus an introductory chant for a total of 100. Each song develops into triplets, rhyming according to a chained ABA BCB CDC scheme. In addition, each verse is composed by 11 syllables.
For Dante, as for Plato, Pythagoras and Saint Augustine, numbers are not just tools for counting or measuring. Numbers are signs to be interpreted to reveal the secrets of the universe, the divine project of creation, to understand the order underlying the disorder and randomness of world events.
Dante assigns a decisive value to his encounters with his muse Beatrice. She was 9 years old at the first meeting and then 18 (9 + 9) at the second meeting. But 9 are also the skies that surround the earth according to medieval astronomy and 9 is equal to 3 x 3, where 3 is the number of the divine Trinity according to the Christian religion. Having made all these numerical connections, Dante deduces that Beatrice is the sign sent from heaven to inspire him towards the poetry of salvation forhimslef and the whole humanity.
Mathematics in Dante is not only the structural foundation of the poem. The poet uses Euclidean geometry, logic and arithmetic to give concrete form to incontrovertible truths and to communicate mental processes, such as the induction or the faculty of the blessed to see the future. The most daring metaphor is the impossible vision of the divine trinity, which cannot be understood by reason as a circle whose circumference cannot be manually measured by the formula radius x pi, because pi is an irrational number with infinite digits. To measure the circle it is necessary to truncate pi = 3,14159265 … There is no more creative use in literature than the terrible Pythagorean discovery of irrational numbers.