"I turned to a book as if to a person" — Tiromancino, lyrics by Franco Califano

It is an apparently very simple question, which nevertheless requires complex and profound answers, partly traceable only in our innermost being. Well, this is one of those cases where that gesture manifests itself appropriately.

Those who believe in the Divine, regardless of religion, almost always perform an act of faith, that is, they are called to believe in what they cannot see or perceive with the five senses. In this manuscript, particularly powerful and solid clues of a perfect and total Harmony are found: not a mathematical demonstration, but rather reliable support in the journey along the paths that lead to Truth.

There is, moreover, a curious and revealing aspect of man's incompleteness: Fibonacci wrote the Liber Abbaci as a practical manual, without any philosophical or religious aspiration and without understanding its exceptional significance beyond the mathematical field. Centuries have filled this awareness gap with their accumulation of thought due to human research in various fields: mathematical, philosophical, artistic.

But where, Precisely, Can these Signs of Divinity be Found?

The first clue is in plain sight, before us: they are the numbers themselves. The so-called "Arabic" numbers, which Fibonacci managed to impose in 13th-century Christian Europe — although the dispute with Roman numerals went on for centuries — are, in truth, of Indian origin.

In India, between the 5th and 9th centuries, two decisive breakthroughs were consolidated: the positional value of digits and zero, both as a digit and an operational idea. Not just an additional symbol, but an apparently empty place that gives meaning to other places: an absence that structures presence. In the texts of Aryabhata, Brahmagupta, and others, we already see calculation methods that presuppose such grammar, in which the writing of the number is already an algorithm.

That system migrated and was translated into Arabic. In Baghdad, in the 9th century, the Bayt al-Ḥikma — House of Wisdom — became a crossroads of translations and commentaries from Sanskrit and Greek. Al-Khwarizmi codified methods with the "Indian numerals" and gave us two bridge words: algorithm (from his name) and algebra (from al-jabr). But the migration was not only of books: it was of practices. The shapes of the digits changed (ghubār and mashriqī traditions), tools adapted, schools commented, markets adopted. Through commercial and intellectual routes, the system opened up towards al-Andalus, the Maghreb, and the great cities of the Mediterranean.

Latin Europe encountered it not only on scholars' desks but on the docks of ports. Here, knowledge entered out of necessity: counting goods, changing currencies, calculating interest, dividing profits. In this landscape, the parable of Leonardo of Pisa, known as Fibonacci, was born. Son of a merchant active in Bugia (Béjaïa, Algeria), he learned "in situation" the power of positional notation. In the Liber Abbaci (1202, then revised in 1228), he did not "invent" numbers: he did something equally great, he translated them across civilizations. He brought mixed knowledge — theoretical and practical — into Latin and clothed it in concrete problems (exchanges, weights, prices, incomes, commercial partnerships). It was not an abstract treatise: it was a manual for expert hands.

This migration crossed centuries, hindered by different cultures, languages, and religions. It is worth remembering that science and culture then traveled on the legs of men and horses: the extraordinary tools for transmitting information that we take for granted today were not available. Let's contextualize the scene: in a deeply Christian Europe, at war with the Arab world, while the Crusades were being fought and while the naval confrontation that culminated centuries later in the Battle of Lepanto was beginning, a great Christian mathematician sought to impose and succeeded in making Christians adopt the numbers of the "infidels," against whom they were at war. On closer consideration, it is something miraculous, which allowed Europe an incredible leap forward, whose beneficial effects would have long propagation over the centuries.

Numbers thus become a universal language that overcomes and nullifies physical, religious, linguistic, and moral distances: a language that, in its usefulness and especially in its universality, suggests to us that there may be many paths, but only one Truth.

After Fibonacci, a season of competition between abacists and algorists opens: on one side the abacus and the tradition of manual calculation; on the other, positional writing, which allows for faster, verifiable, replicable operations. At the end of the 15th century, almost three centuries later, a friar, Luca Pacioli, with the treatise De Divina Proportione, would place the Golden Section at the center and show its applications in geometry, architecture, painting, and sculpture. For accounting enthusiasts, we should mention that he also invented double-entry bookkeeping.

Why is the Proportion "Divine"?

For Pacioli, the proportion is "Divine" because it is not only a calculation tool, but a rule that crosses many forms with singular coherence. The same law, in fact, supports geometry, architecture, painting, and sculpture: a single principle that becomes the common language of form. In the golden division, then, something particular happens: the part is to the whole as the whole is to the greater part; the ratio repeats itself. It is a recursive harmony, in which each fragment reflects the structure of the whole. There is, moreover, incommensurability: φ is an irrational number ((1+√5)/2); it does not close in fraction, it always remains "a little beyond" measure. In this, Pacioli glimpses a sign of order that the mind recognizes but does not exhaust. And here Fibonacci returns: the ratios between successive terms of his sequence, F(n+1)/Fn, tend precisely to φ — the Fibonacci Sequence meets the proportion of beauty.

Let us now turn our gaze to the formula that defines the Golden Section φ ≈ 1.618033988....

The Golden Section is calculated as the limit, as the number of elements in the Sequence tends to infinity, of the ratio between two Fibonacci Sequences where the one in the numerator has one more element. This determines that the result is a number greater than one.

Let's look at this formula with a different eye.

In the ratio between Fn+1 and Fn, that is, in the ratio between the Fibonacci Sequence with one more element and that with one less element, we can see the allegory of the relationship between the Divine, complete, and the incomplete Man. A relationship in which Man's limits are made explicit and laid bare compared to the absolute and perfect completeness of the Divine. The mathematical limit to infinity expresses man's tension towards perfection: research, innovation, ascent towards Beauty, towards the Golden Section, towards the Divinity hidden in nature and forms. However — as Pacioli had intuited — we can appreciate and recognize it, but not fully understand it: the irrationality of the number reminds us of this.

If we dwell on it, this is precisely what happened with Fibonacci: from the observation of a pair of rabbits began one of the most fruitful pages in the history of mathematics; but it was the subsequent centuries of human thought — in which you are participating with this reading — that showed us the Divine nature of things.

Reproducing the Liber Abbaci today is an act of trust in the future: because behind every number lives an idea of infinity and harmony. If you recognize it, hold it in your hands: choose your edition today.