When Andrea (Giovannetti) asked me to write an article about Fibonacci, my first thought was: "Domine, non sum dignus". While in the left hemisphere of the brain – the one dedicated to rationality – the Latin liturgical formula was flashing, the right part, evolutionarily predisposed to creativity, had already moved forward with the work.
Article by Maurizio Morolli
After all, I told myself, mathematics is one of my passions, especially when it comes to great enigmas like Fermat's Last Theorem, studying Game Theory applied to betting and investments, or exploring the mystery of the Golden Ratio.
It must be said that Andrea knew how to press the right button: seeking the point of view of a non-mathematician, that is, that of a simple accountant, like myself. But the part of the brain delegated to touchiness – decidedly well-developed, in my case – immediately retorted: "What do you mean by non-mathematician? I've taken three Mathematical Analysis exams, I've even studied post-graduate history: ugh"!
Let's start with the basics, as in elementary school before the dreaded "class essay".
The Great Transcendental Thinker Chat GPT tells us that Leonardo of Pisa, better known as Fibonacci (circa 1170 – circa 1242), is famous mainly for the sequence that bears his name, in which each number is the sum of the two preceding ones.
So far, artificial intelligence has added little.
Fibonacci's true contribution to mathematics and modern accounting, however, goes well beyond the famous sequence. The son of Bonaccio introduced the Indo-Arabic numeral system to Europe, based on ten digits (0-9) and decimal position. Before its introduction, calculations were still made with Roman numerals, lacking both zero and positional representation, making calculations complex, especially for multiplications and divisions.
The adoption of the decimal system described by Fibonacci allowed European merchants and administrators to calculate with greater ease and precision, revolutionizing the management of accounting books, tax collection, and the evaluation of commercial transactions. In other words, with Fibonacci, the figure of the accountant is born.
In the Liber Abbaci – his famous manuscript, which Andrea is now bringing to bookstores – Fibonacci did not limit himself to presenting the new number system, but addressed practical issues such as interest calculation and the present value of money. These themes are still central in finance today, where the relationship between time and money is essential for management and investment decisions.
The decimal number system simplified economic calculations and laid the foundations for modern finance. Thanks to his insights, Fibonacci has profoundly influenced the world of accounting and finance, leaving a legacy that still shapes the way we understand money today.
He dealt with practical problems of financial mathematics, land surveying, puzzles, and mathematical riddles, often presented in story form; some became classics as early as the 13th century (who can forget the seven old women in Rome with the seven mules?).
But let's set aside serious considerations and move on to the playful aspect of his work: that which has fueled technical analysis, financial data prediction, and surpassed the "Crystal Ball", providing (sometimes unexpected) bases for the doctrines developed by Vanna Marchi and Mago Otelma.
A friend, who is indeed a Mathematician, often repeats that statistics and mathematics explain the past very well, but when it comes to the future, analysts' predictions have the same reliability as the entrails of the Geese of the Capitol.
"But how, Mathematics is an exact science!" my (few) readers grumble.
Of course, that's what is taught in elementary school; yet, the Son of Bonaccio (or was it Bonacci? or Pisani?) taught us something more: mathematics is creativity, interpretation, and philosophy.
Among other things.
But let's try not to digress too much, otherwise Andrea might not pay me for the piece.
Again, the Great Transcendental Thinker Chat GPT reminds us that, according to numerous studies, price corrections in financial markets respect certain percentage factors linked to the values of the Fibonacci series, often used to determine support and resistance levels and to identify possible trend reversals. The key numbers are: 23.6%, 38.2%, 50%, 61.8%, and 76.4%.
And then, thanks to the "Strange but True" column of the Settimana Enigmistica, we discover that the horns of goats and rams grow following spirals constructed on the Golden Ratio, and that many flowers arrange their petals according to Fibonacci numbers to optimize growth and exposure to light.
What do goat horns and petals have to do with trading? Technically nothing. But the real reason why Fibonacci retracement is popular among traders lies precisely in its widespread use: the more an indicator is followed, the more it tends to become self-fulfilling. When enough market participants rely on the same levels, these end up actually functioning as supports and resistances.
Paradoxically, therefore, Fibonacci ends up being justified by self-fulfilling collective phenomena – here the quote from Vanna Marchi and Mago Otelma appears less irreverent!
We – that is, I – like to think of Fibonacci as a gigantic figure for his time: an innovator who laid the foundations for mathematics in the following millennia.
Bernard of Chartres, in the 12th century, wrote that we are dwarfs on the shoulders of giants and that we see further not thanks to our sight, but because we are lifted by the greatness of those who came before us.
In my personal "all-time" podium of innovative giants, Fibonacci is there, alongside Galileo and Leonardo.
And I challenge anyone to contradict me.
Ad astra.
