Ancient numerology: the Pythagoreans, the tetractys and numerical harmony
From the Pythagoreans described by Aristotle to the tetractys, from Philolaus to Nicomachus of Gerasa and Boethius: how antiquity saw the symbolism of numbers.
Today the word numerology calls to mind calculations based on a name and a date of birth. In antiquity, however, the idea that numbers had a deep meaning arose in a very different setting, that of Greek philosophy. It was the Pythagoreans, from the sixth century BC onwards, who held that number was the key to understanding the structure of the cosmos. Their doctrines, handed down in fragmentary form, influenced Western mathematics, music, cosmology and theology for centuries.
Pythagoras between history and legend
About Pythagoras, born on Samos and active at Croton, we know very little for certain. He left no writings, and much of the information about his life comes from late biographies, such as those by Porphyry and Iamblichus, full of legendary elements. Even in antiquity the Pythagorean school was wrapped in secrecy, and disciples attributed the community's discoveries to the master, making it hard to separate his personal contribution from that of his followers.
The most sober source is Aristotle. In the first book of the Metaphysics he reports that the so-called Pythagoreans believed the principles of numbers to be the principles of all things. According to this view, numerical proportions explained the order of the heavens, musical harmonies and even moral qualities, such as justice, which was associated with a specific number.
The tetractys and harmony
The most famous symbol of the school is the tetractys, a triangular figure of ten points arranged in four rows: one, two, three and four. Their sum is ten, a number considered perfect. According to tradition, the Pythagoreans swore by the one who had handed down the tetractys to them, that is, by the master himself, and regarded it as the source and root of eternal nature.
The same figures contained the ratios of the main musical consonances: two to one for the octave, three to two for the fifth, four to three for the fourth. The story, told by late authors, that Pythagoras discovered these ratios by listening to a blacksmith's hammers is a legend, but it expresses well the idea that sound and number obeyed the same law.
From Philolaus to Boethius
Among the first Pythagoreans of whom fragments survive is Philolaus of Croton, who lived in the fifth century BC and held that number makes things knowable. In the imperial period Nicomachus of Gerasa, in the second century AD, wrote an Introduction to Arithmetic that combined mathematical notions with symbolic reflections. A work on the theology of numbers is also attributed to him, known through later excerpts.
It was Boethius, at the beginning of the sixth century, who passed this heritage on to the Latin Middle Ages with his De institutione arithmetica, based largely on Nicomachus. The treatise became a fundamental schoolbook, and with it the ideas about even and odd, perfect and harmonic numbers entered the monastic schools. The name arithmancy, divination by means of numbers, appeared later in learned catalogues.
Ancient numerology, then, was not a set of formulas for predicting the future but a vision of the world. For the Pythagoreans and their heirs, counting meant discovering a hidden order, and in that order mathematics, music, ethics and religion were interwoven. Much of what is called numerology today is, by contrast, a modern invention.