The Pythagoras Square Explained, with Leonardo da Vinci’s Birth Date

7 October 202614 min read

In 1452 a grandfather in Tuscany noted the birth of a grandson named Leonardo. Five centuries later, that short note makes a perfect test case for the Pythagoras square, the numerology grid also known as the psychomatrix. Below we build Leonardo da Vinci’s square step by step, so you can build your own alongside, read all nine cells, and look honestly at what the method can and cannot tell you.

What is the Pythagoras square?

The Pythagoras square, also called the Pythagorean square or the psychomatrix, is a numerology chart calculated from a date of birth. You write down the digits of the date, add four “working numbers” derived from them, and count how many times each digit from 1 to 9 appears. Every digit has its own cell in a three-by-three grid, and every cell carries a symbolic meaning: character, energy, curiosity, health, logic, work, luck, duty and memory.

Leonardo da Vinci makes an unusually good test case. His grandfather Antonio recorded the birth in the family register: a Saturday, 15 April 1452, at the third hour of the night (hours were counted from sunset, so this was late in the evening). That gives us an exact date, and Leonardo’s notebooks give us a remarkable life to check the result against.

Pythagoras, music and number: what is really ancient

Pythagoras was born on the Greek island of Samos around 570 BCE and died around 490 BCE; even these dates are careful estimates. Around 530 BCE he settled in Croton, in southern Italy, and gathered a community of followers who lived by strict shared rules.

He left no writings of his own. The detailed biographies that survive were written some eight hundred years later, when his reputation had already grown into legend. The earliest evidence presents him less as a mathematician than as a teacher of the soul: someone who believed that souls are reborn and who gave his followers strict rules of life, famously including rules about beans.

Number entered the story mainly through his followers. Aristotle reports that the so-called Pythagoreans took the principles of numbers to be the principles of all things. They had a striking reason: halve the vibrating length of a string and the note rises an octave; two thirds of the length gives a fifth, three quarters a fourth. Simple ratios of 2:1, 3:2 and 4:3 lie behind the harmonies people love. Philolaus, an early Pythagorean, went further: everything that is known has number. The tetractys, a triangle of ten points (1 + 2 + 3 + 4), was probably already sacred in this tradition.

Two popular stories do not survive scrutiny. The tale that Pythagoras discovered harmony by listening to blacksmiths’ hammers first appears about six centuries after him, and the physics does not work. And the theorem that bears his name was used by Babylonian scribes more than a thousand years before he was born. Most importantly for us, no ancient source shows Pythagoras reading character from a date of birth.

Where the modern Pythagoras square comes from

Modern numerology took shape in the early twentieth century. Between about 1903 and 1908 an American writer known as Mrs L. Dow Balliett published books presenting a system of numbers “as taught by Pythagoras”. Even the word numerology, in its occult sense, appears only in that period. An ancient name lent these new teachings an air of inherited authority.

The square itself is younger still. Its trail leads to the Russian-language books of Alexander Alexandrov. In his own foreword he writes that he came across a five-page description of “Pythagoras’s system” in a small brochure, spent about three years developing it and named his version the psychomatrix. He dates his first published version to 1999. Who wrote the brochure has never been established.

So the Pythagoras square is a documented modern method wearing an ancient name. That does not make it worthless: a symbolic exercise does not need to be ancient to be interesting. But it is best treated as a modern language for reflection, not as a secret preserved from ancient Greece and not as a personality test.

How to calculate the Pythagoras square, step by step

You need a date of birth, a pencil and a few minutes. We will use the date Leonardo’s grandfather wrote down: 15 April 1452, or 15.04.1452.

1. Write the date as digits: 1 5 0 4 1 4 5 2. Day, month, year. The zeros stay in for now.
2. First working number: add all the digits. 1 + 5 + 0 + 4 + 1 + 4 + 5 + 2 = 22.
3. Second working number: add the digits of the first. 2 + 2 = 4.
4. Third working number: from the first number, subtract twice the first non-zero digit of the birth day. Leonardo was born on the 15th, so that digit is 1: 22 − 2 × 1 = 20.
5. Fourth working number: add the digits of the third. 2 + 0 = 2.
6. Count the digits. Take the date together with the four working numbers (22, 4, 20 and 2), ignore the zeros and count how many ones, twos, threes and so on up to nine you have. Each count goes into its own cell.

Leonardo’s result: two 1s, five 2s, three 4s and two 5s. Not a single 3, 6, 7, 8 or 9. Five of his nine cells are empty, more than half the square. On paper it looks strikingly thin, but a sparse pattern of digits is not a sparse supply of talent.

Two practical notes. In Alexandrov’s layout the top row holds cells 1, 4 and 7, the middle row 2, 5 and 8, and the bottom row 3, 6 and 9; the Sacred Avatar report turns the grid so that 1, 2 and 3 run across the top. The cells and their contents are the same either way. And books disagree about leading zeros, how numbers are reduced and what the cells mean: this article follows Alexandrov’s version, not a rulebook shared by every numerologist.

The meaning of the cells, using Leonardo’s square

Each cell carries a symbolic label, and books on the square describe what one, two or more digits in it are supposed to mean. Here we read those descriptions as a symbolic language, not as measurements of a person, and compare them with what we actually know about Leonardo.

Cell 1: character and will (11)

Books on the square read two ones as a softer, more diplomatic character: someone who persuades rather than commands. It sounds like a good fit. Giorgio Vasari’s Lives, published in 1550, praises Leonardo’s charm and grace. But charm is not the same as a gentle will. Notice how quickly we start helping the reading to fit.

Cell 2: energy (22222)

Five twos are treated as an unusually strong supply of drive. Leonardo’s interests ranged astonishingly wide: painting, anatomy, engineering, flight, rivers and machines of war. Yet a list of achievements is not a measurement of energy, and counting digits measures nobody’s stamina.

Cell 3: interest and curiosity (empty)

Here is the twist. The cell of curiosity, the appetite for knowledge, is completely empty for one of the most curious people who ever lived. Thousands of his notebook pages survive. One list of reminders from around 1508 includes: obtain a skull, describe the tongue of the woodpecker and the jaw of a crocodile.

Popular readings offer a way out: an empty cell is not a verdict but a quality to be developed. Convenient, certainly, but adjusting the interpretation to fit the person does not validate the chart. Still, the notebooks show something worth noticing. Leonardo practised curiosity: he asked, sketched, observed and returned to the same problems for years. Whatever he was born with, his curiosity was also a daily habit. That is where an empty cell can be useful: as a question rather than a proof. What would it look like to practise this quality on purpose?

Cell 4: health (444)

Three fours are read as a sturdy constitution, and Leonardo lived to sixty-seven (1452–1519). But no count of digits is a health assessment, for Leonardo or for you.

Cell 5: logic and intuition (55)

His canal plans and studies of bird flight certainly show careful reasoning. The historical work is evidence; the match with the digits is interpretation.

Cells 6 and 7: work and luck (empty)

An empty work cell could be read as trouble with routine, yet his surviving drawings show enormous patient labour. A critic could point to unfinished projects: the Adoration of the Magi was left incomplete when he moved to Milan around 1482, and his great battle mural in Florence was never finished either. For the empty luck cell, one could pick a setback: in 1494 the bronze intended for his enormous horse monument in Milan was diverted to make cannons. Real facts, but one setback cannot measure a lifetime’s luck.

Notice the move: pick a label, search the biography, find an episode that fits. With a life like Leonardo’s there is always something. The harder question is what would count as evidence against the reading.

Cells 8 and 9: duty and memory (empty)

The man who wrote everything down, with an empty memory cell? One could say he kept notes because he distrusted his memory, but that is a guess. This is how a mismatch becomes a persuasive story without gaining any evidence. An honest test fixes its rules before the results are in; otherwise every hit is kept and every miss is explained away.

One birth, two squares: the calendar problem

Antonio’s date belongs to the Julian calendar. The Gregorian calendar began replacing it in parts of Europe in 1582, and in the fifteenth century the two were nine days apart. In today’s calendar Leonardo was born around 24 April 1452: the same moment, the same baby, different digits.

Run the method again and the working numbers become 22, 4, 18 and 9. The square changes:

Suddenly cells 8 and 9 are no longer empty, and the fives drop to one. Three cells stay empty in both versions: curiosity, work and luck. That is a feature of the arithmetic, not proof of anything Leonardo lacked. Choosing a calendar makes the arithmetic consistent, but it cannot tell us which reading is true. Leonardo did not change; only the notation did.

For anyone alive today the question does not arise: Ukraine, France and Canada all use the Gregorian calendar, so the date in your documents is the one to use.

Why a reading can feel so accurate

In a study published in 1949, the psychologist Bertram Forer gave 39 students what they believed was an individual personality profile. Every student received the same text, drawn largely from a newsstand astrology book. On a scale from 0 to 5 they rated its accuracy at 4.26 on average. Broad statements can feel deeply personal; the phenomenon became known as the Forer effect, or the Barnum effect, a name coined by the psychologist Paul Meehl in 1956. Flattering statements, and the belief that a profile was written just for us, make it more convincing.

Direct tests of numerology have found nothing either. A study published in 2017 examined the birth numbers of 806 Nobel laureates awarded between 1901 and 2010: their distribution did not differ from what chance would predict.

And the coincidences? Leonardo’s digits add up to 22 in both calendars, and a tarot deck has 22 cards now called the major arcana. A numerologist might gasp; a statistician would shrug. Digit sums of dates fall within a narrow range, so matches like this are bound to turn up. Tarot itself began as a fifteenth-century Italian card game, and the occult readings familiar today developed only from the late eighteenth century.

How to use your own square for reflection

So what remains? A possible starting point for reflection, not a discovery about your character. The labels can prompt questions you might never have asked yourself. Whether they help is something to judge from your own experience.

• Take a full cell and ask: where does this quality really show up in my life, and where do I merely like to believe it does?
• Choose an empty cell without assuming anything is missing in you. Would you like to practise what its name describes? If so, name one concrete step. The choice comes from you, not from an absent digit.
• Notice your reactions. A label may flatter you, irritate you or mean nothing at all. None of these responses proves the reading, but a strong reaction can still be worth exploring.
• Keep the big decisions for yourself. No square should choose your career, your partner or your treatment; for those, seek qualified advice. Treat the chart as a mirror, not a map.

Leonardo’s square in a Sacred Avatar reading

The Sacred Avatar sample report is calculated from the same date, 15 April 1452, and its Pythagorean square matches the one above: two 1s, five 2s, three 4s, two 5s and five empty cells. In a Sacred Avatar reading the square is one part of a larger chart of 37 positions: positions 1 to 9 are the cells, 10 to 17 are the rows, columns and diagonals, and the rest describe the past, the present and the direction of a life. Each position is written out in full, not reduced to a keyword. The guide to the method explains how the parts fit together.

You can see your own complete chart, with every number and three positions opened in full, before paying anything. Like this article, it is offered for reflection and self-enquiry, not as medical, psychological, legal or financial advice.

Questions

Sources

1. Carl Huffman, “Pythagoras”, Stanford Encyclopedia of Philosophy. plato.stanford.edu
2. “Leonardo da Vinci”, Encyclopaedia Britannica. britannica.com
3. Forer, B. R. (1949). The fallacy of personal validation: a classroom demonstration of gullibility. Journal of Abnormal and Social Psychology, 44(1), 118–123. doi.org
4. Genovese, J. (2017). A test of numerology: do birth numbers predict Nobel Prize winners? Journal of Articles in Support of the Null Hypothesis, 13(2). jasnh.com

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