There is a square that has been inscribed on amulets for over a thousand years. It is a 3×3 grid of nine cells, filled with numbers arranged so that every row, every column, and both diagonals sum to exactly 15. In Arabic it is called the buduh square, named after the four letters that occupy its corners: ba’, dal, waw, and ha’. It is the oldest documented Islamic amulet of its kind, and it has been written onto paper, engraved on metal, and sewn into leather pouches worn against the skin from Morocco to Java.
The buduh square is not magic in the way the word is often used today, meaning tricks or illusions. It is something older and more precise: a system for encoding the attributes of the divine into numerical form, so that the person who carries the object is, in a very specific sense, carrying a compressed mathematical argument about the nature of God.
This is the intellectual core of the taweez tradition that most people never hear about.
The First Documented Islamic Amulet Square
The earliest appearance of the wafq – the Arabic term for a magic square, meaning literally “the harmonious disposition of numbers” in Islamic literature occurs in the alchemical writings attributed to Jabir ibn Hayyan, the 8th-century scholar known in medieval Europe as Geber. According to the National Library of Medicine’s survey of Islamic medical manuscripts, this early square was recommended as a charm for easing childbirth, and researchers believe it was of Chinese or Indian origin, transmitted into the Islamic world through the extensive scholarly networks of the early Abbasid period.
The square consisted of nine cells with the numbers 1 to 9, with 5 in the center, so that every row, column, and diagonal summed to 15. The numbers were written not in the Arabic numerals we know today, but in the abjad letter-numeral system – the ancient alphanumeric code in which each of the 28 letters of the Arabic alphabet carries a specific numerical value. Alif equals 1, ba’ equals 2, continuing up to 1000 for the letter ghain. Because the four corners of the 3×3 square contained the letters ba’, dal, waw, and ha’, the square came to be known as buduh – a word that had no prior meaning in Arabic, but became, through this grid, a word of power.
This was not a coincidence that practitioners ignored. It was a feature.
The Abjad System: Where Mathematics and Sacred Language Meet
To understand how taweez makers encoded protection into numbers, one must understand the abjad system, which is the foundation on which the entire tradition rests.
The abjad numerals, also called hisab al-jummal (meaning “the calculation of totals”), are a decimal alphabetic numeral system in which each of the 28 letters of the Arabic alphabet is assigned a fixed numerical value. They have been used in the Arabic-speaking world since before the eighth century, predating the widespread adoption of positional Arabic numerals. The system means that every Arabic word carries an inherent numerical value – the sum of the values of its letters.
This has a direct consequence for sacred language: the Names of God in Arabic each carry a specific numerical value. The name Allah, the most fundamental of all divine names in Islam, has an abjad value of 66 (1+30+30+5). The opening phrase of nearly every chapter of the Quran – Bismillah al-Rahman al-Rahim, “In the name of God, the Most Merciful, the Most Compassionate” has an abjad value of 786. This is why the number 786 appears on the doors and thresholds of Muslim homes across South Asia: it is not decoration, it is Bismillah, compressed into its numerical form.
For a taweez maker working within this tradition, a square filled with numbers was therefore not a mathematical exercise. It was a spatial arrangement of divine attributes, engineered so that the harmony of the grid – every path through it summing to the same constant mirrored a theological claim: that the attributes of God are in perfect balance, that the universe is ordered, and that the person who carries the object is held within that order.
The Brethren of Purity and the “Small Models of a Harmonious Universe”
By the year 983 CE, Islamic scholars in Baghdad had significantly advanced the mathematical study of these squares. In that year, a remarkable anonymous philosophical encyclopedia was compiled in the city – the Rasa’il Ikhwan al-Ṣafa’, the “Epistles of the Brethren of Purity.” It contained the first documented specimens of magic squares of orders 3 through 9, including the first known example of a 6×6 magic square.
The Brethren described their magic squares explicitly as “small models of a harmonious universe.” This phrase is not incidental. Their entire philosophical system, influenced by Pythagorean mathematics and Neoplatonic thought, held that the universe is structured numerically that every aspect of existence, including religion, follows a numeric pattern. Their encyclopedia adopted the Pythagorean tenet that “existing beings correspond to the nature of number.” For them, the wafq was not a curiosity or a superstition. It was a philosophical proof, made portable.
Their 3×3 square was explicitly associated with the moon and various astral phenomena – the earliest known instance of a magic square being linked to celestial bodies in the Islamic tradition. This astrological dimension would later become a standard feature of taweez construction, with different squares assigned to the seven classical planets, each made from a different prescribed material.
Ahmad al-Buni and the Science of Letters
The scholar whose name is most permanently associated with the encoding of divine names into geometric form is Ahmad al-Buni, a Sufi who died in 1225 CE, born in Buna (modern-day Annaba, Algeria) and who lived and worked in Ayyubid Egypt. Al-Buni was a mathematician and a mystic, a contemporary of Ibn Arabi, and his writings on what he called ʿilm al-ḥuruf – the science of letters became the reference point for taweez making across the Islamic world for the next eight centuries.
Al-Buni’s authenticated writings focus on the esoteric properties of Arabic letters and their numerical values. He constructed, for example, 4×4 Latin squares using letters from individual names of God – physical grids in which the divine name was distributed across sixteen cells, so that any path through the square spelled out a permutation of the same sacred letters and summed to the same value. His works on traditional healing, drawing on this framework, remain a point of reference among Muslim healers in Nigeria and other parts of West Africa to this day, according to his Wikipedia entry sourced from academic scholarship.
The work most associated with his name – the Shams al-Ma’arif al-Kubra, meaning “The Great Sun of Gnosis” is a vast compendium dealing with the magical use of numbers and magic squares, and the occult properties of certain Quranic verses and the Asma’ al-Husna (the 99 Names of God). A copy of the final volume of this work is held in the Khalili Collections, one of the world’s major repositories of Islamic art, and its catalogue describes it as comprising 40 chapters on the magical use of numbers and magic squares, alongside numerous descriptions of amulets and talismans with instructions for their manufacture. It is important to note that scholars, including Jean-Charles Coulon, have argued that the famous version of Shams al-Ma’arif in wide circulation may be a later compilation rather than al-Buni’s own direct composition – a “corpus Bunianum” of authors working in his tradition. This scholarly dispute does not change the documented historical impact of the tradition bearing his name.
What is not disputed is the significance of al-Buni’s authentic writings on ʿilm al-ḥuruf: the systematic assignment of spiritual properties to Arabic letters, the construction of talismanic grids from divine names, and the development of a formal discipline – ʿilm al-awfq, the science of harmonious squares that linked mathematics, language, and divine attributes into a single unified practice.
The 99 Names of God and Their Numerical Architecture
Central to the taweez tradition is the Asma’ al-Husna – the 99 Names, or Most Beautiful Names, of God. The Quran instructs believers to call upon God by these names: “Call upon Allah or call upon the Most Compassionate whichever you call, He has the Most Beautiful Names” (17:110). A hadith recorded in Sahih al-Bukhari states that God has 99 names, and that whoever commits them to memory will enter paradise.
Each of the 99 names has an abjad value. Each can therefore be arranged into a numerical grid – a square, a border, a column in which the numeric harmony of the arrangement encodes the theological properties of the name. A taweez maker working within this tradition was doing something technically precise: choosing the correct name for the specific purpose of the amulet, calculating its abjad value, constructing a grid in which that value appears as the row-sum and column-sum, and inscribing the result in the correct ink on the correct material at the correct hour.
The Khalili Collections manuscript of al-Buni’s work devotes its longest chapter (chapter 39) entirely to the Asma’ al-Husna, followed by a chapter on prayers and invocations, and an appendix giving chains of scholarly authorities for the correct use of letter-numerals. This is not folk magic. It is a documented scholarly tradition with named authorities, verified transmission chains, and formal methodology.
The 15th-century Ottoman scholar ʿAbd al-Raḥman al-Bistami extended this work further, writing extensively on the connections between the divine names and the construction of wafq amulets. A manuscript held at the Bibliotheque nationale de France (MS Arabe 2689) contains a wafq incorporating three of the most fundamental names of God – al-Ḥayy (The Living), al-Qayyum (The Eternal), and al-Waḥid (The One) arranged in a magic square. This manuscript is documented in the work of Bink Hallum, Arabic Scientific Manuscripts Curator at the British Library.
What the Yale Amulet Reveals
At the Beinecke Rare Books and Manuscript Library at Yale University, researchers have studied an Arabic block-printed amulet that contains something remarkable: two magic squares, one of which is of order 13 – perhaps the only documented example of a 13×13 wafq in any published amulet. A 13×13 grid contains 169 cells. For every row, column, and diagonal to sum to the same constant, the maker would have needed formal mathematical knowledge of the kind documented in the 10th-century treatises by Abu’l-Wafa al-Buzjani and Ali ibn Ahmad al-Antaki.
This object, published in academic literature under the title “Math and Magic: A Block-Printed Wafq Amulet from the Beinecke Library at Yale,” confirms what the manuscripts had always claimed: the production of a taweez at the highest level of the tradition required not just religious knowledge, but formal mathematical competence. The construction of bordered magic squares of high order – squares that work at any size by surrounding smaller squares with symmetric borders was a documented achievement of Islamic mathematics by the end of the 10th century. The same techniques used to solve mathematical problems were applied to the production of amulets.
From Calculation to Protection: The Logic of the Taweez
What emerges from this history is a picture very different from the one most people carry when they hear the word “amulet.” The taweez, at its most sophisticated, was the product of an intersection between at least three separate disciplines: Islamic theology (the properties and hierarchy of divine names), Arabic numerology (the abjad system and its application to sacred words), and formal mathematics (the construction of magic squares of any order).
The practitioner who wrote a taweez was making a specific argument. The argument was: the attributes of the divine are in balance; this grid demonstrates that balance numerically; the person who carries this grid carries proof of that balance, and is held within it. To explore the living tradition of taweez and its scholarly foundations, visit taweez.eu.
Whether or not one accepts the theological premises of this argument, the intellectual structure behind it is real, documented, and traceable across more than a thousand years of manuscripts, mathematical treatises, and material objects from the Jabirean corpus of the 9th century, through the Baghdad encyclopedias of 983 CE, through the Sufi scholars of North Africa and Egypt in the 12th and 13th centuries, through the Ottoman court manuscripts of the 15th century, and into the leather pouches worn by enslaved Muslims in 19th-century Bahia and the handwritten amulets made by traditional practitioners today.
The geometry is old. The names are older. And the tradition that joins them is, against considerable odds, still alive.