Unity and Disunity in Mathematical Magic Squares across Cultures and Languages


Emilia Calvo (Departament de Filologia Clàssica, Romànica i Semítica. University of Barcelona)
Rosa Comes (Departament de Filologia Clàssica, Romànica i Semítica. University of Barcelona)
Bink Hallum (Arabic Scientific Manuscripts Curator. British Library)


Magic squares are potent symbols of unity. Composed of cells in an equal number of rows and columns containing a string of consecutive natural numbers arranged such that the sum of each row, column and main diagonals is the same, the numerical relationships within a magic square remain the same however it is rotated or presented as a mirror image. Magic squares also symbolise disunity, since as the number of cells in a square is increased there is a corresponding – almost exponential – increase in the number of its possible magical arrangements.

Historical and modern discourse on magic squares also reveals elements of unity and disunity as magic squares appear in a variety of literary and artistic settings across a huge chronological and geographic range.

In Islamicate literature, magic squares first appear in 9th- and 10th-century medical contexts, where their healing power was imagined to have a natural cause. The earliest Arabic treatises devoted to magic squares, however, were written by well-known mathematicians such as al-Būzjānī (10th c.) and Ibn al-Haytham (10th-11th c.) and were purely mathematical in scope. The Islamicate tradition of mathematical interest in magic squares inspired the Byzantine grammarian Moschopoulos to write the first European mathematical treatise on magic squares in the 14th century. In the 10th-century Epistles of the Brethren of Purity, we find the first discussion of the magic squares in an environment that is both mathematical and arguably magical. The Andalusian astronomer al-Zarqālī (11th c.) was perhaps the first to propose the astrological-talismanic use of the first 7 magic squares associated with the 7 planets. The first dateable reference to a magic square in Latin Europe derives directly from the work of al-Zarqālī and is found in the Alfonsine Astromagia (13th c.). In fact, the standard European term “magic square” arose because only Arabic magical and not mathematical treatments of the squares were known.

Later Islamicate treatises, such as those attributed to al-Būnī (12th -13th c.), combine discussions of the magical uses of the squares with mathematical descriptions of their construction, and the earlier astrological and natural philosophical explanations of their talismanic powers give way to explanations rooted in letterist and Sufi traditions. In Europe, Athanasius Kircher (17th c.) wrote the first known European mathematical description of magic squares since Moschopoulos, and employed his insights in this area to his attempts to decipher the hieroglyphs of the ancient Egyptians.

Many Arabic and Persian treatises dealing with purely mathematical squares have been surveyed in recent decades, but most of the Arabic and Latin works dealing with their magical and astrological aspects are neglected. More generally, modern scholarly research into the history of magic squares has been hindered by a tendency to impose artificial unity on the historical source material while assuming disunity between, for example, authors dealing with mathematical aspects of the squares and their magical applications.

This symposium seeks to reassess the history of magic squares, focussing on instances of unity and disunity, while accepting both their mathematical and their magical and astrological aspects.

Please, send abstracts of up to 500 words.

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Deadline for paper submission

Decembre 12, 2017