The oldest recorded magic square in India appears in Varāhamihira’s encyclopedic work, the Bṛhat-Saṃhitā (c. 550 CE). This early 4×4 magic square was not just a mathematical curiosity but was used practically—it indicated combinations and proportions of ingredients for making perfumes.
A magic square is a grid of numbers arranged such that the sum of the numbers in each row, column, and both diagonals is the same. Varāhamihira’s modified magic square was designed for practical applications in perfumery.
Example of a standard 4×4 magic square:
[11514412679810115133216]\begin{bmatrix} 1 & 15 & 14 & 4 \\ 12 & 6 & 7 & 9 \\ 8 & 10 & 11 & 5 \\ 13 & 3 & 2 & 16 \end{bmatrix}
In this square, the sum of numbers in each row, column, and diagonal equals 34.
Varāhamihira adapted this structure to symbolize specific ingredient quantities in his recipes for making perfumes.
- Earliest Recorded Magic Square in India: This predates later Indian developments, including Dürer’s 1514 magic square and Lo Shu magic squares from China.
- Application in Perfumery: Unlike purely mathematical studies, his magic square was practical, helping in the balanced formulation of perfumes.
- Influence on Later Indian Mathematics: Indian scholars like Bhaskara II (12th century CE) and Narayana Pandit (14th century CE) expanded on the concept, using it for astrological and mathematical purposes.
Bhaskara II (12th century CE) studied 3×3 and 4×4 magic squares and linked them to astrological predictions.
Narayana Pandit (14th century CE) wrote about higher-order magic squares and their algebraic properties in his work Ganitakaumudi.
Magic squares became a part of Indian recreational mathematics, influencing Islamic and later European mathematicians.
They found applications in mysticism, astrology, architecture, and even Yantras (mystical diagrams used in Hinduism and Buddhism).
