Magic squares in history

Magic squares are not a modern puzzle. The first ever RECORDED 4 × 4 magic square is found in a 10th century inscription at the Pārśhvanath Jain temple in Khajuraho, India. It is known as the Chautīsā Yantra (चौंतीसा यंत्र).

Why that name? Chau̐tīs means 34 — and every row, every column and every diagonal in that square adds up to 34. Look at it and try to find other patterns of four numbers in it that also add to 34; there are surprisingly many.

The first magic square ever recorded anywhere is older still: the LO SHU Square of ancient China, dating back over 2000 years. The legend tells of a catastrophic flood on the Lo River, during which the gods sent a turtle to save the people — and the turtle carried a 3 × 3 grid on its back, with the numbers 1 to 9 arranged in a magical pattern.

Magic squares were studied in many parts of the world at different times, including India, Japan, Central Asia and Europe.

Indian mathematicians worked on them extensively, describing general methods of constructing them — not just solving particular cases. Their work was not limited to the 3 × 3 and 4 × 4 grids we have considered, but extended to 5 × 5 and larger square grids.

They are not confined to scholarly works either. A 3 × 3 magic square is carved on a pillar in a temple at Palani in Tamil Nadu, which dates back to the 8th century CE.

And they are found in homes and shops across India. The Navagraha Yantra is one such example, with a different magic sum associated with each graha; the Kubera Yantra is another. A piece of mathematics proved in a classroom turns out to be centuries old and carved in stone.