Bija: Seeds of the Unknown

Why Indians called algebra 'seed mathematics' and what the metaphor still teaches us

Long before Europe had a word for algebra, Indian mathematicians called it bijaganita, the mathematics of seeds. This lesson unpacks the metaphor and shows how treating the unknown as a seed shaped how India did algebra for a thousand years.

The Swan Problem at the Slate

In a stone-floored room at the Ujjain observatory, sometime around 1150 CE, the astronomer Bhāskara II sets down his pen, turns to his daughter, and asks her a question about a flock of swans.

A flock is resting on a lake, he tells her. Ten times the square root of the flock has flown off to a lotus cluster. An eighth has wandered to a hillside. Three couples remain on the water. How many swans were there?

Līlāvatī is perhaps twelve. The slate in front of her is a thin board of dark wood, dusted with chalk. She has chalk on her fingers and ink on her sleeve. She has been working through her father's verses for months, and the swans are not the hardest problem he has set her. But the move he wants her to make next is the one that matters. He wants her to give the unknown flock a name. He wants her to call it something, write that name on her slate, and start computing with it as if she already knew the answer.

If you are inclined to write the swan problem down yourself, you will reach for the same move. You will write √x flying off, x/8 wandering away, 6 remaining, and arrange these into an equation. You have not been trained in the Bhāskarīya tradition and yet, twelve seconds in, you have already done the one thing that makes algebra algebra. You named the unknown. You called it x. You agreed it stood for a number you did not yet know, and you started to compute with it as if you did.

The Indian name for this move is bīja. Seed.

What the Metaphor Is Actually Saying