The History of X


Al-Khwārizmī on a 1983 Soviet Union postage stamp celebrating his 1200th birthday. 

When al-Khwārizmī codified algebra he made a bunch of algorithms to find unknown quantities. The problems were expressed in everyday language as you can see in this example taken from an 1831 translation of his work.

“two squares and ten roots are equal to forty-eight dirhems; that is to say, what must be the amount of two squares which, when summed up and added to ten times the root of one of them, make up a sum of forty-eight dirhems? You must at first reduce the two squares to one; and you know that one square of the two is the moiety of both. Then reduce every thing mentioned in the statement to its half, and it will be the same as if the question had been, a square and five roots of the same are equal to twenty-four dirhems; or, what must be the amount of a square which, when added to five times its root, is equal to twenty-four dirhems? Now halve the number of the roots; the moiety is two and a half. Multiply that by itself; the product is six and a quarter. Add this to twenty-four; the sum is thirty dirhems and a quarter. Take the root of this; it is five and a half. Subtract from this the moiety of the number of the roots, that is two and a half; the remainder is three. This is the root of the square, and the square itself is nine.”

As I’m sure you see from the above paragraph, using common language to explain math problems could be tedious and time consuming.
To compare, here is a translation into our modern symbolic algebra.


Look how far we’ve come.


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