Given that ancient Greek and Indian mathematicians were able to calculate complex problems such as the value of pi and the square root of two, to high degrees of accuracy, it is hard to imagine that they weren’t using algebra – a method of mathematical problem-solving that we now take for granted. However, the Greeks and Indians were using far more cumbersome techniques, and it was not until the ninth century that algebra as we now recognize it was invented by the Persian mathematician Muhammad ibn Mūsā al-Khwārizmī. His treatise Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-1-muqābala was translated into English as The Compendious Book on Calculation by Completion and Balancing. The word al-ğabr or ‘completion’ referred to the practice of moving terms from one side of an equation to the other, while muqābala referred to the practice of reducing equations by dividing both sides by the same amount. The spread of his ideas around the Near East, China and Europe led to a gradual revolution in the way that mathematics was understood and practised.