History: Al-Khwarizmi, maths master

Renowned author Terry Pratchett has described Jack Vance’s The Dying Earth as “one of the best and most influential fantasy works of the 20th century”.

The four-book series was written between 1950 and 1984. Each is a collection of stories about Earth in the far-off future, when the Sun is dying, our planet dimly lit by its fading red glow, and magic returns to the land, practised by a handful of wizards.

Early in the tale, one wizard is apprenticed to another, where he learns about “a strange abstract lore termed Mathematics”.

“Within this instrument resides the Universe,” the apprentice is told. “Passive in itself and not of sorcery, it elucidates every problem, each phase of existence, all the secrets of time and space.”

Such sentiments also exist outside the realm of magic and fiction, of course. In its “History of Mathematics”, the website Explorable cites German mathematician Johann Carl Friedrich Gauss (born 30 April 1777) as calling mathematics “the Queen of Sciences”.

Explorable adds that mathematics “permeates every area of our lives. Whether you are filling in your accounts, building a cabinet, or watching the stars, you are using mathematical principles laid down through the ages, and it is a discipline that underpins life as we know it.”

Our high regard for mathematicians is demonstrated by the number of books and films produced by or about them, including A Beautiful Mind (John Nash), A Brief History of Time (Stephen Hawking) and The Imitation Game (Alan Turing).

Less well known is the Persian mathematician Mohamet ibn Musa al-Khwarizmi, though Cosmos has noted his achievements. In 2011, when Kiri Beilby named “the top 10 most influential scientists from the Arabic Golden Age who made advances in science and technology while Europe was in a cultural decline during the Dark Ages”, Al-Khwarizmi was in top spot.

J J O’Connor and E.F Robertson, writing for the School of Mathematics and Statistics at Scotland’s University of St Andrews, agree with Beilby’s assessment.

“In the foremost rank of mathematicians of all time stands Al-Khwarizmi,” they say, referencing two separate works. “He composed the oldest works on arithmetic and algebra. They were the principal source of mathematical knowledge for centuries to come in the East and the West. The work on arithmetic first introduced the Hindu numbers to Europe… and the work on algebra… gave the name to this important branch of mathematics in the European world.”

Beilby says Al-Khwarizmi, who lived from around 780 to 850, produced “a comprehensive guide to the numbering system, developed from the Brahmi system in India, using only 10 digits (0-9, the so-called ‘Arabic numerals’)”.

She says he also “used the word algebra (‘al-jabr’) to describe the mathematical operations he introduced, such as balancing equations, which helped in several day-to-day problems.”

Given the antiquity of Al-Khwarizmi and his work, most of his original writings have been lost, but O’Connor and Robertson go to contemporary translations and later analysis to tell his story.

They say Al-Khwarizmi wrote a treatise on Hindu-Arabic numerals, the Arabic text of which is lost, but “a Latin translation, Algoritmi de numero Indorum, gave rise to the word algorithm, deriving from his name in the title”.

They say the first use of zero as a place holder in positional base notation was probably due to Al-Khwarizmi in this work. Methods for arithmetical calculation are given, and a method to find square roots is known to have been in the Arabic original although it is missing from the Latin version.”

They note “the decimal place-value system was a fairly recent arrival from India and… Al-Khwarizmi’s work was the first to expound it systematically. Thus, although elementary, it was of seminal importance.”