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Persian mathematician Muḥammad ibn Mūsā al-Khwārizmī, sometimes known as the father of algebra, was one of the most influential thinkers of all time. He revolutionised algebra and his seminal works in mathematics, astronomy and geography have proved to be the keystone for centuries of advances across the world.

Al-Khwarizmi was born in about AD 780, and although his birthplace isn’t known for sure, the al-Khwārizmī in his name can mean “the native of Khwarazm”, which at the time was part of Greater Iran, but is now part of Turkmenistan and Uzbekistan, so many believe he grew up in that area.

Al-Khwārizmī worked at and then became director of the House of Wisdom in Baghdad, in modern-day Iraq, which was the capital of the Islamic empire at the time. At this centre of scientific research and teaching, he oversaw the translation of many major Greek and Indian mathematical and astronomy works into Arabic. He also produced original work that had a lasting influence on the advance of Muslim and European mathematics.

The founder of algebra

The terms algebra and algorithm are derived from al-Khwārizmī’s name and his work. A Latinisation of his name as Algoritmi led to the term “algorithm”. And the word algebra comes from al-jabr in the title of a landmark book he wrote in about AD 820, al-Kitāb al-Mukhtaṣar fī Ḥisāb al-Jabr wal-Muqābalah, or The Compendious Book on Calculation by Completion and Balancing. The book introduced fundamental methods for solving equations and established the discipline of algebra.

Al-Jabr itself means “restoration” and refers to adding a number to both sides of an equation to consolidate or cancel terms. However, al-Khwārizmī used words to explain mathematical problems, and diagrams to solve them rather than the kind of algebraic notation generally used today.

The book showed how to solve polynomial equations, and algebraic methods of writing an expression in a simpler form, a tactic known as reduction. It also covered key concepts such as moving a negative quantity from one side of an equation to the other and changing its sign, called completion, and subtracting the same quantity from both sides, known as balancing. In particular, al-Khwārizmī developed a formula for systematically solving quadratic equations by using completion and balancing to reduce any equation to one that is solvable.

Master of algorithms

Influenced by the translations done in the House of Wisdom, al-Khwārizmī came to see the great potential of the Hindu numerical system. His work on arithmetic using 1 to 9 and the number 0 was ultimately responsible for introducing what we now call Hindu-Arabic numerals or Arabic numerals, first to the Islamic world and then to the Western world.

His revolutionary approach to mathematics has made our current algorithmically based computers possible, but he didn’t invent algorithms. Arithmetic algorithms were used as far back as around 2500 BC by the ancient Babylonians.

Al-Khwārizmī is also the lattice, or sieve, multiplication method of multiplying large numbers. His lattice method was introduced into Europe by Italian mathematician , which helped spread his work in the West.

Astronomical breakthroughs

The works that al-Khwārizmī conducted went far beyond maths. He made important contributions to astronomy, developing the first quadrant for determining the time by observing the sun or stars. He compiled a set of astronomical tables, known as Zīj al-Sindhind (Astronomical tables of Siddhanta), based on many Hindu and Greek sources, and covering aspects including calculating the positions of the sun, moon and planets, and when eclipses would happen.

Al-Khwārizmī also improved the theory and construction of sundials, and, because of his work, sundials were frequently placed on mosques to show the time of prayer. His work in this field led him to write several other works including .

The main other area that al-Khwārizmī produced significant works in was geography. His Kitāb ṣūrat al-arḍ (The Image of the Earth; and often translated as Geography), essentially covered the world as it was known then. Supervising some 70 geographers, he revised and expanded Egyptian polymath Ptolemy’s earlier work on geography to cover the coordinates of some 2400 places throughout the world, particularly around the Mediterranean Sea and cities in Africa and Asia, including lists with latitudes and longitudes, cities, seas, mountains, islands and rivers.

He also assisted in the construction of a map of the world for his patron, the , and was part of a project to determine Earth’s circumference to its most accurate measure yet.

Al-Khwārizmī died in about AD 850, having done works that would end up shaping the future of the world. He , but through his crafting of algebra, he has essentially influenced every mathematician since.