Mathematicians, physicians and the science of light

Part oneNumbers and the word algebra

Look at the word algebra. It comes from the title of a book written in Baghdad, around the 820s, by Muhammad ibn Musa al-Khwarizmi. The book was called a short work on calculation by al-jabr and al-muqabala, which can be translated as completion and balancing.

Al-Khwarizmi was born around 780, in the region of Khwarazm in Central Asia, and he worked in Baghdad under the caliph al-Ma'mun until his death around 850. Al-Ma'mun asked him for a practical book, one that ordinary people could use for dividing inheritances, settling trade accounts, measuring land and planning canals. Al-Khwarizmi answered with a step-by-step method for solving equations. He wrote it in plain words, with worked examples, and without the symbols we use now. Mathematicians in several cultures had worked on such problems before him. His book put them into an organised form that students could learn.

He also wrote about the Indian system of numerals, with its ten symbols, zero among them. That book survives only in Latin, and it helped spread the system to Europe, where it arrived by way of Spain and North Africa. When Europeans translated his name, it turned into algorismi, and in time into the English word algorithm. The numerals we call Arabic came to Europe by this route, and are often now called Hindu-Arabic, because they began in India.

The tradition did not end with him. Al-Battani, who observed the skies from Raqqa and died in 929, measured the length of the solar year with great accuracy, and his tables were used by astronomers for centuries. Al-Biruni, who lived from 973 to 1048 and came from the same Khwarazm region, wrote on astronomy, geography and mathematics. He spent years in India and wrote a large and careful book about its people, languages and sciences. He also worked out the size of the Earth from the height of a mountain, and the result was close to the modern figure.

Part twoPhysicians and hospitals

Hospitals, called bimaristans, appeared in Baghdad in the early Abbasid centuries and spread to Damascus, Cairo and other cities. Doctors there were trained by watching and working with patients, and they wrote down what they saw. In 931 the caliph's officials began to require doctors in Baghdad to pass an examination before they could practise, so that patients were protected from untrained healers.

Muhammad ibn Zakariyya al-Razi, known in Europe as Rhazes, lived from about 865 to 925. He came from Rayy, near modern Tehran, and worked in hospitals there and in Baghdad. He wrote a short book that described smallpox and measles and told them apart, and a very large medical encyclopedia known as al-Hawi. His books paid close attention to the course of a disease and to how patients responded to treatment.

From the hadith

Narrated Abu Huraira:

The Prophet (ﷺ) said, "There is no disease that Allah has created, except that He also has created its treatment."

Ibn Sina, known in the West as Avicenna, was born around 980 near Bukhara. He trained as a doctor while still young and became a philosopher too. His Canon of Medicine, in five books, gathered and arranged the medical knowledge of Greek, Arab and Persian writers into one orderly work. It was copied and taught across the Muslim world and, in Latin, in European universities, for centuries. Ibn Sina also wrote the Book of Healing, a vast work on logic, natural science, mathematics and philosophy. He died in 1037 at Hamadan, in Iran.

Part threeIbn al-Haytham and the science of light

How do we see? Greek thinkers had offered different answers. One was that the eye sends out rays that touch the objects it looks at. Another was that objects send forms to the eye.

Ibn al-Haytham, who was born in Basra around 965 and later lived in Cairo, worked out an answer by experiment. Light travels in straight lines from a source, such as the sun or a lamp, and bounces off objects into the eye. He used dark chambers with a tiny opening, to show how light passes through a small hole and forms an image on the opposite wall. He studied mirrors and lenses, how light bends on passing from air into water or glass, and the structure of the eye. His great work, the Book of Optics, was finished around 1020.

What made the book unusual was its method. Ibn al-Haytham argued that a claim about nature should be tested by repeated experiments and not accepted on the authority of a famous name. The Book of Optics was translated into Latin around 1200. European scholars, among them Roger Bacon and later Johannes Kepler, read it and built on it.

These scientists wrote in Arabic, but they came from many places and many backgrounds, from Central Asia, Iran, Iraq and Egypt. Their work left traces in everyday words. Algebra and algorithm, alchemy and alcohol, zenith and azimuth all come to English from Arabic. So do the names of many stars, among them Altair and Aldebaran, still used by astronomers today.

The word algebra comes from the title of a book written in Baghdad twelve centuries ago.

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Lecture Al MuqaddimahThe Golden Age of Islam, an Introduction (opens on YouTube)

The mapWhere it happened

• Khwarazm
• Bukhara
• Rayy
• Baghdad
• Basra
• Cairo

This map is a simple sketch to help you picture where events took place. Positions, distances and borders are approximate, so please use it for reference only, not as an accurate map.

SourcesSources for this chapter