Three great Arab mathematicians who made important discoveries for science

“Neither mathematics nor modern physics would exist without algebra. There would be no computers without algorithms, and no chemistry without alkali,” according to theoretical physicist Jim Al-Khalili.

Al-Khalili, a professor at the University of Surrey in the UK, produced the BBC documentary Science and Islam (“Science and Islam”, in free translation).

“The language of modern science still has many references to its Arab roots,” he said on the TV show. “From the 12th to the 17th century, European researchers made frequent references to Islamic texts from the past.”

And shows a copy of the Liber Abbaci (“The book of calculus”, in free translation) by Leonardo of Pisa, better known as Fibonacci, who would become the first great mathematician of medieval Europe.

“The fascinating thing is that on page 406 there is a reference to an ancient text called Modum algebre et almuchabale and in its margins is written the name Maumeht —the Latinized version of the Arabic name Mohammed”, according to Al-Khalili.

This was Abu Abdallah Muḥammad ibn Mūsā al-Jwārizmī, whose western name is Al-Khwarizmi (Al-Cuarismi, in Portuguese), which derives from the word algorithm. He lived approximately between the years 780 and 850. Al-Cuarismi described the revolutionary idea that it is possible to represent any number you want with just 10 simple symbols.

This great mathematician, who emigrated from eastern Persia to Baghdad (now the capital of Iraq), gave the West numbers and the decimal system. He is often referred to as the father of algebra.

“It is now known that many of the ideas that were once thought to be brilliant new concepts thanks to 16th, 17th and 18th century European mathematicians were developed by Arab/Islamic mathematicians some four centuries earlier,” according to John Joseph O’Connor and Edmund Frederick Robertson of the University of St. Andrews in the UK.

For them, “in many respects, the mathematics studied today has a style much closer to the Arab/Islamic contribution than to the Greeks”.

Throughout history, there have been great mathematicians in the Arab and Islamic world. Here we present three of them.

al-Batani

For Juan Martos Quesada, retired professor and former director of the Department of Arab and Islamic Studies at the Complutense University of Madrid, Spain, one of the main contributions of Arab mathematicians “was to rescue Greek and Latin science with their translations.”

But they also recovered the best of the science developed by the Indians. “The great importance of Al-Batani was to have managed to unite astronomy and mathematics, composing a single field of study”, as Martos Quesada told BBC News Mundo, the BBC’s Spanish service.

“He applied many mathematical formulas to astronomy. He determined with great precision, for example, the solar year with 365 days – which was quite an achievement, since we are talking about the end of the 9th century and the beginning of the 10th century.”

“With regard to the equinoxes, he studied them and concluded that there were errors in the accounts made by Ptolemy. This served to improve the entire Greek heritage of Ptolemy that was received by the Arab mathematicians”, according to Martos Quesada. Al-Batani also established a series of trigonometric relationships.

For the BBC documentary, Al-Khalili visited the University of Padua in Italy and saw one of the most important books in the history of science: From revolutionibus orbium coelestium (“On the Revolution of the Celestial Spheres”, in free translation), published in 1543 by Nicolaus Copernicus.

“The importance of this book is enormous”, emphasizes Al-Khalili. “In it, Copernicus argues for the first time since Greek antiquity that all the planets, including the Earth, revolve around the sun. Many historians consider him the initiator of the European scientific revolution.”

Copernicus mentions the astronomer Machometi Aracenfis, who is the great Al-Batani.

“It’s a great revelation to me that he explicitly mentions a Muslim from the 9th century, who provided a lot of information about his observations,” Al-Khalili points out. “Copernicus made extensive use of Al-Batani’s observations of the position of the planets, sun, moon and stars.”

Al-Batani was born in 858 near Urfa in Syria and died in 929 in Iraq.

Jaime Coullaut Cordero, professor of Arabic and Islamic studies at the University of Salamanca in Spain, spoke to BBC News Mundo about Ibn Al-Shatir, an astronomer and mathematician who was born in Damascus, now the capital of Syria, around 1304.

“He was little known in the West because his works were not translated into Latin,” according to Cordero. But he points out that in the 1980s, “researchers discovered Ibn Al-Shatir’s planetary models and realized that they were the same as the models proposed by Copernicus a few centuries later.”

Al-Hazen

Shaikh Mohammad Razaullah Ansari, professor emeritus of physics at the Muslim University of Aligarh, India, wrote an article for the Unesco website about a 10th and 11th century Arab scholar who was dedicated not only to mathematics but also physics, mechanics , astronomy, philosophy and medicine.

This is the great Abū Ali al-Ḥasan Ibn al-Haytham al-Baṣrī, whose English name is Al-Hazém. He was born in Iraq in the year 965 and died in Egypt in 1040. He was one of the famous scientists of Cairo, Egypt, and called “the second Ptolemy” by the Arab scholars.

Al-Hazem is considered the father of the modern scientific method. He developed the methodology of “experimentation as another way of proving the hypothesis or basic premise”, according to Razaullah Ansari.

Martos Quesada highlights his contributions to the principles of optics. Indeed, Razaullah Ansari teaches that his most famous work was on optics: Kitab fi al-Manaẓirtranslated anonymously into Latin in the 12th and 13th centuries with the title Opticae Thesaurus (“The book of optics”, in free translation). In seven volumes, Al-Hazém studied the properties of light, experimentally and mathematically.

But Al-Hazém was also a great mathematician, as Ricardo Moreno, a writer and professor at the Faculty of Mathematics at the Complutense University, explains on the page of the Virtual Center for the Dissemination of Mathematics.

“He was one of the first Arab mathematicians to successfully study equations of a degree higher than the second, when he geometrically solved an equation of the third degree proposed by Archimedes, more than 1,200 years earlier, in his work About the Sphere and the Cylinder“, according to Moreno.

In the field of number theory, Al-Hazem made important contributions with his work on perfect numbers. He also developed elementary geometry and researched specific cases of Euclid’s theorems.

Abu Kamil

Ricardo Moreno points out that Al-Cuarismi’s death “coincided approximately with the birth, in Egypt, of Abu Kamil ibn Aslam ibn Mohammed, known as the Egyptian calculator”.

“He lived 80 years and left numerous mathematical works – among them, a treatise on algebra, whose original in Arabic has been lost, but of which two translations have come down to us, one in Latin and one in Hebrew. He solves quadratic equations of geometric shape, like its predecessor from Baghdad, but leaning more directly on the Elements [de Euclides]”, according to Moreno.

A brief biography of O’Connor and Robertson indicates that very little is known about Abu Kamil’s life—but enough to understand his role in the development of algebra. According to the authors, “Kamil was one of Al-Cuarismi’s immediate successors”. And indeed, Kamil himself highlights Al-Cuarismi’s role as the “inventor of algebra”.

“But there is another reason for Abu Kamil’s importance: his work was the basis for the Fibonacci books,” according to O’Connor and Robertson. “Kamil is important not only in the development of Arabic algebra, but also because, through Fibonacci, he is of fundamental importance in the introduction of algebra in Europe.”