We have all learnt about the outstanding contributions that the ancient Greeks and European mathematicians of the 16th, 17th and 18th centuries, however recent research reveals that there is a forgotten population that made extremely valuable advancements in mathematics: the Arabics. In fact, in many ways the mathematics we study today is stylistically more similar to that of the Arabics, not of the Greeks.
When I talk about ‘Arab mathematicians’ I refer to those that came from the region that was centred in Iran/Iraq. However, this area varied with military conquest during the period. At its greatest, the empire stretched west through Turkey and North Africa, and came as far east as the borders of China.
It is widely believed that after the period of when the Greeks lay the foundations for modern mathematics, there was a period of stagnation before the Europeans took over at the beginning of the 16th century. This perception is highlighted in statements such as that made by Duhem in ‘Le Système du Monde’:
“…Arabic science only reproduced the teachings received from Greek science.”
However, this is a major misconseption. During the Arabic period, beginning in the 9th century, there were many talented mathematicians who made some important discoveries. This period started when Al-Ma’mum established Baghdad as the new centre of wisdom and learning. A research institure, called ‘Bayt al-Hikma’ which translates to ‘The House of Wisdom’, was created and lasted for more than 200 years. Al Ma’mum was also responsible for the large translation project, which saw the major works of the Greeks being translated. Furthermore, they learned the mathematics of the Babylonnians and the Hindus.
Abu l’Hasan al-Uqlidisi (c. 950)
- In his book ‘The book of chapters on Hindu Arithmetic’, two significant contributions were made: he gave an algorithm for multiplication on paper and used decimal fractions for the first time.
Abu Ja’far Muhammad (around 790 – 850)
- His most important work was presented in his book ‘Al-jabr wál Mugabala’, written in 830, and was translated into Latin and used in Europe for generations. In it, heuses the word ‘algebra’ for the first time, classifies the solution of quadratic equations and gives geometric methods for completing the square. He also notes six different types of quadratic equations.
Abu Kamil Shuja ibn Aslam ibn Muhammad ibn Shuja (around 850 – 930)
- He worked on integer solutions of equations as well as giving the solution of a fourth degree equations and of quadratic equations with irrational coefficients. It is argued that his biggest advance was his use of irrational coefficients.
- His work was the basis of Fibonacci’s books.
Abu’l-Hasan Thabit ibn Qurra (826 – 901)
- Thabit inherited a large family fortune, enabling him to go to Baghdad and obtain mathematical training.
- He generalised Pythagoras’s theorem to an arbitrary triangle and is regarded as the Arabic equivalent of Pappus – the commentator on higher mathematics.
- Additionally, he founded a school that translated works by Euclid, Archimedes, Ptolemy and Eutocius (Diaphantus and Pappus were unknown to the Arabics until the 10th century). Many ancient books would have been lost without his effort.
- Furthermore, he also made an impressive contribution to amicable numbers, which are two numbers who are each the sum of the divisors of the other.
Mohammad Abu’l-Wafa al’Buzjani (940-998)
- He translated many works of Euclid, Diophantus (for example ‘Arithmetica’) and Al-Khwarizmi that had been lost.
- He is most famous for his use of the tangent function for the first time and compiling tables of sins and tangents at 15 degree intervals. These values are accurate to 8 decimal places – an astonishing achievement considering Ptolemy’s were only accurate to 3 decimal places!
Abu Bakr al-Karaji (early 11th century)
- He gave a numerical solution to equations of the form:
- He proved the fact below, using mathematical induction, meaning it was extendable to all integers.
- More than any other Arabic mathematician, his mathematics pointed in the direction of Renaissance mathematics.
Omar Khayyam (1048 – 1122)
- He discovered a geometrical method to solving cubic equations by intersecting a parabola with a circle. His work on algebra was known throughout Europe in the Middle Ages, and he also contributed to a calendar reform.
- Furthermore, he gave important results on ratios, by giving them a new definition, to include the multiplication of ratios.
Ghiyath al’Din Jamshid Mas’ud al’Kashi (1390-1450)
- He calculated to 16 decimal places and considered himself the inventor of decimal fractions.
- Additionally, al’Kashi applied the method (now known as fixed-point iteration) to solve a cubic equation having as a root. He also worked on solutions of systems of equations and developed methods for finding the root of a number, which is known Horner’s method today.
And this is only a brief summary of some Arab mathematicians! It is astonishing to think that there is a whole period of mathematical advance that was unknown to me!
Let me know if this is a series you’d like me to continue! M x