By Dr. Zohor Shanan Idrisi

Following the collapse of the Roman Empire
at the beginning of the 5th century man’s concern was primarily focused upon
security and stability, whilst art and science were neglected. For two
hundred years all progress stagnated in the wake of barbarian invasions and the
resulting lack of maintenance of public works, such as dams, aqueducts and
bridges. With the advent of Islam in the 7th century a new type of
society emerged, which quickly established its supremacy and its constructive
identity in large sections of the known world. The citizen, whether
Muslim or not, soon became confident in the future stability of his
environment, so that trade not only reached its previous levels but also began
to expand.

In
an empire that stretched from the Pyrenees to India, security of communications
was vital. The resultant priority given to safety of travel provided a
stimulus to trade. There followed a rapid expansion of commerce in which
the economic strengths of the Sassanid, Byzantine, Syrian and western
Mediterranean areas were united. The establishment of an efficient fiscal
system meant that the state could now invest in large public works projects:
mosques, schools (*madrasas*), public baths, palaces, markets and
hospitals. Princes and merchants became patrons of intellectual and
scientific development. Trusts (*waqf*) were created to provide
better education.

This
sponsorship engendered a creative enthusiasm and a flowering of scientific
works and scholarly research. The world in effect became greater as
mathematicians, geographers, astronomers and philosophers all contributed to a
gradual but definite extension of the horizons of man’s existence.
The dividend of all this expenditure on learning made an immense
contribution to the sum of the increase in man’s scientific knowledge that
occurred between the 9th and the 16th centuries.

Foremost
in the achievements of Muslim scholars was the treatment of numbers. It
is impossible to conceive how science could have advanced without a sensible
logical numeric system to replace the clumsy numerals of the Roman Empire.
Fortunately, by the 9th century the Muslim world was using the Arabic system of
numerals with the essential addition of the zero. Without the latter, it
was impossible to know what power often accompanied each digit. Hence 2 3
might mean 23, 230 or 203. The introduction of this numeric system with
its zero was thus the ‘sesame’ of scientific advancement.

The
new numeric system did not only affect science. Its value was manifest in
many aspects of daily life, from the calculation of customs dues, taxes,
almsgiving (*zakat*) and transport charges, to the complexity of divisions
of inheritance. A further useful innovation was the mine of separation in
fractions, which eliminated many frustrating confusions.

Islamic
civilization produced from roughly 750 CE to 1450 CE a succession of
scientists, astronomers, geographers and mathematicians from the inventor of
Algebra to the discoverer of the solution of quadratic equations.
The list is far reaching, some are well known whilst others remain
anonymous. One of the major advances was contained in the work of
Al-Khawarizmi, who wrote a mathematical work called “Al-Jabr wa Al-Muqabala”
(820 CE), from whose title is derived the name “algebra”, this book may be
considered the first book written on the topic of algebra. Amongst the
achievements that Al Khawarizmi left to posterity were: (1) Solutions to first
and second-degree equations with a single unknown, using both algebraic and
geometric methods. (2) A method of algebraic multiplication and division.

Al
Khawarizmi defined three
kinds of quantities: (1) Simple numbers, such as 5, 17 and 131. (2) The
root which is the unknown quantity ‘*shay’* in Arabic meaning “a thing” However,
in translations made in Toledo, (the centre for translation of Arabic books),
the absence of a “sh” sound in the Spanish language meant that a suitable
letter had to be chosen. The choice fell upon “x”, which may well explain
why Don Quixote is often pronounced as “Don Quishote”. (3) “Wealth” (*mal*)
the square of the root (x²).

The
algebraic equation expressing the Golden Ratio could therefore be written as:
“x:y = (x + y)/x”. Another virtuoso of algebra was Abu Kamil, a 10th
century mathematician nicknamed the “Egyptian calculator”. He was capable
of rationalizing denominators in expressions that involved dealing with powers
of x (the unknown) as high as the eighth and solving quadratic equations with
irrational numbers as coefficients. Al Biruni (9th/10th centuries)
mathematician and physicist, worked out that the earth rotates on its own axis
and succeeded in calculating its circumference. Abu Bakr Al Karaji (10th
century) is known for his arithmetization of algebra. He also drew the
attention of the Muslim world to the intriguing properties of triangular arrays
of numbers (Berggren 1983). Al Nasawi (10th century) and Kushyar Ibn
Labban worked on problems of the multiplication of two decimals.
Subsequently Kushyar explained the arithmetic of decimal addition, subtraction
and multiplication and also how to calculate square roots. Abu Al Hassan
al Uqlidisi (Damascus 10th century) invented decimal fractions, which proved
useful for judges (*qadis*) in inheritance decisions. Al Karkhi
(d.1019) found rational solutions to certain equations of a degree higher than
two.

Mohamed
Al Battani (Baghdad 10th
century), mathematician and astronomer, computed sine, tangent and cotangent
tables from 0° to 90° with great accuracy. One of his works: Astronomical
Treatise and Tables (*Al-Zij*), corrected Ptolemy’s observations on the
motion of the planets. Al Samaw’al Ben Yahya al Maghribi (1171) drew up
charts of computations of long division of polynomials; one of the best
contributions to the history of mathematics. Ibn Shatir Al Muwaqqit
(Damascus 1375 CE) was an astronomer and the timekeeper of the Damascus
mosque. His treatise on making astronomical devices and their usage and
his book on celestial motions bear great resemblance to the works of Copernicus
(1473-1543 CE). Ghiyat al Din al Kashi (1427 CE) raised computational
mathematics to new heights with the extraction of fifth roots. He also
showed how to express the ratio of the circumference of a circle to its radius
as 6.2831853071795865, identical to the modern formula 2pr.