Serious mathematical sciences were learnt by the Arabs from the Greeks. [but
not everything was learnt from them]
Two main sources of the early information of the theory of numbers [not Arab]
1)
Elements by Euclid: 1
st
major Greek mathematics book - translated by Ishaq
bin Hunayn [later revised by
Thabit bin Qurrah
– translator of most
mathematical works]

2)
The Introduction to the Science of Numbers by Nicomachus: translated by
Thabit bin Qurrah. This book strongly influenced the authors of the Epistles of
the Brethren of Sincerity.
For the ancient Greeks [Elements], irrational numbers existed as geometrical
magnitude. However, some Islamic mathematicians prefer to express ratios in
terms of continued fractions but eventually regarded all ratios as numbers.
Thabit bin Qurrah:
Wrote noteworthy remarks on infinite collections, believing that an infinite
collection could be a part of another infinite collection.
Was one of the mathematicians that worked on parallel problems.
He argued that motion is at the base of the whole of geometry. [supported
by Ibn al-Haytham, refuted by al-Khayyami].
Umar al-Khayyam
:
Persian polymath.
Philosopher, mathematician, astronomer and poet.
Wrote treatises on mechanics, geography, mineralogy, music and Islamic
theology.
Wrote the influential
Treatise on Demonstration of Problems of Algebra
.
This developed the principles of algebra.
He derived general methods for solving cubic equations and equations
with higher orders.
Mohammad al-Khawarizmi:
Muslim scientist from Persia.
Adapted Ptolemy’s Geographike Hyphegesis [Geographic Guidance].
Wrote the first book in arabic on figure reckoning.
Used indian and Greek sources, and a Euclidean geometrical method.
“Father of Algebra”; “algorithm”.
Kitab Al-Jabr wa Al-Muwabalah
at the end of the 12
th
century.
Al Hassan Ibn al-Haytham:
Muslim scientist of Arab origin [most likely Egyptian].
Contributed to mathematics and physics, particularly optics.
He wrote
Kitab al Manazir
[Book of Optics] where he formulated “Alhazen’s
problem” – for any two points opposite a reflecting surface to find the
point(s) on the surface at which the light from one of the two points will be
reflected to the other.
This book discusses vision and light, and the basic idea of a camera comes
from this book.
Hisab: the art of reckoning. Three different systems were inherited by the Arabs:
1.
Finger reckoning
: numbers expressed in words, not in symbols. Also known as
the arithmetic of the scribes. Counting by fingers
2.
Figure reckoning
: came from India. Able to express any number by means of
nine figures and a symbol [0] indicating an empty place in an array of figures.