The History of Mathematics: A Brief Course

3. THE MUSLIMS^57

Abu-Kamil. Although nothing is known of the life of Abu-Kamil (ca. 850-93), he

is the author of certain books on algebra, geometry, and number theory that had

a marked influence on both Islamic mathematics and the recovery of mathematics

in Europe. Many of his problems were reproduced in the work of the Leonardo of

Pisa (Fibonacci, 1170-1226).

Abu'l-Wafa. Mohammad Abu'l-Wafa (940-998) was born in Khorasan (now in

Iran) and died in Baghdad. He was an astronomer-mathematician who translated

Greek works and commented on them. In addition he wrote a number of works on

practical arithmetic and geometry. According to RTashid (1994), his book of prac-

tical arithmetic for scribes and merchants begins with the claim that it "comprises

all that an experienced or novice, subordinate or chief in arithmetic needs to know"

in relation to taxes, business transactions, civil administration, measurements, and

"all other practices... which are useful to them in their daily life."

Al-Biruni. Abu Arrayhan al-Biruni (973-1048), was an astronomer, geographer,

and mathematician who as a young man worked out the mathematics of maps of

Earth. Civil wars in the area where he lived (Uzbekistan and Afghanistan) made

him into a wanderer, and he came into contact with astronomers in Persia and Iraq.

He was a prolific writer. According to the Dictionary of Scientific Biography, he

wrote what would now be well over 10,000 pages of texts during his lifetime, on

geography, geometry, arithmetic, and astronomy.

Omar Khayyam. The Persian mathematician Omar Khayyam was born in 1044 and

died in 1123. He is thought to be the same person who wrote the famous skeptical

and hedonistic poem known as the Rubaiyat (Quatrains), but not all scholars agree

that the two are the same. Since he lived in the turbulent time of the invasion of the

Seljuk Turks, his life was not easy, and he could not devote himself wholeheartedly

to scholarship. Even so, he advanced algebra beyond the elementary linear and

quadratic equations that one can find in al-Khwarizmi's book and speculated on

the foundations of geometry. He explained his motivation for doing mathematics in

the preface to his Algebra. Like the Japanese wasanists, he was inspired by questions

left open by his predecessors. Also, as with al-Khwarizmi, this intellectual curiosity

is linked with piety and thanks to the patron who supported his work.

In the name of God, gracious and merciful! Praise be to God, lord

of all Worlds, a happy end to those who are pious, and ill-will to

none but the merciless. May blessings repose upon the prophets,

especially upon Mohammed and all his holy descendants.

One of the branches of knowledge needed in that division of

philosophy known as mathematics is the science of completion and

reduction, which aims at the determination of numerical and geo-

metrical unknowns. Parts of this science deal with certain very dif-

ficult introductory theorems, the solution of which has eluded most

of those who have attempted it... I have always been very anxious

to investigate all types of theorems and to distinguish those that

can be solved in each species, giving proofs for my distinctions, be-

cause I know how urgently this is needed in the solution of difficult

problems. However, I have not been able to find time to complete

this work, or to concentrate my thoughts on it, hindered as I have

been by troublesome obstacles. [Kasir, 1931, pp. 43-44]