A History of Mathematics From Mesopotamia to Modernity

108 A History ofMathematics

BD A

E

F

G

C H

Fig. 2Ab ̄u-l-Waf ̄a’s construction of the regular pentagon.

Greek ‘We...’ is mixed with the artisans’ ‘If someone asks you,...do’. And one wonders how often

artisans might have needed to construct a regular pentagon. There is an evident wish to publicize

Greek geometry and to extend its audience, as al-Uql ̄idis ̄i wishes to make propaganda for the Hindu

numbers. ‘Real’ mathematics, expounded systematically in books, has suddenly entered a realm of

popularization for practical men.

Exercise 1.Explain al-Uql ̄idis ̄i’s calculation.Why does one say ‘Is, is not, is’?

Exercise 2.Justify ab ̄u-l-Waf ̄a’s construction.

4. The golden age

The most venerable legal scholar Ab ̄u Bakr ibn Muh.ammad al-Yafrash ̄i told me in Zab ̄id the following story: It is related

that a group of people from F ̄ars with a knowledge of algebra arrived during the caliphate of ‘Umar ibn al-Khat ̄ .t.ab

[634–644]. ‘Al ̄i ibn Ab ̄iT.alib—may God be pleased with him—suggested to ‘ ̄ Umar that a payment from the treasury ̄

be made to them, and that they should teach the people, and ‘Umar consented to that. It is related that ‘Al ̄ ̄i—may God

be pleased with him—learned the algebra they knew in five days. Thereafter the people transmitted this knowledge

orally without it being recorded in any book until the caliphate reached al-Ma’mun and the knowledge of algebra had

become extinguished among the people. Al-Ma’m ̄un was informed of this and he made inquiries after someone who

had experience in (algebra). The only person who had experience was the Shaykh Ab ̄u Bakr Muh.ammad ibn M ̄us ̄a

al-Khw ̄arizm ̄i, so al-Ma’mun asked him to write a book on algebra, to restore what had been lost of (the subject).

(Brentjes 1992, pp. 58–9)

The above apocryphal story^5 of the arrival of algebra links the beginning of Islam with the

beginning of mathematical knowledge among the Arabs. Significantly, however, it also introduces

a ‘group of people from F ̄ars’ (Persia) who are responsible for its introduction; and it illustrates

our ignorance of the first century of Islam, particularly in drawing attention to the oral tradition

and the lack of writing. All other evidence which we have tells a different story: while the origins

of Greek and Chinese mathematics are unclear and undocumented, Islamic mathematics begins

5. From the ease with which ‘Al ̄i learns algebra, the story appears to be Shi’ite in origin, but Brentjes gives no further information
   on this.