Hindu and Arabic Algebra

Little is known about Hindu maths before the fourth or fifth century A.D. because few records of the ancient period have been found. India was subjected to numerous invasions, which facilitated the exchange of ideas. Babylonian and Greek accomplishments, in particular, were apparently known to Hindu mathematicians. The Hindus solved quadratic equations by "completing the square" and they accepted negative and irrational roots; they also realized that a quadratic equation (with real roots) has two roots. Hindu work on indeterminate equations was superior to that of Diophantus; the Hindus attempted to find all possible integral solutions and were perhaps the first to give general methods of solution. One of their most outstanding achievements was the system of Hindu (often called Arabic) numerals.

Algebra in Europe

In the eleventh century many Greek and Arabic texts on maths were translated into Latin and became available in Europe. However, even more important for Europe, especially Italy, was the Liber Abaci (1202) of Fibonacci (Leonardo of Pisa) in which he solved equations in the rhetorical and general style and strongly advocated the use of Hindu-Arabic numerals, which he discovered on his journeys to many lands as a merchant and trades­man. It is not surprising that at first the local chambers of commerce (in Pisa and neighbouring city-states of Italy) resisted the adoption of the "new" Hindu-Arabic numerals and, in fact, viewed them with suspicion; but they were gradually adopted, and the old abacus was stored in the attic.

The algebra that entered Europe (via Fibonacci's "Liber abaci" and translations) had retrogressed both in style and in content. The semisymbolism of Diophantus and relatively advanced accomplishments of the Hindus were not destined to contribute to the eventual breakthrough in European algebra.

Active Vocabulary

abacus	cumbersome
accomplishment	destine
advanced	eventual
appropriate	invasion
attempt	merchant
attic	rectangle
avoid	sophistication
breakthrough	suspicion
chamber of commerce	tablet
clay	facilitate
clumsy	lack
content	subject

2. Answer the following questions:

1. Where did algebra probably originate?

2. What is Babylonia credited with?

3. What equations were the Babylonians able to solve?

4. When did algebra appear in Egypt?

5. What did Egyptian algebra lack?

6. What explains the lack of sophistication in Egyptian algebra?

7. What was the algebra of the early Greeks?

8. What were the difficulties the Greeks experienced?

9. What style did the Greek mathematicians use?

10. What caused the Greeks to give their algebra geometrical formulation?

11. Why is it known little about Hindu maths before the fourth and fifth century A.D.?

12. What equations did the Hindus solve?

13. What did the Hindus attempt to find?

14. What are the most outstanding achievements of the Hindus?

15. When did Greek and Arabic texts on maths become available in Europe?