Give Indians proper credit for Algebra
By Vir Gupta
During his speech on June 4 in Cairo, Egypt, President Barack Obama gave credit to Muslims for invention of many things, including algebra. I would like to bring out the facts about the history of Algebra.
The credit for the first use of algebra probably goes to the Babylonians, who solved some quadratic problems verbally, but recognized only positive roots. During the time of Plato, Greeks used geometry to solve algebraic problems. Later, Diophantus (about 350 A.D.) wrote some rules for multiplication and division and solved some simple problems in “Arithmetica”. His algebra was syncopated and rhetorical.
Indians have a long history of using mathematics.Fire altars were constructed using Pythagora’s theorem long before Pythagoras. A decimal system for weights and measures was used in the Indus Valley (2500 B.C.). Numbers in multiples of 2, 7, 10, 100 and even one million are found in several books, including “Narad Vishnu Purana” (1000 B.C.), “Anuyog Dwara Sutra ” (100 B.C.), “Lalitvistara” (100 A.D.) and several Mahayana Buddhist books. “Anuyog Dwara Sutra” also gives multiplication of square roots of square roots. Basic use of logarithm appears in “Satkhandagama” (150 A.D.).
The Bakhshali manuscript (200 A.D.) found near Peshawar in Pakistan includes fractions, square roots, quadratic equations, simultaneous equations, arithmetic and geometric progressions etc.
Aryabhatta (499 A.D.), a great Indian astronomer, wrote 118 verses in “Aryabhattiya” which cover several areas including arithmetic, algebra, plane and spherical trigonometry. It includes continued fractions, square roots, cube roots, quadratic equations, sum of power series and a table of sines. He introduced the Kuttaka method (breaking down of original factors into smaller numbers). He gave the circumference of Earth as 4,967 yojanas (24,835 miles) and stated that Earth moves around the sun long before Copernicus.
Brahmgupta (628 A.D.), another eminent Indian astronomer, wrote “Brahm-saphuta-siddhanta”, containing 25 chapters in which he gave several rules for arithmetical operations involving zero. He solved several quadratic equations and gave both positive and negative roots. In his book, he also solves several indeterminate problems.
In addition, he worked on trigonometry and gave the area of cyclic quadrilaterals and the interpolation formula for computation of sines. In astronomy, he dealt with lunar eclipses, etc. He introduced some symbols in algebra, but it was mostly syncopated.
Other Indians who made significant contributions to arithmetic/algebra include Varahamihir (505 A.D.), Bhaskara I (680 A.D.), Mahavira (800 A.D.), Madhva (850 A.D.) and Bhaskara II (1114 A.D.). Mahavira wrote solutions to several arithmetic operations, including fractions, permutations and combinations, and areas of ellipses. The works of Bhaskara II, include beej ganita (algebraic root extraction), astronomy, the solution to Pell’s equation, solutions to indeterminate problems by the Chakrawaat method and Diophantine problems. He broached the fields of infinitesimal calculation and integration. He postulated the existence of gurutava (gravitational attraction).
Destruction of several universities by Muslim invaders around 724 A.D., 786 A.D. and 1200 A.D. brought an end to India’s dominance in the field of mathematics.
During the 8th century A.D., several Sanskrit works were translated into Arabic in Baghdad. (Baghdad means “gift of God” in Sanskrit.) During the 9th century A.D., Caliph al-Mamun established a “House of Wisdom” in Baghdad and invited scholars from many countries, including India, Persia, and Greece, etc., to translate mathematical and other works into Arabic. Persian scholar al-Khwarizmi wrote about half a dozen books on astronomy and mathematics.
His most famous work, “Hisab al-jabr wa’l muqabalah”, was written around 830 A.D. It consists of six chapters, each dealing with a different formula. Muslims give him credit for the invention of algebra. As per O’Connor and Robertson, researchers at the University of St. Andrews, Scotland, al-Khwarizmi visited India and took with him several mathematical works to Baghdad. His book on algebra was based mostly on the works by Brahmgupta (628 A.D.). Most of his algebra can be described as rhetorical.
Muslim scholars never developed symbols, which were necessary for advancement. They also rejected negative roots of quadratic equations, although they had learned from Hindus, as per O’Connor and Robertson. However, they improved upon the Hindu number system and the positional notations. Other notable Muslim scholars include al-Karkhi (953 A.D.), Omar Khayyam (1050 A.D.), al-Tushi (1135 A.D.) and Jamshid al-Kashi (1380 A.D.). The work of al-Khwarizmi and other Muslim scholars reached Europe around 1200 A.D. and they mistakenly gave credit for the invention of zero and other numerals – and algebra – to Muslims.
On the whole, Muslims’ contribution to the advancement in algebra is very small.
The real credit should go to Indians. As far as Obama is concerned, he should present only the facts.
Shree Vir Gupta is a nuclear/chemical engineer with a deep interest in Hinduism and Buddhism.