The Indian civilisation, one of the most advanced in ancient times, made immense contribution to development of scientific knowledge. The Vedas integrated the spiritual and physical sciences and handed the knowledge down to generations through sages and seers. The digit zero and the decimal place value system with numerals 1 to 9 was used in India since the Vedic period. The concept of numerals, which the Arabs introduced to the Western world, was carried over from India.
Algebra or bija ganitha was recognised as the bija or seed of arithmetic. It was in AD 860 that calculations and symbols for unknown quantities called bija ganitha were assigned by Pradhudaka Swamy, since others called it avyakha ganitha to distinguish it from vyaktha ganitha or arithmetic of real numbers. In AD 1150, Bhaskaracharya defined bija ganitha as ?mathematics of unknown quantities to enhance the intellectual capacity of laymen. He said that his branch of mathematics had been invented by mathematicians of the earlier period and he had merely explained it for the benefit of the common man. Hence, it is simply impossible to trace the period of origin of bija ganitha in India.
In AD 1350, Narayana had said that it was Brahma Himself who had handed this knowledge down to man. Bhaskara wrote a comprehensive mathematical treatise which was divided into four parts?the first called ?Lilavathi? dealt with arithmetic, the second called ?Siddhanta Siromany? with mathematical works, the third was ?Goladhyaya? dealt with spherical astronomy and the fourth was ?Graha Ganitha? or motion of planets.
Dr V. Balakrishna Panicker with a doctorate in science has divided his book into two parts to explain basic operations and analyses. The basic mathematical operations of addition, subtraction, multiplication and division, using positive and negative unknown quantities, squaring and finding square roots, and operations with zero and surds are explained in the first part while the second part focuses on the solution of algebraic equations of second degree involving one or more variables. He adds that calculations with negative numbers were common during Bhaskara'speriod. Dr Panicker briefly explains the processes like addition, the six operations with zero, multiplication and division with zero. He says that addition and subtraction of zero from a positive or negative number makes no change in the number; that products of zero are zero; any number multiplied by zero is zero and a number divided by zero gives infinity where infinity is called khahara. He continues that if any number is added or subtracted from infinity, it remains same without change. (This is similar to God [Achyut] who is also endless (anant) and remained unaffected during the period of deluge or creation.) ?During the deluge, infinite number of beings merged with Him and at the time of creation, infinite number of beings emerged out of Him? while God remained unaffected.
In the Vedic period, the acharyas assumed symbols to represent magnitudes of unknown factors in terms of yavat tavat and colours such as black, blue, yellow, red, etc. for unknown factors. Letters ya, ka, ni, pi, etc. were used to identify the different unknowns. Today, however, English alphabets like x, y, z, etc. are used in Algebra for variables.
The author provides problems and equations on vargaprakriti where Nx2 ? c = y2 where N is a non-square integer known as prakriti. It was in AD 628 that Brahmagupta suggested a method of solution for this problem. Similarly a number of other concepts have been explained in this book under which it would prove valuable in developing children'sintelligence in numbers, as numerals constitute the essence of all mathematics.
(Bharatiya Vidya Bhavan, Kulapati Munshi Marg, Mumbai-400007.)
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