A process apparently as simple as counting has passed through many stages before reaching the present level. The Indian invention of Zero has revolutionized the very practice of arithmetic the world over. It is now fairly well established that the so-called Arab Numerals are an Indian invention and are now referred to as Hindu - Arabic Numerals. India gave to the world an ingenious method of expressing all numbers by means of symbols, each symbol representing a value of position as well as an absolute value, a profound and important idea that appears so simple now that we tend to ignore its true merit. Other important Indian contributions in mathematics include calculation of the value of pi, and calculating the square and cube roots of numbers by , Aryabhatta the golden rule of three, and Brahma Gupta's important contribution in the solution of second order indeterminate equation that was later recognized by Europe as the Pell's equation. His lemmas in this connection were rediscovered by Euler (1764CE) and Lagrange (1768CE). The so called Pythagoras theorem also seems to have been worked out by the Indians as evidenced in the verses of Sulba-sutra treatises which predate Pythagoras. Bhaskara II (1150 CE), another stalwart, developed the early concepts of calculus.


Figure 9 : A page from Lilabati, a very important mathematical treatise by Bhaskara II




Ancient Indians achieved great progress in alchemy. It is interesting to note that Joseph Needham claims that earliest distillation of alcohol can be traced back to the archaeological finds at Taxila. Much of ancient chemistry in India grew out of the early efforts to develop an elixir and to turn base metals into gold. The earliest available documented alchemical text in Sanskrit, Rasaratnakara by Nagarjuna was probably part of a larger text Rasendramangala written by the same author. Nagarjuna was the most prominent scholar in the field of Indian alchemy. Rasashala, a typical alchemical laboratory of Nagarjuna, depicts use of a number of special types of yantras, for different chemical purposes like distillation.


Figure 10 : The oldest known distiller in the world (circa 4,000 B.C.) made up of Terra Cotta preserved at the Taxila Museum in Pakistan.