Mathematical Sciences

The most extensive cultivation which astronomy received at the hands of the Hindus is in itself a proof of their high proficiency in mathematics. The high antiquity of Hindu astronomy is an argument in support of still greater antiquity of their mathematics. The Hindus were the inventors of the numerals and the great German critic Schiegel says that “the decimal cyphers the honour of which, next to letters is the most important of human discoveries, has, with the common consent of historical authorities, been ascribed to the Hindus.”

Sir M. Monier William says “From them (Hindus) the Arabs received not only their first conceptions of algebraic analysis, but also those numerical symbols and decimal notations now current everywhere.”

Says W V Hunter “To them (Hindus) we owe the invention of the numeral symbols on the decimal scale, the Indian figures 1 to 9 being abbreviated forms of initial letters of the numerals themselves, and the zero or 0 representing the first letter of the Sanskrit word for empty, “Shunya” The Arabs borrowed them from the Hindus and transmitted them to Europe.”

Algebra

In Algebra the ancient Hindus understood well the surd roots and the general resolution of equations of the second degree. Algebra developed with astronomy; so one can assume that it was in practice around 3000-2500 B. C.

Sage Bhaskaracharya wrote the book the Siddhanta Siromani, containing treatises on algebra and arithmetic. His division of a circle is remarkable for its minute analysis, which is as follows:

60 Vikalpa (seconds) - A Kala (minute)
60 Kala - A Baga (degree)
30 Bhaga - A Rasi (sign)
12 Rasi - A Bhagana (revolution)

Aryabhata and Bhaskaracharya were well known scientists of the time. Bhaskaracharya, according to Mr. Lethbridge, “... discovered a mathematical process very nearly resembling the differential calculus of modern European mathematicians.

Geometry


The ancient Hindus made remarkable progress in geometry, which was known in India long before the writing of Surya Siddhanta (2000 B.C.); which contains a rational system of trigonometry. It is founded on a geometrical theorem employing the sine of arcs and involves theorems not discovered in Europe till a couple of centuries later.

“They (Hindus) demonstrated various Properties of triangles, specially one which expresses the area in terms of the three sides and the knowledge of the proportions of the radius to the circumference of a circle, by applying one measure and one unit to the radius and circumference. This proportion was not known out of India until modern times.”

Researches have brought to light astronomical tables in India which must have been constructed by the principles of geometry and are said to be older than 3000 B. C. Some well known ancient scientists were Aryabhata (5th century A.D.), Sridharacharya, author of Patiganita (9th century A. P.), Bhaskara (629 A. D.) and Bhaskara 11(1114 A.D.).