ORIGIN OF MATHEMATICS IN INDIA
The Beginnings
The great Indian mathematician Aryabhata (476-529) wrote the Aryabhatiya ─ a volume of 121 verses. Apart from discussingastronomy, he laid down procedures of arithmetic, geometry, algebraand trigonometry.He calculatedthe value of Pi at 3.1416 and covered subjects like numerical squares and cube roots. Aryabhata is credited with the emergence of trigonometry throughsinefunctions.
Around the beginning of the fifteenth century
Madhava (1350-1425) developed his own system of calculus based on his knowledge of trigonometry.He was an untutoredmathematician from Kerala, and preceded Newton and Liebnitz by a century.
Aryabhata
The twentieth-centurygeniusSrinivas Ramanujan (1887-1920) developed a formula for partitioning any natural number, expressing an integer as the sum of squares, cubes, or higher power of a few integers.
Origin of Zero and the Decimal System
The zero was known to the ancient Indians and most probably the knowledge of it spread from India to other cultures. Brahmagupta (598-668),who had worked on mathematics and astronomy, was the head of the astronomy observatory in Ujjain, which was at that point of time, the foremost mathematical centre in India; he and Bhaskar the second (1114-1185), who reached understanding on the number systems and solving equations, have together provided many rules for arithmetical operations with the zero.
Srinivas Ramanujan
Varahamihira (505-668) who was educated in
Kapitthaka and was one of the patrons of the schoolof mathematicsin Ujjain, worked on Hindu astronomy before Aryabhata.He wrote manuals called Panchasiddhantika which refer to the addition and subtractionof zero.
Vasubhandu (around 400 AD), who was born into a Hindu family but later converted to Buddhism, expressed his belief that the stars were representativeof the zero and placed thereby the Creator to remind humankind of the transience of the world and all beings. The symbols for nine numerals and a symbol for zero were well-establishedby the fifth centuryAD.
The decimal systemis believedto have originated in India. Arab Mathematicians – Al Khawarizmi and Al-Nasavi in 825 AD and 1025 AD respectively– refer to it as ta-rikh ai Hindi and
al-amal al-Hindi.
The Three Pramanas
The acquisition of mathematical knowledge and competencecovers three aspects that are in fact the mainstay for masteringany discipline:
a) Pratyakshai.e. perception
b) Anumana i.e. inference
c) Agama or Sabda i.e. traditional or textual knowledge.
These three together are knownas pramanas.
History of Geometry
The science of geometry originated in India in connection with the construction of the altars meant for Vedic sacrifices. Sulbas are studies in early Hindu geometry.
The Sulbas or the Sulba Sutras are the manuals for the construction of the altars for worship.Dr BibhutibhushanDatta, author of History of Hindu Mathematics,in his The Scienceof the Sulba has described a number of postulates, which must have been tacitly assumed by the geometers of the Sulba for the geometric operations. The postulates of the Sulba are connected with the division of figures such as straight lines, rectangles,circles and triangles.
The postulates
1. A given finite straight line can be divided into any numberof equalparts.
2. A circle can be divided into any number of equalparts by drawing diameters
3. Each diagonalof a rectanglebisectsit.
4. The diagonals of a rectangle bisect one another.
5. The diagonals of a rhombus bisect one another at rightangles
6. A triangle can be divided into a number of equal and similar parts by dividing the sides into an equal number of parts and then joining the pointsof divisiontwo and two.
7. An isoscelestriangleis divided into two equal parts by the line joining the vertex with the middle pointof the base.
8. A triangleformedby joining the extremitiesof a square to the middle point of the opposite sideis equal to half the square.
9. A quadrilateral formedby the lines joining the middle point of the sides of a square has an area half of thatof the originalsquare.
10. A parallelogramand a rectanglewhichare on the same base and within the same parallels are equalto oneanother.
11. The maximum square that can be described within a circle is the one thathas its corners on the circumferenceof the circle.
Overall, many core mathematics formulae and theorems originate from India. The roots of the presentprogressin algebraand astronomycan all be traced back to the work done by our ancient mathematicians
