### GENIUS OF INDIAN MATHEMATICAL BRAINS

GENIUS OF INDIAN MATHEMATICAL BRAINS

Mathematical knowledge that exists today is a gift from ancient India. Believe it or not, it is true.

One of the Twentieth century’s greatest brains, Albert Einstein had said about India’s contribution in the following words,

“We owe a lot to the Indian’s, who taught us how to count through decimal system, without which no worthwhile scientific discovery could have been made”.

Decimal system: Nine numbers and a zero can be combined to form infinite mathematical expressions and measurements. This knowledge is said to be the unique contribution of ancient Indian genius to world’s progress.

During Vedic times, this decimal system was very much in vogue in India. Yujur Vedha Samhita 17th chapter, 2nd mantra describes the numerical values in a sequence like

Eka, dasa, sata, sahasra, ayuta, laksha, niyuta, koti, arbud, vrinda, kharav, nikharav, Shankla, Padma, saagar, antya, Madhya, parardha etc. Parardha’s value is equal to 10 power 12

A Buddistic text called “Lalitha Visthara” (1st century BC) describes upto 10 power 53 and called that numerical value as “Talakshna”. Another Jain text (Anuyogadwara) describes numbers up to 10 power 140.

During the ancient period, Greeks gave the biggest numerical value called myriad, which is equal to 10 power 4, ie.10000 only.

Biggest Roman numericals were 10 power 3. ie 1000 only. It was called as “milli”.

The numbers from zero to nine were first adopted by Arabs from India and had spread to Europe. Today we call these numericals as Indo-Arab numericals.

Zero’s Glory: Without India’s richest “zero”, the whole of mathematical knowledge becomes zero. Indians used zero not only as the mathematical expression but also as philosophical concept.

Vedas, Upanishads, Puranas and many Indian classical texts had dealt with zero in various ways.

Pingala (2nd century BC) in his Vedagana text “Chandas Sastra” (a guide to study Vedic prosody), while explains Gayatri Chandas mentions zero.

Gayatre sadsamkhyamardhes panite dvyanke avasista srayastesu
Rupampaniya dvyankashah sunyam sthapyam!!

In the domain of Mathematics, usage of negative numbers came into existence because of zero’s inventions.

In Isavasya Upanisat, in the Shanti mantra, there is a verse, which describes the philosophy of zero

purna madah purna midam purnat purna mudacyate

“From zero or completeness everything came and into zero or completeness everything merges zero or completeness alone exists”. In Sanskrit, “purnam” is used to donate “zero” or “completeness.”

Brahma Gupta in his mathematical text “Brahma sputa siddhanta” (written during 620 AD) proves that any number divided by zero becomes infinity.

“Suryapragnapti” (400 BC), a Jain text had classified the numbers into three varieties. It describes five kinds of infinities.

Additions, substractions, multiplications and divisions: squares, square root and cube roots were known to Indians and can be found in most of the mathematical texts in India.

Bhaskaracharya (11 century AD) had said, all kinds of mathematical expressions can be said in two processes. They are (1) Process of increase (2) Process of Decrease. From them all the mathematical concepts evolved.

In the text Ganitasarasangraha (850 AD), Sridharacharya explains LCM, zero, finding square roots and solving quadratic equations etc.

Sridharacharya i his text Pathi-Ganithamdescribes concepts of calculating simple interest, compound interest, problems on time and distance, time taken for filling the water etc.

In Jain manuscripts of Bhakshali, we can find about negative numbers, fractions, sequences of Arithmetic progression and geometric progression etc.

Geometry: Geometry, an important branch of Mathematics had originated in India. The word Geometry is a Sanskrit word which means measuring the earth. “Jya” in Sanskrith means earth, “miti” means measurement. “Jyamiti” or geometry means measuring the earth.

kalpa, Sastra, a part of Vedaganas contains “Sulba Sutras”, which explains the techniques of constructing yajna vedicas (vedic sacrificial altars and platforms). From these verses, the branch of Geometry evolved.

Today, what we call, Pythagoras Theorem is a mere repetition of what had been said in baudhayana “Sulba Sutras”, written five to six hundread years before pythagoras.

dirgha caturasasyaksnya rajjuh parsvamani tiryak mani ca

In a right-angled triangle, the square of the diagonal on the hypotenuse is equal to the sum of squares of other two sides.

Pi value: The value of pi had attracted the attention of every Mathematician whether India or Western, ancient or modern. The pi is constant value of the ratio between circumference and diameter in a circle.

Great Indian Astronomer Aryabatta (5th century AD) had calculated the value of Pi as 3.1416, which is accurate upto four decimals. (Aryabhattiyam-ganitapada-chapter 2-10 verse)

Apart from aryabhatta, Mahaviracharya, Bhaskaracharya, Nilakanta Somayaje, Ramanujam also had calculated the value of pi.

Circling a square and rectangle, which are equal in areas, can be found in Indian Mathematical texts.

Brahmagupta in his text Brahma Sputa Siddanta (12th chapter, 28th verse) describes the mathematical methods for finding the lengths of diagonals of rectangle that is embedded in a circle.

Bhaskaracharya in his book “Leelavati” describes cyclic quadrilateral, cyclic pentagon, cyclic hexagon and cyclic octotogen, and further postulates that sides of quadrilaterals and the diameter of the circle that is circumscribing them shall be in a constant ratio.

Aryabhatta in his text Aryabhattiyam gives the formula for calculation of area of triangle as 1/2BH where “B” is is the base of triangle and “H” is the height of the triangle.

tribhujasya phala sariram samadalakoti bhujartha samvargah |

Trigonometry: Trigonometry is a gift of ancient India in the mathematical world. The concepts of sign and cosign had been evolved by Indian Mathematicians.

Aryabhatta had tablated the several values from sign from 00 to 900 in his famous mathematical workAryabhattiyam.

Bhaskaracharya had postulated various trigonometric principles and equations in his text Leelavathi.

Vaharamihara, Brahmagupta, Lalla and other Indian Mathematicians had given various Trigonometric formulae.

Kerala Mathematician Madhava (1340-1425) in his book “karana paddathi” dealt extensively with Trigonometric formulae and functions.

Calculus: What we call today, “Calculus” was called by ancient Indians as “Kalana Ganana Sastra”. Ages before newton had made use of it, Aryabhatta and Bhaskaracharya had dealt with this branch of Mathematics in their Astronomical calculations.

Bhaskaracharya in his work “Siddhanta Siromani” (4th chapter, Graha Ganita) deals with the concept of differentiation and its application by considering the temporal positions of various planets.

Aryabhatta had pioneered this method of calculating the temporal positions of various planets and had introduced to the world knowledge of Calculus.

Brahmagupta and Madhava had developed this branch of mathematics by introducing Integral Calculus.

Algebra: This branch of mathematics is also an Indian invention. During 9th century AD, Arabs adopted it and from them it has spread to the other parts of the world.

Indian seers of yore like Apasthambha, Baudhayana and Katsyayana in his Kalpa Sutras had intoduced the “unknown’ value in their Mathematical expressions. Afterwards, Aryabhatta, Brahmagupta, Bhaskaracharya, Madhava and others developed various Algebraic formulae, equations and functions.

Bhaskarachaya calls Algebra as Ayakta Ganita or Bija Ganitha’. He had said that Vyaktha Ganitha leads to Ayakthaganita. In his book Leelavathi he deals with vyathaganitha (Arithmetic) before dealing with Ayaktha Ganita.

Indian Mathematical genius is evident from seers of Vedic times to Twentieth century Ramanujam. Today, what we call as computer language (Bakus Normal form) is a replication of Panini’s grammar rules.