Indian Mathematicians

CONTRIBUTION OF RENOWNED INDIAN MATHEMATICS

The height which mathematics is occupying today and the progress which it has made through the ages are all due to the dedicated and sustained work of many great indian mathematicians also .The life history and contribution of some great indian mathematicians such as Aryabhata,Bhaskaracharya,Brahmagupta and Ramanjujan are presented below.

1.     Aryabhata

Aryabhata was the first among the great Indian mathematician.He lived from 475 to 550 AD near Patna.He was the first person to present arithmetic,algebra and geometry in his astrological calculation.He had written four famous books on mathematics. Tese are Aryabjatyia which is a collection of astronomical tables, Ayastasata which is a note on numeration in arithmetic, Kalakriya which is a note on time and its measurement, and Gola which is a note on the sphere.

Aryabhatyia has been divided into four parts: i. Gati-Paadika, ii. Ganti-Paadika, iii.  Kaal-Kriyapaad and iv. Ga-paad. In shlokas of this collection, he has mentioned five basic principles of mathematics,decimal system,methods for calculating area of a rectangle,triangle,circle,curved surface of cone and volume of sphere. In one shloka, it has been explained that if the diameter of a circle be 2000 units, then its circumference will be 62832 units. This gives the value of pie correct to four decimal places. In other shlokas, the methods of construction of triangle, circle, quadrilateral, etc. have been given

He suggested the use of letters to represents unknown. He gave a general solution of a linear indeterminate equation by the method of continued functions. He gave the formula for the volume of a pyramid as half of the product of the base and the height. He gave almost all the formulas for calculating the areas of different geometrical figures.

He gave the identity,. He explained the famous Pythagoras theorem as under: “The sum of square of Bhuja and the square of Koti is equal to the square of Karna.”

He was also the master of astronomy. He wrote a book containing a collection of astronomical tables. He propounded the fact that the earth body and that it revolves round the sun. This fact was realized by Copernicus and Galileo in  century after about 1100 years. He had also made calculations of the rotation of the earth on its axis. In this way he contributed to almost all the braches of mathematics. He was one of the greatest Indian mathematicians of whom the country is really proud. In his memory and honour the first satellite launched to the space by India was given the name ‘Aryabhatta’.

2.    Bhaskaracharya

Bhaskaracharya was also known as Bhaskara the learned. He was born in 1114 A.D in Bijapure, Mysore state. He belonged to an old learned and noble family, possessing an established tradition of scholarship. His father as well as Guru, Maheshwar was learned man in the Vedas and Shastras. Bhaskara has been the mostelegant and creative mathematician India ever produced. He served as head of the astronomical laboratory at Ujjain

Bhaskara wrote Sidhanta Siromani in 1150 A.D at the age of 36 years. It is divided into four mini parts namely Lilavati, Vijajanit, Goladhyaya and Grahganit. Each part is sub-divided into several chapters. The first part is known as “Lilavathi”, in memory the name of his daughter. In this book, questions have been composed in avery interesting manner in the form of slokas. In addition to this he wrote other valuable books like Karam Kotuhal, Samaya, Sidhanta Siromani, Rasguna, Surya Sidhanta, etc.

For the first time, he introduced the idea that dividing a number by zero will result in infinity. He contributed much to the field of mensuration and gave many important formulae for the computation of the areas and volume to the different figures/solids.

Bhaskara presented a complete and systematic explanation of the Indian method of solving determinate and indeterminate problems. His problems included the topics of sales and purchase, interest, gems, gold, permutation of syllables in stanza, military marches, excavations and the measures of grains.

He is known for the poetic presentation of complicated and abstract problems. In this way, he presented for the first time a suitable method of teaching mathematics in interesting manner, revealing the real beauty of the subject. His work may be qualified as poetry in mathematics. He also had the knowledge of gravitational power long before newton. In every sense he was a celebrated astronomer and mathematician

It is said that bhaskara’s grandson, chagadwan, was the chef astrologer to king singhana and that in his time a college was founded to expound the doctrines of Bhaskara, which was a great tribute to his great memory. He shines like sun in the world of mathematics.

3.    Brahmagupta

Brahmagupta was the son of vishnugupta and was born in Punjab in 598 A.D. He lived in Ujjain and worked as head of the great astrological laboratory at Ujjain, which was foremost mathematical center of ancient India.

He wrote Brahma-Sphuta-siddhanta (The opening of the universe) and the age of 30. It consists of 21 chapters and contains great knowledge on arithmetic, geometry, algebra and astronomy. This book helped the Arabs to get acquainted with Indian astronomy. It was translated into Arabic in the  century.

In his calculation he was consider the value of  as 10. In the chapter in arithmetic he was given a detailed account of progression, areas of triangles and quadrilaterals, volumes of trenches and slopes, account of grains in heaps, etc. He also invented for different methods of multiplication, namely i. Gan Mutrika. ii. Khanda. iii. Bheda, and iv. Ista.

He was particularly concerned with series and permutations. He gave the rules of signs for their operations and distinguished between the two classes of numbers by writing a dot or a small circle over those that were negative. His work on arithmetic includes integers, fractions, progressions, barter, simple interest, mensuration of plan figures and problems on volume. In writing the fractions, the scheme of writing the numerator above the denominator was used by him.

Brahmagupta was the first Indian writer, who applied algebra to the astronomy. He was a great mathematician, an astronomer and a poet. While commenting on his contribution the famous mathematician Baskaracharya designated a brahmagupta as “Gem of the circle of mathematicians” and surely brahmagupta was quite fit for such honour.

4.   Ramanujan

Ramanujan was born in 1887 in Tamil Nadu. His father was an accountant of cloth merchant at Kumabaka Konam while his mother was the daughter of a petty official in the district Munsif’s caught at Erode. Ramanjun was quiet and meditative and possessed and extraordinary memory. He passes his matriculation exam at 16 but he could not do well at college. After a while, he took up a small appointment a rupees 30 per month in Madras Port Trust Office. One of was published in the journal of the Indian Mathematical Society in 1911 at the age of 23. In 1912, Ramanujan got a scholarship of rupees 75 per month from the Madras University. In 1914 he was invited to Cambridge University to study mathematics at the expense of the University of Madras. In 1915, prof. hardy wrote, “He is beyond question the best Indian of modern times”. In 1916 he got honorary of B.A. degree from the University of Cambridge. About Ramanujan prof. Hardy writes, “I learned from him much more than he learned from me”. In 1918 he was elected as fellow of Royal Society.

He produced a number of results in the field of Definite integrals in the form of general formulae. The partition of whole number is also one of the problems which encaged the attention of Ramanujan. Take the case of number 3. There are alternative ways to write it 3+0, 1+2, 1+1+1. You may easily verify that there no other ways of partitioning this number if we do not wish to use fractional numbers.

                      Gobbacki conjecture is one of the important illustrations of Ramanujan’s contribution. The statement is that every even integer greater than 2 is the sum of two primes, that is number having divisors. Thus 4 is the sum of two primes 2 and 2; 6 of the prime of 3 and 3; 8 of the primes of 3 and 5 and so on.

Through he had no schooling in modern mathematics; he could work out modular equations and theorems of complex multiplications in a manner unheard of. His mastery of continued fraction was beyond that of any mathematicians in the world