Achievements of Indians in S&T – S Ramanujan's Birth Anniversary

Achievements of Indians in S&T – S Ramanujan

S Ramanujan (1887 - 1920) was an Indian mathematician who lived during the British Rule in India. He was born on 22 December, 1887. Ramanujan was extremely intelligent and had also built a vast knowledge in subjects besides mathematics. He was self taught and had no formal training in Mathematics. He attained distinctions among his peers in arithmetic, English, geography, and Tamil in 1897.

Ramanujam made substantial contributions to the analytical theory of numbers and worked on elliptic functions, continued fractions and infinite 1900 he began to work on his own on mathematics summing geometric and arithmetic series.

He compiled as many as 3900 results and identities in his lifetime. The most important contributions were to mathematical analysis, number theory, infinite series, and continued fractions.

His work on Ramanujan prime, the Ramanujan theta function, partition formulae and mock theta functions continue to open new areas of research.

Among the most famous are Ramanujan Number- also called the magic number which is 1729. It is the smallest number that can be expressed as a sum of cubes of two different sets of numbers. Ramanuja Square is another mathematical puzzle that enthralls all.

A self-taught mathematician who made extraordinary contributions, S Ramanujan was one of the most influential mathematicians of his time.

He worked on divergent series. He sent 120 theorems on imply divisibility properties of the partition function.

He gave a meaning to eulerian second integral for all values of n (negative, positive and fractional). He proved that the integral of xn-1 e-7= ¡ (gamma) is true for all values of gamma.

Goldbach’s conjecture: Goldbach’s conjecture is one of the important illustrations of ramanujan contribution towards the proof of the conjecture. The statement is every even integer greater that two is the sum of two primes, that is, 6=3+3 : Ramanujan and his associates had shown that every large integer could be written as the sum of at most four (Example: 43=2+5+17+19).

Journal of the Indian mathematical society: Ramanujan continued to develop his mathematical ideas and began to pose problems and solve problems in the journal of the Indian mathematical society. He developed relations between elliptic modular equations in 1910.

Besides his published work, ramanujan left behind several notebooks filled with theorems that mathematicians have continued to study. The English Mathematician G.N Watson, from 1918 to 1951, published 14 papers under the general title theorems stated by Ramanujan and in all he published nearly 30 papers which were inspired by ramanjan work. In 1997 ramanujan journal was launched to publish work in areas mathematics influenced by Ramanujan”.

Ramanujan returned to India in 1919 and a year later, he breathed his last at the age of 32. Ramanujan passed away after a long battle with tuberculosis. Many of his mathematical theorems are still in use today.