# Ramanujan Contribution To Mathematics

(1) Ramanujan was born on 22nd of the December 1887 in a small town Erode, Madras Presidency. He had made many extraordinary contributions to the mathematical analysis, infinite series, number theory, and continued fractions.

(2) He had demonstrated an unusual mathematical skill at the school, winning some accolades and awards.

(3) By 17, he had conducted many of his own mathematical research on the Bernoulli numbers and many on the Euler-Mascheroni constant.

(4) He had discovered many theorems of his own and then rediscovered the Euler’s identity independently.

(5) He had even sent a set of total 120 theorems to the Professor Hardy of Cambridge. As a result he had invited Ramanujan to the England.

(6) He independently compiled nearly about 3900 results (mostly identities and various equations).Nearly all of his claims have now been proved correct.

(7) Ramanujan had showed that any kind of big number can be easily written as the sum of not more than four prime numbers.

(8) He showed the method of how to divide any number into two or more type of squares or cubes.

(9) Ramanujan’s Number: When the Mr. G.H. Hardy came to see the Ramanujan in taxi number 1729, G.H Hardy also stated Ramanujan that the number 1729 seemed to be a dull number, and hoped that it does not turn out to be any kind of unfavorable omen. But the Ramanujan in contrary said it is a very unique and interesting number, 1729 is the smallest number which can be easily written in the form of the sum of cubes of any two numbers in these two ways, i.e 1729=1³+12³=9³+10³. Since than the number 1729 is called as Ramanujan’s number.

(10) In 1918, Ramanujan and the Hardy studied the partition function P(n)extensively and gave a new non‐convergent asymptotic series that had permited exact computation of the new number of partition of any integer.

(11) He discovered that the mock theta function in the very last year of his life .For many years these kind of functions were a type of mystery, but they are now formally known to be as the holomorphic parts of the harmonic weak mass forms.

Total Ramanujan’s published papers — 37 in total — by the professor Bruce C. Berndt reveals that &quot;a very huge portion of his work was left behind in only three notebooks and 1 lost notebook. These kind of notebooks contain approximately about 4000 claims, all without any proof. Most of these type of claims have now been successfully proved, and like his all published work, he continue to inspire the modern-day mathematics.