# One Man, Infinite Possibilities

Updated: May 9

"An equation means nothing to me unless it expresses a thought of god."- S. Ramanujan

It was January 31, 1913, British mathematician G.H. Hardy from Trinity College (Cambridge University) received a parcel from India covering an unfamiliar name, Srinivasa Ramanujan. The parcel contains some papers and a letter addressed to G.H. Hardy by an aspiring Indian youth Srinivasa Ramanujan. In the first paragraph of the letter, Ramanujan introduced himself as a young boy of 23 years working as a clerk in the Accounts Department of the Port Trust Office at Madras (Chennai) on a salary of only £20 per annum. He also wrote about his schooling at an ordinary school with no formal university degree but showed a keen interest and passion for mathematics.

**Facts to know**
He was the first Indian to be elected as a Fellow of the Trinity College and only the second Indian after Ardaseer Cursetjee to be elected as a Fellow of the Royal Society (1918).

The second paragraph of the letter was about the details of his work on mathematics, especially his capability to give the meaning of the negative values of the Gamma function. Hardy was highly surprised by the formulae given in the paper and the exceptional work on prime numbers and gamma function. The second paragraph of the letter made him believe that Ramanujan is not any ordinary person but an exceptional mathematician who has originality and the capability to take mathematics to the next level. Hardy in a statement described this letter as the most important letter he had ever received in his entire life.

**Facts to know**
S. Ramanujan was born as Srinivasa Ramanujan Ayanger in a middle class Brahmin family in Erode (Tamil Nadu). He was a gifted child and exceptionally brilliant in mathematics but he could not clear college exams due to poor performance in other subjects.

In the third paragraph of the letter, Ramanujan showed his knowledge and passion for mathematics. He highlighted his finding and the new theorem that can be of great value for mathematics. Being poor and inexperienced, he also expressed his inability to get it published and urged him to help if he is convinced by his work.

**Facts to know**
Ramanujan credits his mathematical genius to the goddess of Namagiri (Mahalaxmi). He claimed that the goddess gave him visions for his theories in his sleep and he would later try to practically prove them.

This letter introduced a great mathematician to the world who was going to take the field to newer heights. In the reply to the letter, Hardy called Ramanujan a visionary mathematician and expressed his willingness to work together and also help bring his extraordinary work before the world. Ramanujan's work on prime numbers and gamma function was published in leading journals and his work was recognized in the world of Mathematics.

**Facts to know**
G.H. Hardy was a British mathematician associated with the Trinity College, Cambridge University. He was the one who invited S. Ramanujan to Trinity College, Cambridge University, and helped Ramanujan to get published his work.

Ramanujan lived a very short life but before leaving this world at 32, he left behind his great legacy and inspired the generations to come. He independently compiled nearly 4,000 results. His original and highly unconventional results, such as the Ramanujan prime, the Ramanujan-theta function, partition formulae, and mock-theta functions, have opened entire new areas of work and inspired a vast amount of further research.

**Facts to know**
Dr. P.C.Mahalanobis, known as the 'Father of Indian Planning' was the classmate of Ramanujan during his Trinity College days. He is best remembered for Mahalanobis distance.

The genius of man is not bound by age. The great Indian mathematician Srinivas Ramanujan has cast an impact so huge on the mathematical world that people are still trying to fathom his intellect. Ramanujan is regarded as one of the greatest mathematicians the world has ever seen. He lived his life in great misery and struggle but he overcome those odds to become a man of inspiration. To commemorate his contributions to mathematics, his birth anniversary (22 December) is celebrated as National Mathematics Day in India.

**Ramanujan's first letter to ****G****.****H****.**** ****Hardy**
(January 16, 1913)
Dear Sir,
I beg to introduce myself to you as a clerk in the Accounts Department of the Port Trust Office at Madras on a salary of only £20 per annum. I am now about 23 years of age. I have had no University education but I have undergone the ordinary school course. After leaving school I have been employing the spare time at my disposal to work at Mathematics. I have not trodden through the conventional regular course which is followed in a University course, but I am striking out a new path for myself. I have made a special investigation of divergent series in general and the results I get are termed by the local mathematicians as ‘startling’.
Just as in elementary mathematics you give a meaning to when is negative and fractional to conform to the law which holds when is a positive integer, similarly the whole of my investigations proceed on giving a meaning to Eulerian Second Integral for all values of . My friends who have gone through the regular course of University education tell me that is true only when is positive. They say that this integral relation is not true when is negative. Supposing this is true only for positive values of and also supposing the definition to be universally true, I have given meanings to these integrals and under the conditions I state the integral is true for all values of negative and fractional. My whole investigations are based upon this and I have been developing this to a remarkable extent so much so that the local mathematicians are not able to understand me in my higher flights.
Very recently I came across a tract published by you styled Orders of Infinity in page 36 of which I find a statement. that no definite expression has been as yet found for the number of prime numbers less than any given number. I have found an expression which very nearly approximates to the real result, the error being negligible. I would request you to go through the enclosed papers. Being poor, if you are convinced that there is anything of value I would like to have my theorems published. I have not given the actual investigations nor the expressions that I get but I have indicated the lines on which I proceed. Being inexperienced I would very highly value any advice you give me. Requesting to be excused for the trouble I give you.
I remain, Dear Sir, Yours truly,
S. Ramanujan

**About the Ramanujan Mathematics Challenge ****2023**
The genius of man is not bound by age. The great Indian mathematician Srinivas Ramanujan has cast an impact so huge on the mathematical world that people are still trying to fathom his intellect. Although he lived a very short life, he gave millions of Indians a chance to look back and be proud of our unmatched intellectual heritage. This year marks the completion of 76 years of our independence as well as the 136th birth anniversary of the mathematics genius. To commemorate these significant occasions, Youthisthan Foundation is organizing a national-level mathematics olympiad- "The Ramanujan Challenge" for school students from all across the country.

Name the movie based on S. Ramanujan?

- The Founder
- The man who knew infinity
- Infinity
- Pi