# The Prince of Intuition

Ramanujan was born on 22nd December 1887 in Madras Presidency (now Tamil Nadu), at the residence of his maternal grandparents. His father Kuppuswamy Srinivasa Iyengar worked as a clerk in a sari shop while his mother Komalatammal used to sing bhajans at a nearby temple.

Ramanujan’s full name was Srinivasa Ramanujan Iyengar. Here Srinivasa was just his father’s name and it was rarely used. Iyengar was the caste name which indicated from which branch of South Indian Brahmins does the family belong to. Ramanujan means the younger brother(anuja) of Rama (the seventh avatar of the Hindu god Vishnu). His mother often called him Chinnaswami which meant little lord.

When Ramanujan passed his primary exams in English, Tamil, Geography and Arithmetic, he got the best score in the district. But still he didn’t like the schools in Madras and tried to avoid it, so his family had to hire a constable to scare him back to class. One day, his mathematics teacher pointed out that anything divided by itself is equal to 1. Then Ramanujan asked the teacher was 0 divided by 0 equal to 1.

In the year 1893 Ramanujan received the book – SL Loney’s Trigonometry which was his first exposer to the advanced realms of mathematics. He had mastered the book by the time he was 13. From an older boy, he learnt how to solve cubic equations. He understood trigonometric functions not as the ratios of the sides of right-angled triangles but in a far more complex way that involved infinite series. He would complete the exams in half of the allotted time. Students that were 2 years senior to him would hand him problems that they thought to be difficult which would be solved by Ramanujan with just a glance.

At a ceremony in 1904, Ramanujan was awarded the K. Ranganatha Rao prize for mathematics. Headmaster Krishnaswami Iyer introduced him to the audience as a student who, were it possible, deserved higher than the maximum possible marks.

Ramanujan had complete faith on Namagiri of Namakkal to whom later in his life he credited for helping him it mathematics by providing him with formulas. Therefore Ramanujan once quoted that – “An equation for me has no meaning unless it expresses a thought of God.”

The book that brought the most change in Ramanujan was George Shoobridge Carr’s Book – Synopsis of Pure Mathematics. This book was a compilation of nearly 5000 theorems that were written one after another that ranged in different areas of mathematics. He divided the book into 2 parts(the second part Ramanujan didn’t see until later). The results that Carr provided in his book had no proves and sometimes he gave a vague idea how to approach to prove a theorem as he wanted the students to be actively participated in mathematics rather than being passive.

Later in his college, he started to stop giving focus to other subjects except for mathematics so he started to fail in other subjects so his scholarship was taken from him. His parents were also under financial burden. So one so not able to handle the situation he ran away from his home.

The first problem that Ramanujan published in the Journal of Indian Mathematical Society asked the readers to evaluate the following infinite series:-
latex \begin{aligned}\sqrt{1\ +2\sqrt{1\ +\ 3\sqrt{1\ +\ 4\sqrt{…}}}}\\ \\ \\\end{aligned}

Three issues of the Journal went by but (which was 6 months) but no solution was offered. So Ramanujan supplied the solution himself. He used the following formula to solve the problem:-
latex \begin{aligned} x\ +\ n\ +\ a\ =\ \sqrt{ax\ +\ ( n+a)^{2} \ +\ x\sqrt{a( x+n) \ +\ ( n+a)^{2} +\ ( x+n)\sqrt{…}}}\\ \end{aligned}

So here the value of a = 0, x = 2 and n = 0 so the answer to the problem was 3. But how Ramanujan came up with formula is scarcely obvious.

The problem that Ramanujan asked the readers was difficult as it didn’t deal with a finite thing but something of infinite length.

Ramanujan is called to be the man who knew infinity as no one had explored this terrain more enthusiastically and knew it more intimately than him.

In the year 1913, Narayana Iyer, Ramachandra Rao and E.W. Middlemast presented Ramanujan’s work to the British Mathematician M. J. M. Hill of the University College of London. He found Ramanujan’s papers to have errors so he only gave Ramanujan serious and thorough professional advice on his work. So later with the help of Ramanujan’s friends, he wrote 3 letters to leading mathematicians at Cambridge University. The first 2 professors, H.F. Baker and E.W. Hobson returned Ramanujan’s papers without any comment. The third professor was GH Hardy.

Hardy categorised the results that Ramanujan sent him into 3 categories, i.e, those that are completely wrong, those that have already been discovered and those which in Hardy’s words – “defeated me completely: I had never seen anything in the least like them before. A single look at them is enough to show that they could only be written down by a mathematician of the highest class. They must be true because, if they are not true, no one would have the imagination to invent them.”

Hardy with the help of Neville brought Ramanujan to Cambridge. When he was first offered to travel to Cambridge he rejected as he would lose his caste as it was prohibited for Brahmins to cross the seas. But once in Ramanujan’s mother’s dream, Namagiri instructed Ramanujan’s mother to let Ramanujan cross the seas after which Ramanujan went to the Namagiri’s temple in Namakkal until he receives her order. So when he did, he started to prepare to go to Cambridge. So in 17th Match 1914 on the ship S. S. Nevasa, he travelled to England.

Madras University supported Ramanujan by giving him a research scholarship. In England, under the supervision of GH Hardy, he started to do his mathematical research. Before he came back to India he had become a Fellow of Trinity College and he was the second Indian to be a Fellow of the Royal Society for the contributions he made in mathematics.

Once another great Indian Mathematician, Prasanta Chandra Mahalanobis came into Ramanujan’s room. He asked Ramanujan a problem. The problem was as follows:-

Imagine that you are on a street with houses marked 1 through n. There is a house in between such that the sum of the house numbers to the left of it equals the sum of the house numbers to its right. If is between 50 and 500, what is the house number?

This question was solved by Mahalanobis through trial and error method. Ramanujan thought about for a while and said – Please take down the solution,” he said and then he proceeded to dictate a continued fraction, a fraction whose denominator consists of a number plus a fraction, that fraction’s denominator consisting of a number plus a fraction infinitely. Ramanujan’s continued fraction comprised within a single expression all the correct answers. Mahalanobis was astounded. How, he asked Ramanujan, had he done it? “Immediately I heard the problem it was clear that the solution should obviously be a continued fraction; I then thought, Which continued fraction? And the answer came to my mind.”

The answer came to my mind. That was the quality of Ramanujan which is the reason for people calling him the Prince of intuition.

Ramanujan was found to diseased with Tuberculosis which is the reason for his early death on April 26, 1920. Even when his death was drawing closer he still was producing mathematical results which are used in various fields of science till date.

Due to the contribution that Ramanujan has done to mathematics, he is still considered to be one of the greatest mathematicians that India has ever produced.

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