Srinivasan Ramanujan : Mathematical Genius


Srinivasa Ramanujan, the Indian mathematician of the early twentieth century,  whose contributions to number theory, continued fractions, and infinite series revolutionised the field of mathematics.  Mathematician across the globe are even today trying to prove or disprove many theorems left behind by him.

While at Sainik School Amaravathinagar, we had Mr. Venkitesha Murthy (VM) teaching us mathematics in 1977 in Grade 11.  He was a great fan of Srinivasa Ramanujan and had taken up extensive study of his works and life.  The effort would have been really painstaking in those days (without internet and Google) to collect such enormous data, that too sitting in a remote village of Thamizh Nadu, called Amaravathinagar.

In 1977, to mark the ninetieth birthday of Ramanujan, Mr. Murthy staged a one hour play on his life and achievements.  Veteran Commander Reginald was responsible for the light effects and I did the sound effects.  We both sat through many rehearsals and the personality of Ramanujan left a deep impression on us.  Teachers and students enacted different roles with Mr. Murthy as Ramanujan leading from the teachers’ side and Ashok Kumar (now Vice Admiral) from the students’ side.

SRamanujan Skit Gp Photo
Group Photo of the Play on Ramanujan- Extreme Left :  Mr K Ekambaram as Ramanujan, Vice Admiral G Ashok Kumar as Komalambal (Mother of Ramanujan), Mr KM Koshy as Professor Hardy, Mr Venkatesha Murthy as Collector of Nellore, Mr M Selvaraj as Father of Ramajujan, Mr AKR Varma, Mr R Subramanium as Professor EH Neville (Photo Courtesy Mr Venkatesha Murthy).  You may click on the names of our teachers to read more about them.

Mr Murthy helped his students to be aware of the achievements of Ramanujan, when many in India (including my siblings) had not even heard of him.  This post is based on some of the scenes from Mr. Murthy’s play.  The announcement of the release of a movie ‘The Man who knew Infinity’ rekindled my thoughts about Ramanujan.  I hope the movie will bring in significant awareness about a mathematical genius from India.

Ramanujan was born in Erode (1887), and schooled in Kumbakonam (Thamizh Nadu), where his father worked as a clerk in a cloth merchant’s shop.  Until high school, Ramanujan was a ‘good’ student, interested in the curricula.  During his high school days, he began to display his immense mathematical sense; worked on his own on summing geometric and arithmetic series.  He had a great memory and could rattle out the value of the constant ‘pi’ to any number of decimal places.  Here he came across a book ‘ Synopsis of elementary results in pure mathematics’ by GS Carr.  This book is said to have moulded the mathematical thought process of Ramanujan and had a great influence on his early works.  The irony was that the book, published in 1856, was out of date by the time Ramanujan used it.

In 1904, Ramanujan joined Government College in Kumbakonam. The following year his scholarship was not renewed because Ramanujan devoted most of his time to mathematics and neglected all other subjects.  In 1906 Ramanujan joined Pachaiyappa’s College at Chennai (then Madras). His aim was to pass the First Arts examination, ended up passing only in mathematics and failing is all others.  In the following years he worked on mathematics, developing his own ideas without any help .  The only guidance he had was Carr’s book, which had theorems, but hardly any proofs.  Ramanujan is said to have developed his theorems using a slate as he could not afford paper.  This aspect along with the proof-less theorems in Carr’s book might have influenced Ramanujan in that he noted mostly the results and hardly any proofs.  He married on 14 July 1909 to a ten year old S Janaki Ammal.  

Ramanujan continued to develop his mathematical ideas and began to pose problems and solve problems in the Journal of the Indian Mathematical Society.  He became well known among the mathematicians of Madras area after he published a research paper on Bernoulli numbers in 1911 in the Journal of the Indian Mathematical Society.

In 1911 Ramanujan approached the founder of the Indian Mathematical Society for advice on a job. He got a temporary post in the Accountant General’s Office in Madras and in 1912.   Ramanujan later became a clerk in the accounts section of the Madras Port Trust.  

In January 1913 Ramanujan wrote to Professor GH Hardy of Cambridge, having read his book ‘Orders of infinity.’  He had enclosed some unproved mathematical theorems and some proofs.  Hardy, together with his colleague, Professor JE Littlewood, studied the theorems.  It seems that Hardy initially thought him to be a crank or a prankster as most of the 120 theorems had no proofs.  Hardy replied to Ramanujan that he wanted proof for the theorems.    

Ramanujan was delighted with Hardy’s reply and then he wrote to him “I have found a friend in you who views my labours sympathetically. … I am already a half starving man. To preserve my brains I want food and this is my first consideration. Any sympathetic letter from you will be helpful to me here to get a scholarship either from the university or from the government.”

Madras University awarded Ramanujan a scholarship in 1913 for two years and, in 1914, Hardy brought Ramanujan to Cambridge, to begin an extraordinary collaboration – between a believer and an atheist – an educated and an uneducated genius.  Ramanujan, being an orthodox Brahmin and a strict vegetarian, did not want to cross the seven seas (a taboo in Hindu culture).  He was convinced by Professor EH Neville, Hardy’s colleague, who met with Ramanujan while lecturing in India.

Hardy entrusted Littlewood with the task of teaching Ramanujan ‘formal’ pure mathematics.  Littlewood failed miserably as the classes would end up with volley of questions from Ramanujan.  World War I took Littlewood away on war duty but Hardy remained in Cambridge to work with Ramanujan.  He remained sick, mainly due to the cold winter – a difficult proposition for anyone from Chennai even today.  He had problems with his diet as the outbreak of the war resulted in a scarcity of vegetables which worsened his health.

Ramanujan credited his mathematical gift to Goddess Mahalakshmi-Namgiri who he said appeared to him in his dreams.  He claimed that he had unusual experiences and dreams while asleep and Goddess Mahalakshmi would appear to him and show him the answers to the puzzles in his mind. As soon as he woke up, he would write them down.

On 16 March 1916 Ramanujan graduated from Cambridge with a Bachelor of Science by Research (the degree was called a Ph D from 1920).  Ramanujan’s dissertation was on Highly composite numbers and consisted of seven of his papers published in England.

Ramanujan fell seriously ill in 1917 and his doctors feared that he would die. Hardy went to see him when he was ill.  On reaching Ramanujan’s bed, Hardy said that he rode a taxi cab with a dull number 1729 .  Ramanujan said that it is a very interesting number as it is the smallest number expressible as the sum of two cubes in two different ways 1729 = 13 + 123 = 93 + 103Click here to read my earlier post ‘Arithmetic of Licence Plates’, inspired by this anecdote.

On 18 February 1918 Ramanujan was elected a fellow of the Cambridge Philosophical Society and then three days later, the greatest honour that he would receive, his name appeared on the list for election as a fellow of the Royal Society of London and on 10 October 1918 he was elected a Fellow of Trinity College Cambridge.

Ramanujan returned to India in 1919 and died the following year.  His birthday, 22 December, is celebrated as the National Mathematics Day in India.

‘The Man who knew Infinity’  – the movie is being released world-wide on 29 April 2016.  Waiting to see what the movie offers beyond the Mr. Murthy’s play of 1977.  Review of the movie follows (after I watch it).

Here is a photograph (1968)  of Sir Dr CV Raman with  Mr. Venkitesha Murthy and Cadets of  Sainik School, Amaravathinagar.  Photo Courtesy Vetran N Vijayasarathy



In 1971, after the anti-Hindi agitation that raged through Thamizh Nadu, I joined Sainik School Amaravathinagar in the state then known as Madras.   The school almost resembled any British Military School as all the military words of command were in English like “Attention” and “Stand-at-Ease”. There I started to learn Thamizh and also English and Hindi.

Thamizh is one of the longest surviving classical languages in the world and the script has only 18 consonants unlike Devnagari script which has about 37 consonants. When Devnagari script has क, ख, ग, घ (ka, kha, ga, gha), Thamizh has only க (ka) and similarly for the other corresponding consonants. All the other South Indian languages namely Malayalam, Kannada and Telugu follow their own script similar to the Devnagari script. Further these three languages unlike Thamizh, have a lot of Sanskrit vocabulary. Hence learning of Hindi or any Devnagari script based language becomes difficult for a Thamizh in comparison to the people from the other states.

After the anti-Hindi agitation in Thamizh Nadu, the Official Languages Act was amended in 1967 by the Indian Government to guarantee the indefinite use of Hindi and English as official languages. This effectively ensured the current bilingualism and use of English in education in India. This bilingualism has helped the Indians to a great extent in ensuring acceptance all over the world.

Hindi as a national language was not accepted all over India due to the implementation issues. The Hindi Pundits coined many a difficult terms to replace commonly used English terms. Many of the terms coined were not even accepted by the Hindi speaking population. Lot of money and efforts were pumped in by the government for the enhanced use of Hindi as an official language, but it never had any results other than a few Members of Parliament making a foreign sojourn to study the use of Hindi in some country or the other and the practise still continues.

To further make the matter worse, all forms were printed in both Hindi and English and so also all the government publications. This resulted in higher production costs without serving any purpose. While serving in the Indian Army, I recommended all my subordinates to read and understand the pamphlet ‘Glossary of Military Terms’. The pamphlet was printed in Hindi on the left page and English on the right. I also used to advise them to read the Hindi side whenever they got bored – the Hindi equivalents were hilarious and many a times grossly incorrect.

In our school the English department was headed by Mr KG Warrier and the Thamizh department by Mr M Selvaraj. Both of them were strong linguists and always ensured that they spoke the language with purity in that when they spoke, they always used only one language. Both had excellent communication skills and were near perfect in their pronunciations. Both of them never taught me at school, but I had extensively interacted with them during various extra-curricular activities.


(Mr KG Warrier with our Class-mate AP Sunil Kumar at Kottakkal.  The photo is of 2013 when Mr Warrier turned 90)

Mr KG Warrier hails from the family of world renowned Ayurveda Physicians of Kottakkal in Kerala. He is currently enjoying his retired life at Kottakkal. He is staying with his daughter, Rathi. The Warrier community connected to the Vaidya Sala stay at ‘Kailasa Mandiram’ in the Vaidya Sala premises at Kottakkal, Malappuram District, Kerala.

His specialty was that he dressed in his starched and pressed cotton pants and shirt, wear a felt hat and hold a pipe in his hands. I was always intrigued as to how he managed to maintain the crease of his pants perfect even at the end of the day.

A few days before leaving school to join the National Defence Academy I met Mr KG Warrier and he asked me in Thamizh as to when I was joining the academy and how the preparations were progressing. My answer was in the usual ‘mixed language’ of Thamizh, Malyalam and English. To this he said “உனக்கு தமிழும் தெரியாது, மலையாளவும் தெரியாது, ஆங்கிலவும் தெரியாது. உனக்கு என்ன தெரியும்? (You do not know Thamizh or Malayalam or English. What do you know?)”.

I still recollect a few words of advice Mr KG Warrier had given us.  He said that everyone should always carry and use three books – a Dictionary, an Atlas and a Wren & Martin Grammar book.  At the beginning of each year at the school, these were the first set of three books we were issued with.  Later on during my army service I did carry these three books.  Nowadays with the power of the internet with browsing tools like the Google, most information is at one’s fingertips and these three books have become almost extinct.

Mr M Selvaraj was well known for his voice and his oratory skills which were showcased during all the cultural programmes at the school. His orations in both Thamizh and English will be remembered by all his students. I was very curious as to how he managed to handle the two languages independently and so effectively. During my final year in school, I did manage to summon enough courage and asked Mr M Selvaraj about the secret.

Mr M Selvaraj said that when he joined the school he had very little grasp of English having done his Masters degree in Thamizh. Major MMR Menon, then Headmaster of the school had advised him that to be a successful teacher in a school like this, mastery over English would go a long way. So with reluctance he approached Mr KG Warrier, but was surprised when Mr KG Warrier accepted to be his Guru and thus he started to learn English. He ended the chat by saying “the English I speak is all what Mr KG Warrier and Ms Sheela Cherian had taught me like any student who graduated under these great teachers.

Mr M Selvaraj left our school in 1987 to be the first Principal of Navodaya Vidyalaya at Mahe. After establishing the school, he moved as the Principal of Navodaya Vidyalaya at Pondichery and now leads a retired life in Trichy.

After leaving the school, I always tried to complete a sentence in one language and many a times I did fail. After joining the army, I picked up Hindi. Luckily for me, I served mostly with the Brahmin soldiers from North India and that helped me improve my Hindi to a great extent. Now with Hindi also joining the bandwagon of languages in my mind, maintaining purity of language became near impossible.

Hats-off to all those Thamizh news readers in any television channels, they speak pure Thamizh only and would use another language vocabulary only in case it is unavoidable.