India celebrates 22nd, December, the birthday of the legendary mathematician - Srinivasa Ramanujan, as the National Mathematics day, in his memory for it was on this date - 22nd December, that Ramanujan was born in Erode, Tamilnadu in the year 1887. This year happens to be the centenary of the Punyatithi of Ramanujan who died at a very young age of just 32 years on 26th April 1920 in Madras (now Chennai). The genius of Ramanujan and his goddess - Namagiri, gifted mathematics has remained an enigma, which is made out from the foreword that was written by CP Snow, friend of Ramanujan’s mentor GH Hardy, a great mathematician of his time in England. C.P. Snow, in his preface to Hardy’s remarkable memoir, ‘A Mathematician’s Apology’, writes ‘Hardy did not forget that he was in the presence of a genius - Ramanujan’. It must be remembered that GH Hardy was considered as one of the leading mathematicians of the world during this period. Hardy’s respect for Ramanujan and his genius in maths can be seen in another incident, which Hardy narrates. In one of his interaction with CP Snow, Hardy says ‘His protégé Ramanujan really had natural genius in the sense that the greatest mathematicians had it’. Hardy on another occasion modestly says ‘ I have done one thing that most others could never have done, and that is to have collaborated with the greats like Ramanujan on something like equal terms’. The legend and the myth that surrounds Ramanujan and his gifted mathematics therefore comes from such examples and on this centennial punyatithi year it is an honour for me to be paying my respect to the legendary Ramanujan by recalling the blogpost, which I had written last year with some minor changes.
My admiration for Ramanujan grew exponentially during the time of the 125th birth centenary of Ramanujan - 2012. I was then posted at the Visvesvaraya Museum in Bangalore. The government of India rightfully decided to celebrate the 125th birth anniversary of the great Srinivas Ramanujan and while announcing this birth anniversary celebrations, the then Prime Minister of India, Shri Manmohan Singh, also announced that the birth day of Ramanujan will also be celebrated as the National Mathematics Day, in memory of Ramanujan and ever since the 22nd December - the Birthdate of Ramanujan, is celebrated in India as the National Mathematics Day. In the previous year - 2011, which was the sesquicentennial birth anniversary of the legendary Sir M Visvesvaraya, I had volunteered to develop an exhibition on the life and works of Sir MV and this exhibition was highly appreciated and perhaps this success of making the biographical exhibition prompted DG NCSM to once again ask me to develop an exhibition on the life and works of Srinivas Ramanujan. Although we were tied up with many projects, I took up this challenge to develop the exhibition. The first thing that comes to mind when developing an exhibition on Ramanujan was the outstandingly well researched biography book on Ramanujan which was published by Robert Kanigel under the title - Srinivas Ramanujan : The Man who Knew Infinity’. The first things that we did before we started developing the curatorial concept for the exhibition was to name our exhibition after the title of Robert Kanigel Book. I assigned the task of developing this exhibition to one of my colleague curator Mr Sajoo Bhaskaran. We wrote a request letter to Kanigel and sought his consent and approval for naming our exhibition ‘Srinivas Ramanujan : The Man who Knew Infinity, which he so very kindly agreed and granted us permission to use the title of his book for our exhibition. We worked on a different presentation style for the exhibition and for the first time attempted some new digital interactive to present the complex works of Ramanujan in a manner easily understandable for common people using some of the interesting digital interfaces. This exhibition was developed at the Visvesvaraya Museum when I was its Director in the year 2012, and was successfully opened on the 22nd December 2012, which happened to be the 125th birth anniversary of Ramanujan.
The exhibition was received very well by the people, particularly the new presentation technique which we had attempted for the first time in our council - the National Council of Science Museums. One of the most important lessons that our youngsters can learn from the life and works of Ramanujan, which was very well researched and presented in the exhibition is that failure is something which must not necessarily be allowed to ruin ones life. In his authoritative biography of ‘Ramanujan, The Man Who Knew Infinity’, Robert Kanigel states that ‘Ramanujan appeared for the Intermediate examinations four times and failed in all of them. “Except for math he did poorly in all his subjects. … He’d take the three-hour math exam and finish it in thirty minutes.” T.V. Rangaswami’s Tamil biography (‘Ragami’) on which Kanigel’s account of Ramanujan’s early life is largely based, states that he sat for the F.A. examination three times and failed. Ragami however adds that in his last attempt, in 1907, he got a hundred out of hundred in mathematics. In yet another novel based on extensive research, David Leavitt’s ‘The Indian Clerk (2007)’, underlines the repeated failures of Ramanujan in his intermediate examinations, a point reiterated by the Ramanujan Museum’s website: “Appeared privately for F.A. examination, secured centum in mathematics, but failed to secure pass marks in other subjects.” We effectively communicated this lesson for the young students that failures have also been integral to some of the greatest of scientists and therefore they should not run away from such failures in life.
Notwithstanding his multiple failures in the intermediate exam one thing remained certain for Ramanujan. His love and passion for maths never went down, rather he pursued his passion for maths with that much more focus and managed to publish quite a number of papers in leading mathematical journals in India until managing to earn a job as a Clark in the Madras Port Trust from where he wrote that famous letter to his mentor, G H Hardy in the year 1913 and the rest what they say is now history. Ramanujan was invited to the Trinity College, Cambridge by Hardy. In just five years of his stay in Cambridge, Ramanujan made a profound contributions in mathematics and that too during the most testing times of the World War 1. In 1916 the Cambridge University conferred on S. Ramanujan, the B.A. degree ‘by research’. This was a momentous occasion for Ramanujan who had no formal college degree until this period. This was the first of many great recognitions and honours, which were destined to follow for Ramanujan in the years ahead at England and in India. The Trinity College, London and so also the prestigious Royal Society conferred fellowship on Ramanujan. Incidentally Ramanujan became the first Indian to be so honoured with the fellowship of the Trinity College when he was only thirty.
Ramanujan is almost a household name in India and most students in India will certainly have heard the name of Ramanujan, though not quite familiar with his works in mathematics. Notwithstanding the inspiration that the great Ramanujan has provided for our youngsters, most unfortunately over the years maths as a subject has been overly segmented as a subject meant only for the so called intellectuals, distancing the subject from common folks. Mathematics is one of the most important subjects, which acts as a tool to solve problems of every other science subjects. It provides students an opportunity to think in his or her way and seek solutions to the problems. It makes a student systematic and methodical and encourages them to make their lives orderly. It is perhaps for this reason that Mathematics is often called as the mother of all sciences and it is befitting that the birthday of Ramanujan, the greatest of mathematicians of India, is celebrated as the National Mathematics Day.
Ramanujan, the naturally gifted, non traditional mathematician ( 1887-1920) has been befittingly hailed as an all-time great mathematician of India in modern times and is famously clubbed with the other international greats like Euler, by his discoverer G H Hardy. It is very well known that Hardy was a die hard cricket fan and used cricketing parlance in every field, including in rating scientists and mathematicians in a scale he termed ‘Bradman Scale’. He included the likes of the great mathematician Euler and Newton in the highest scale - the Bradman scale, measured in memory of Hardy’s all time favourite cricket player - Don Bradman from Australia. What his rating for Ramanujan would have been can best be seen in the quote of another mathematician, Bruce C Berndt, who says ‘Paul Erdos has passed on to us, Hardy's personal ratings of mathematicians. Suppose that we rate mathematicians on the basis of pure talent on a scale from 0 to 100, Hardy gave himself a score of 25, Littlewood 30, Hilbert 80 and Ramanujan 100’. From this yardstick of marks assigned by the great Hardy on different mathematicians including himself and Ramanujan, whom he gave 100 marks, it is a given that Ramanujan was a Bradman scale mathematician for Hardy and that Ramanujan fell in the league of the greats like Euler and Newton. It is so heartening to know that Hardy, who was one of the great all time mathematicians of his time and also the man who is credited to be the discoverer of Ramanujan, has rated his prodigy -Ramanujan, far higher than what he rates himself and his close associate Littlewood, two of the great mathematicians of their time.
Although Ramanujan lived only for 32 years out of which he spent just five years in the company of Hardy and Littlewood in Cambridge, he has left behind a very large volume (4000 original theorems) of his works (including the famous works left behind in his ‘lost note books’), which continue to fascinate greatest of mathematicians of the world even today. Legend has it that Srinivas Ramanujan’s mathematical genius came from his goddess Namagiri - his family deity in Kumbakonam - in whose reverence Ramanujan had undying faith. It is often said that Ramanujan credited his ideas and solutions to Namagiri, his family deity, who helped him decipher mathematical theorems in his dreams. An evidence to Ramanujan’s god gifted ability to provide solutions to problems can be seen in another anecdotal story associated with the number 1729. G H Hardy, his mentor, in his memoir, says that he once went to see Ramanujan who was ill and lying in the hospital bed in Putney. Hardy says that he rode to the hospital in a taxi with dull and unimpressive number 1729, and he hoped that it was no bad omen number for him. This dull and unimpressive taxi number has now been immortalised by the genius of Ramanujan’s god gifted ability to seek problems and find their solutions. On meeting Ramanujan in hospital, Hardy informs Ramanujan of this unimpressive number, but then, lo and behold, Ramanujan turns around to say that it is not a dull number, rather it is a very interesting and unique number. Ramanujan with some mental calculations told Hardy that 1729 is a very special number and it is the smallest number expressible as sum of two cubes in two different ways. He instantly gave solution to his thoughts; 1729 = 12cube + 1cube = 10cube + 9 cube. (1³ + 12³ = 1 + 1,728 = 1,729) and 9³ + 10³ = 729 + 1,000 = 1,729. Because of this incident, 1729 is now known as the Ramanujan - Hardy number. Such was his god gifted talent for numbers. It is therefore no wonder that, Little Wood, an associate of Hardy who also mentored Ramanujan, once said ‘Ramanujan could remember the idiosyncrasies of numbers in an uncanny way ‘ courtesy Namagiri Goddess’ and for Ramanujan ‘every positive integer was one of his personal friend’.
Mathematics, which is often referred to as the mother of all sciences, is most unfortunately seen as a subject meant only for the studious and therefore curating an exhibition on this abstract subject, particularly addressing the mathematical contributions of the great Ramanujan, was truly challenging for any curator. Therefore we were confronted with a challenge when we were curating the exhibition Ramanujan- The Man Who Knew Infinity, How do we make it interesting for the visitors who may not be initiated in maths, was our moot question and after several discussions and brain storming we narrowed down on using immersive techniques to make the visitors, part of the story. The best technologies that could adopt this principle became our tools for the development of the exhibition. Two such technologies included what we now most regularly use - projection mapping and Kinect based gaming. Projection mapping technology was used as a story telling medium through which we presented the childhood days of Ramanujan. The house where Ramanujan was born was used as a relief backdrop on which the projection mapping was made to present the story of his childhood days, and this presentation turned out to be very popular among the visitors who had a nostalgic feeling of looking at the historic house, where Ramanujan was born, come alive. We also used the Microsoft Kinect - for the first time in our council (NCSM)) - to present abstract concepts in mathematics and Ramanujan’s profound interest and in-satiable quest for numbers. One of the exhibit was presented in an immersive experience manner where the visitor could immerse herself as a traveller crossing the Cauvery river in Kumbakonam, on the catamaran with two hands raised. As the catamaran moves forward, series of simple arithmetic problems keep coming and the visitor has to either bend left or right to answer the questions. The Kumbakonam ambience provided a world full of mathematical problems for Ramanujan, which the visitors experienced while interacting with this exhibit.
Srinivas Ramanujan, was born to a poor orthodox Tamil Brahmin family on the 22nd of December, 1887 in his grandmother's house in Erode, Tamilnadu. His father worked as a clerk in a cloth merchants shop in Kumbakonam. When he was just 2 years old, Ramanujan contracted smallpox, whose marks were conspicuous during his childhood days. Ramanujan confronted a life of extreme poverty during his younger days. His early studies were in different schools in Kumbakonam from the age of five until entering the Town High School at the age of 11 years. From his childhood, Ramanujan had a huge passion for mathematics. So much so that at the age of 12 he had mastered trigonometry ( SL Loney : Plane Trigonometry) and developed many theorems on his own with no assistance. Ramanujan was a precocious child and did very well in school and hardly evinced any interest in any other activities or games other than his studies. While his friends played, Ramanujan engaged himself in nothing but academics. The first sign of his extraordinary talents in maths was noticed when he was 13 years. It was when he began to work on his own on summing geometric and arithmetic series, far beyond his class. He engaged himself in solving cubic and other fairly difficult problems some of which he failed. He would engage his teachers in some unorthodox questions. He once questioned a teacher, who was teaching the class that any number divided by that number equals one. He asked him whether zero divided by zero would be one.
The major turning point in the life of Ramanujan came when he came across a mathematics book by G S Carr called ‘Synopsis of elementary results in pure mathematics’. This book was simply a compilation of thousands of mathematical results, with most of the results not explained properly with adequate proof. This book was written as an aid to coaching English mathematics students facing the notoriously difficult Tripos examination, which involved a great deal of wholesale memorization. But this book greatly influenced Ramanujan and it inspired him to pursue his passion in maths with great vigour and at a feverish pace. He worked through the book's results and beyond at the cost of other subjects. The style and approach of Carr to write the equations and solutions without giving the proof parts of the problems and equations. Ramanujan fell in love with this book and worked extensively on his slate which was far cheaper than the paper and pen which he could not have afforded. In 1904, he joined Government Arts College in Kumbakonam. Unfortunately Ramanujan by now was completely engrossed in maths with Carr Synopsis and this left him no time for other subjects, which he rarely cared for. The result was expected. He failed in all the subjects in college except excelling in maths. The failure did not help his cause and he had to loose the much need scholarship that he had managed to get while joining the college. Failure played on his mind and he ran away from home to Andhra Pradesh only to return back to get enrolled at Pachaiyappa’s college in Chennai. Here, too, he engaged himself mostly in maths and couldn’t comprehend subjects like physiology and once again failed in the BA Fine Arts exam. He had no way but to leave his college, without attaining a degree. This did not deter him from continuing his independent Mathematics research.
Ramanujan even after failing in his BA Fine Arts exams, decided to concentrate completely on his maths research and it is during this period, 1903-1914, he meticulously kept a record of the final results of his original research work in the form of entries in two large-sized Note Books. By now his works in maths were beginning to be noticed. He worked extensively on his slate and recorded his final results in note books. He was lucky that he could show some of his recorded notebooks to eminent citizens in the city; Diwan, Bahadur Ramachandra Rao, V. Ramaswamy Iyer (Founder of Indian Mathematical Society) R. Narayana Iyer (Madras Port Trust), and to several others to convince them of his abilities as a Mathematician. Fortunately it paid rich dividend and he was employed by the Madras Port Trust as a clerk at a salary equivalent to about 25 Pounds a year. By this time he had already established himself as a fairly well recognised scholar in maths and reports of his unusual abilities had begun to spread far and wide. Fortunately his talents in maths reached Dr. G. T. Walker, in Madras University and courtesy his influence Ramanujan obtained a small scholarship, which relieved him from the necessity of office work and set him free for research.
During this period Ramanujan published several papers in influential Indian Mathematical journals. He also sent his long list of complex theorems to three academics of Cambridge. One of them was G H Hardy. Ramanujan had come across a book by Hardy titled ‘ Orders of Infinity’ which motivated him to write his now famous letter to Hardy. Ramanujan’s life took a major turn in 1913, when his 10-page letter containing 100 statements of theorems on infinite series, improper integrals, continued fractions, and number theory, reached Professor GH Hardy. The letter was a collection of Ramanujan’s self-derived equations and unproven theorems. Hardy was perplexed to see this letter from an ordinary clerk from India who had professed to have discovered some infinite series and had posted some 100 odd findings in his letter. Hardy knew that the letter warranted some merit but was also skeptical. After his dinner he met his compatriot mathematician Littlewood. Hardy mentioned to Littlewood some of the claims he had received in the mail from an unknown Indian. He said some of the assertions made in the letter of Ramanujan were well known, others could be proven, while some others they could disprove. Hardy and Littlewood decided to have a relook at the letter, which they did and agreed that many of the statements made in Ramanujan’s letter were not only fascinating and unusual but also impossible to resolve.
Hardy and Littlewood continued their discussion on this letter over the next couple of days and soon they were convinced that the clerk who wrote this innocent letter must be a genius. Hardy therefore replied to Ramanujan, encouraging him on his works. This was the beginning of a series of letter exchanges between the two of them. Although Hardy by now was sure that Ramanujan was an exceptional mathematician, however, in spite of his amazing feats in mathematics, Hardy realised that Ramanujan lacked the basic tools of the trade of a professional mathematician. Hardy knew that if Ramanujan was to fulfil his potential, he had to have a solid foundation in mathematics, which are normally possessed by the best of Cambridge graduates. For this Hardy extended an invitation to Ramanujan to come to Cambridge. Hardy was completely taken aback when Ramanujan could not make up his mind to accept the rare invitation from a well known mathematician from Cambridge, which most others would have jumped on. He later realised that as a Brahmin, Ramanujan was not expected to cross the ‘seven seas’. His mother was totally opposed to the idea of Ramanujan’s sea voyage. But fortunately Ramanujan could manage to convince his mother and get her consent. Hardy soon swang into action. He asked E.H Neville, another fellow of Trinity College, who was on a trip to Madras, to secure Ramanujan a scholarship from the University of Madras. Neville’s wrote in a letter to the university that “the discovery of the genius of S. Ramanujan of Madras promises to be the most interesting event of our time in the mathematical world ..."
What followed next is now a legend that has entered into the annals of history. Courtesy Hardy and Neville, the Madras University offered Ramanujan the first research scholarship of the University. Hardy also ensured that Ramanujan was offered a scholarship of 250 pounds a year for five years with 100 pounds for passage by ship and for initial outfit to go to England in 1914. Ramanujan, at the age of 26 years set sail to England and reached Cambridge, just before the outbreak of World War I. In the very first year of his stay in Cambridge- 1914 - Ramanujan made some path breaking contributions. However his journey to success faced some hurdles in the initial part of his stay in Cambridge. Ramanujan who may majorly influenced by Carr’s style of summing up his end findings and stating the formula for a infinite series or such other mathematical problem without assigning any deductive solution was something which did not please his mentor Hardy. This incident has been so beautifully depicted in a scene from the film Ramanujan The Man who Knew Infinity. The scene shows the excitement of Ramanujan to publish and in his discussion with Hardy he presents to him two of his note books adding to the 100 formulas, which he had already sent to him and other problems which he had been corresponding with Hardy. One of this was an interesting series which was mind boggling for Hardy to comprehend how Ramanujan could even visualise it. The very equation looks quite deceptive and it goes as follows ; 1+2+3+4+5...... = -1/12. Interestingly Hardy immediately had recognised this to be the theory of analytic continuation ( Reimann Zeta Function) from complex analysis. However Hardy was convinced that Ramanujan must learn to produce mathematical solutions for the answers that so naturally come to Ramanujan so that other mathematicians take him seriously. The scene shows a brief argument that ensues between the two in which Ramanujan- role played by Dev Patel, is seen arguing with Hardy, a role played in the film by Jeremy Irons. Ramanujan expresses his desire to publish while Hardy insists that he must first learn to communicate his mind in the exacting standards that befit the standards of Cambridge. He therefore advises Ramanujan to take some basic lectures to learn a more formal language in maths which he could use to communicate his findings to his fellow compatriots in Cambridge. Hardy managed to convince the need for a formal learning for Cambridge when he takes Ramanujan on a walk through the famous library of Cambridge. He says to Ramanujan that if area of maths are to be challenged you must give proof to the formulas and that too in manner which are understandable to the people. Hardy takes Ramanujan to the hall where Newton’s Principia book is preserved. He says Newton produced this monumental findings which took long time for the people to understand. Hardy says to Ramanujan that if you provide proof to your formulas, which you have noted in your note books, the time will not be far when your note books could find a place in this very precinct of Cambridge where Newton’s book finds his place. Hardy was proved to be right, Ramanujan’s lost note books finally have made their way to Cambridge and are in their priced possession even today. The scene depicts the dichotomy of relationship that existed between Hardy and Ramanujan.
Ramanujan and Hardy had one of the most productive collaborations ever and during his five years of stay in Cambridge, Ramanujan wrote some 30 papers some on his own and some jointly with Hardy. Most of his works transformed the field of mathematics. On his way to achievement Ramanujan had to overcome severe hardships, sense of racism, difficulties of the World War 1 effects on his uncompromising vegan habits. Hardy was no doubt a great mentor for Ramanujan but then there is an argument that he may not have shown that much needed humanitarian considerations for Ramanujan which could have ensured a better living conditions for Ramanujan in England.
Ramanujan’s contributions were soon recognised by his compatriots in Cambridge and he was elected ‘Fellow of Trinity College’, Cambridge, even though he didn’t have a college degree. But unfortunately his stay at Cambridge was the most harshest for Ramanujan. He was a strict vegetarian and he remained uncompromising about his dietetic observance. The World War too did not help his cause, which made availability of choice materials for Ramanujan very scarce. Ramanujan always cooked his own food and most often neglected his health. During his five years stay in England, Ramanujan was mentored by Hardy and he cemented a five year-long outstanding partnership with Hardy. It was during this stay in England that Ramanujan was awarded a BSc (later renamed PhD). In 1918, he was elected as a Fellow of the Royal Society (FRS), as a Research student in Mathematics Distinguished as a pure mathematician, particularly for his investigations in elliptic functions and the theory of numbers. A rare honour for the not so formally educated, that too at a very young age. Ramanujan was also elected to the Trinity College Fellowship, in Oct. 1918 (a prize fellowship worth 250 pounds a year for six years with no duties or condition). Most unfortunately he was not destined to avail of this fellowship.
His health kept deteriorating in England and Ramanujan was often times admitted to hospital. When his health improved slightly he preferred to return back to India. Now an acclaimed mathematician, Ramanujan returned to India in 1919 after World War I, but years of stay in an unfamiliar climate in England clubbed with his uncompromising life style, had taken a heavy toll on his health. When he returned back to India he was diagnosed with tuberculosis. In January 1920, he wrote the last letter to Hardy about his discovery of “Mock Theta functions’ another master class contributions from a man who was almost in his death bed. He died on 26th April of that year. In his small lifetime, Ramanujan compiled more than 3,000 results on equations and identities, many of them posthumously proven right. His ‘Lost' Notebook was found in 1976 by Prof. George Andrews of Pennsylvania State University, and its facsimile edition was brought out by Narosa Publishing House in 1987, on the occasion of Ramanujan's birth centenary. Besides his published work, Ramanujan has left behind several notebooks, which have been the object of much study.
There is no question about the fact that mathematical genius Srinivasa Ramanujan has left behind a rich legacy of problems for mathematicians to solve. In his short life of little over 32 years, he reached unimaginable heights. What is surprising is that his mathematics, done over a hundred years ago, finds applications today in areas other than pure mathematics, which were not even established during his time. Two among these are signal processing and Black Hole physics.
What could have been the contributions of Ramanujan if conditions were more conducive to him and if he had lived longer is some thing which will continue to remain in the realms of speculation. It was a great tribute that his life and works were chosen for making of Dev Patel starrer film ‘The Man Who Knew Infinity’ (2015), which was another great tribute paid by the cinema to the legendary Ramanujan. May he continue to inspire millions not just Indians, but globally.
Rest in Peace Ramanujan.
