RAMANUJAN: Letters from an Indian Clerk

in March 1914 against social and religious taboo a self-taught Indian mathematician called Srinivasa Ramanujan left his wife family and friends in Madras to sail for England and Trinity College Cambridge he was 26 years old six years later Ramanujan was dead but he left behind him some of the most remarkable and beautiful ideas in the history of pure mathematics no one knows quite where these ideas came from many years later the great English mathematician G H Hardy reflected on his brief relationship with Ramanujan I suppose that it is always a little difficult for an Englishman and an Indian to understand one another properly the real difficulty for me is that Ramanujan was in a way my discovery I did not invent him like other great men he invented himself but I was the first really competent person who had the chance to see some of his work and I can still remember with satisfaction that I could recognize at once what a treasure I had found I owe more to him than to anyone else in the world with one exception and my association with him is the one romantic incident in my life dear sir I beg to introduce myself to you as a clock in the Accounts Department of the Port Trust office at Madras on your salary of only 20 pounds per annum I am now about 23 years of age I have heard no university education but I have undergone the usual school course after leaving school I have been employing the spare time at my disposal to work at mathematics I have made a special study of divergent series in general and the results I get are termed by the local mathematicians as startling 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 being inexperienced I would very highly value any advice you give me requesting to be excused from the trouble I give you I remain dear sir it was very sincerely yes Ramanujan Ramanujan had addressed his letter to one of the world's elite academic institutions the recipient of the letter was gh Hardy who together with his friend and collaborator je littlewood dominated English mathematics in the first half of the century bailable aback a Hungarian mathematician and fellow of Trinity was a close friend of Littlewood in his later years little would often spoke about his collaboration with Hardy and of how his relationship with Ramanujan the are difficult partnership is from the greatest scientific partnership effort and it's really curious that though they live in the same College they actually collaborated by sending each other letters they lived only about 50 yards apart and even and porters scurried across the court carrying letters from one to the others these letters tend to be rather impersonal all about mathematics and occasionally Sumter's are details so nyan especially at the beginning they were rather formal I went like dear Hardy and fearlessly would know Christian names ever but later they became derailed eh and 20 years old they almost never wrote and the elocution what said I just started a mathematics so I would say just had an idea for lambda less than one I should like you to begin by trying to reconstruct the immediate reactions of an ordinary professional mathematician who receives a letter like this from an unknown Hindu Clarke the first question was whether I could recognize anything some of the formulas seemed vaguely familiar I thought that as an expert in definite integrals I could probably prove a couple of them and did serve there with a good deal more trouble than I had expected one or two of the formulae I found much more intriguing and it soon became obvious that Ramanujan must possess much more general theorems and was keeping a great deal of his sleeve some of the formulae defeated me completely I had never seen anything in the least like than before a single look of 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 were not true no one would have had the imagination to invent them Hardy began corresponding with the Indian Clark and variably asked Littlewood for his comments on the strange formula which arrived from Madras I've looked at some of the other results D is still wrong of course and rather Ajala six is correct up to X to the 33rd eight here is a mild verification how maddening his letter is in the circumstances I rather suspect he's afraid that you'll steal his work little DeRose that my hopes now are that he has much important discoveries about company infractions and elliptic functions I can believe that he's at least a Jacobi it's tremendously excited to find somebody who turns up out of the blue and who is as good as check away I mean that's that's unheard of course it never happened before unimaginable in fact in mathematics almost everybody has a very good teacher it's very rare to find an outstanding mathematician who was not told by anybody suppose here is the point we must go along the x axis along the y axis all along the y axis our peril to done in this case by the age of 10 Ramanujan had changed such outstanding mathematical ability that he was awarded a scholarship to the Kumbakonam town school and the user units along the or parallel today these are axis he had an insatiable curiosity for all things mathematical and neglected his other school subjects can be lieutenant Victor Samar three Victor's SS within a relatively inflexible English based system he failed to qualify for higher education young peel Excel which is the vector sum we are going to see that this is the resolution vector at the age of 15 Ramanujan borrowed a copy of cars synopsis of pure mathematics a textbook designed to coach bright English boys for university entrance exams he worked his way through this book and it's somewhat peculiar style and methods were probably responsible for Ramanujan Zod ways of working in particular his apparent ignorance of the need for rigorous proof of new ideas Ramanujan to Hardy 27th February 1930 I have found in you a friend who views my Labor's sympathetically this is already some encouragement to me to proceed with my onward course you may judge me hard that I am silent on the methods of proof it is not on account of unwillingness on my part but because I fear I shall not be able to explain everything in a letter I do not mean that the methods should be buried with me it seemed to harden little word essential that Ramanujan be brought to Cambridge where they could introduce him to modern mathematics and help him develop his true potential by chance another Trinity mathematician eh Neville was going to Madras to give a series of lectures hard he asked Neville to contact Ramanujan and invite him to come to England in Madras Neville found that Ramanujan was married to a fourteen-year-old girl called Janaki Amma she is now 87 and lives in a poor area of Madras surrounded by mementos of her husband all I can tell you is that be a knight he worked on sons he didn't do anything else he wasn't interested in anything else just sums he wouldn't stop work even to eat we had to make rice balls for him and place them in the palm of his hand isn't that extraordinary Neville was to find that there were certain very real obstacles too hard his plan the transition of India of the late 19th early 20th century was one in which ship one transferred one's interest from education in Tamil literature or in Sanskrit literature and conforming to the religious practices and then changing over to reading English history and science and ambitions and science they provided an element of conflict I think the way to understand Ramanujan years and one hand he was driven by an ambition a desire to promote this mathematical abilities and at the same time tied to a social background which he felt here to conform Ramanujan and his family were brahmins poor but extremely Orthodox in matters of religious observance it seemed out of the question for Ramanujan to leave India by crossing the Seas to another land a Brahmin loses caste and has seen as polluted in the eyes of other Brahmins Ramana John's family had a favorite hindu deity the goddess namagiri Ramanujan sometimes said it was nama Giri who gave him all his ideas and dreams no this is Robin are all arranged a listener his family told him not to go and at first he agreed not to but then he said he was going to namah chol to ask the goddess namagiri for guidance she told him to go yes and now I remember I know she knows I asked if I could go with him but she told me I was too young Ramanujan to harden 22nd January 1914 dear sir I learned from your letter and mr. Neville that you are anxious to get me to Cambridge I went to mr. Neville of your College who very kindly spoke to me and cleared my doubts that I need not care for my expenses that my English will do that I am not asked to go to England to appear for any examination and that I can remain a vegetarian death so I request that you and mr. little wood will be good enough to take the trouble of getting me there within your very few months you were sincerely yes Ramanujan before he left for London he had his hair long and because he thought it would hurt our feelings he sent us off to Papa Burnham then he cut his hair and dressed in different clothes you can see the photo of how he looked I myself never saw him like that I only saw the photo he didn't like to have his photo taken dear mr. Krishna Rao reached Suez this evening for the first three days I was very uncomfortable and took very little food and after that I have been all right the sea is very smooth and there is no fear of seasickness I do not know whether I shall have to go to Cambridge directly or stay at London and then go I shall write to you after I reach England and everything is definitely settled my best compliments to your brother and warmers - thanks to our uncle Ramanujan was about to enter a world he cannot possibly have imagined from 6000 miles away in Madras when I first joined Trinity hellish apparently was the heightened ambition we were really a band of very excellent people in their particular subject and the rubbing off of one against the other I think did have a very salutary effect we were all the Hennig and we had been order in days gone by when none of us were married when I joined the fellowship at least half the fellows were married and lived at a college didn't live on top of each other as they used to the Kim I suspect from a very poor environment Madras is better than most cities in India infinitely better than Bombay and Calcutta but it was a poor community and to come to the highly privileged conditions we still existed in 1914 and this place was really a very great strain on him my dear Krishna Rao please excuse me for the long delay in writing to you now I am somewhat accustomed to their living here till now I did not feel comfortable and I would often think why had I come here it is due to the difficulty of getting proper food had it not been for the good milk and fruits here I would have suffered more mr. Hardy mr. navel and others here or very unassuming kind and obliging as for my food I have no other go but to cook myself there is no place very near this College where I can get vegetarian food I will be very much obliged if you can send me some tamarind and good coconut oil by postal parcel through the cheapest route it is not merely that he wanted to be a vegetarian but he presumably felt compelled that the food should not be in any way made are produced by foreigners or cooked in vessels in which meat or might have been cooked and if he felt constrained to to be restricted in that way then of course he had to cook his own food on the other hand I mean he was so involved in mathematics that I remember that professor Ananda Rao who was a contemporary of Ramanujan in Cambridge said that he made his meals at extremely odd times because you are so occupied with his word from the Hindu newspaper 13th May 1914 mr. is Ramanujan of Madras whose work in higher mathematics has excited the wonder of Cambridge is now in residence at Trinity he will read mainly with the two fellows of the college mr. Hardy and mr. little wood they are going through masses of work he has already done and are making some surprising discoveries in each Ramanujan Hardy and little would have to be imagined as explorers in an exotic landscape of mathematical patterns harmony and surprising interconnections this landscape was their natural habitat but it is totally impenetrable even invisible to the rest of us in 1940 party wrote an elegant account of his own passion for what he called the real mathematics pure mathematics seems to me to be a rock on which all idealism founders 317 is a prime not because we think so or because our minds are shaped in one way rather than another but because it is so because mathematical reality is built that way I cannot remember ever having wanted to be anything but a mathematician I suppose that it was always clear that my specific abilities lay that way and it never occurred to me to question the verdict of my elders I do not remember having felt as a boy any passion for mathematics and such notions as I may have had of the career of a mathematician were far from Noble I thought of mathematics in terms of examinations and scholarships I wanted to beat other boys and this seemed to be the way in which I could do so most decisively I knew Hardy I went say well I knew and asked me to heart quite well as I had been with him quite a long time I did not know little wood little wood the idea was a little will be invented by Hardy to account very possible mistakes it might have been in little wooden hurry I think he actually was a real character I saw a good deal more and as more temperamentally well disposed to Hardy than I was to Lord but I knew Hardy he was already gained on in age and I think he had shrunk in his frame it to my mind he was small man and wiry tense like an acrobat always casting himself in the role of the next move wanting to pit himself against the obstacle if intellectual curiosity professional pride and ambition are the dominant incentives to research then assuredly no one has a fair chance of gratifying them than a mathematician his subject is the most curious of all there is none in which truth plays such odd pranks it has the most elaborate and the most fascinating technique and gives unrivaled openings for the display of sheer technical skill finally as history proves abundantly mathematical achievement whatever its intrinsic worth is the most enduring of all a mathematician like a painter or poet is a maker of patterns if his patterns are more permanently theirs it is because they are made with ideas a painter makes patterns with shapes and colors a poet with words the mathematician patterns by the painters or the poets must be beautiful the ideas like the colors or the words must fit together in a harmonious way beauty is the first test there is no permanent place in the world for ugly mathematics as most of you know this passage is from Harvey from his apology in emphasizing the importance of beauty in mathematics hardly must have been influenced by his association with Ramanujan the subject of this talk because hardly found Ramanujan's result but there was one great puzzle what was to be done in the way of teaching him modern mathematics the limitations of his knowledge were startling as its profundity here was a man who could work out modular equations and theorems of complex multiplication two orders unheard of whose mastery of continued fractions was on the formal side at any rate beyond that of any mathematician in the world and yet he had never heard of a double periodic function or of cautious theorem and had indeed with the vaguest idea of what a function of a complex variable was this is by five for every value of n okay I think this will be the very last thing I will I be proved but but which we should prove something so let's let's try to see how our Ramanujan did it and actually we can do exactly the proof he gave his ideas of what constitutes a mathematical proof were of the most shadowy description all his results new or old right or wrong had been arrived at by a process of mingled argument intuition and induction which he was entirely unable to give any coherent account it was impossible to ask such a man to submit to systematic instruction to try to learn mathematics from the beginning once more I was afraid too that if I insisted unduly on matters which Ramanujan found irksome I might destroy his confidence or break the spell of his inspiration so I had to try to teach him and in a measure I succeeded though obviously I learned from him much more than he learned from me my dear Krishna Rao I am very slowly publishing my results the other professors here who I know have lost their interest in mathematics going to the present war one of the professors here some days that remote that I have come to England in the most unfortunate time party to the University of Madras 11th of November 1915 Ramanujan has been much handicapped by the war mr. little would who would naturally have shared his teaching with me has been away and one teacher is not enough for so fertile of pupil Cambridge had been transformed Trinity College was turned into a military training camp and temporary hospital for the wounded Ramanujan to his mother September 11th 1915 Ramanujan makes his countless prostrations to his mother please write about your welfare there is no war in this country war is going on only in the neighboring country that is to say war is waged in a country that is as far as Rangoon is from Madras no war like this has raged before the percent war affects millions of people Germans set fire to many a city slaughter and throw away all the people the children the women and the world when the world is mad a mathematician may find in mathematics an incomparable anodyne for mathematics is of all the Arts and Sciences the most austere and the most remote a mathematician should be of all men the one who can most easily take refuge where as Bertrand Russell says one at least of our nobler impulses can best escape from the dreary exile of the actual world when little would returned to Cambridge on leave from ballistics research he was fascinated by what Ramanujan had been doing in his absence there was hardly a field of formulae that Ramanujan had not enriched in which he had not revealed unsuspected possibilities the beauty and singularity of his results was entirely uncanny do i square to some from kill goes from 1 to nu square don't q1 was impressed by his extraordinary profusion variety and power the story of one particular result of Ramanujan is the formula for the number of partitions of n is a romantic one but it resulted in a very astonishing theorem when we think of partitioning a number what we are talking about is breaking it up into a sum of other numbers for example 10 is 6 plus 4 in additive number theory one wishes to look at all possible ways of doing this so for example if we think of a small number like 4 there are five possible ways of doing it 4 can be written as 4 itself a single term sum 3 plus 1 2 plus 2 2 plus 1 plus 1 and a sum of 4 ones there are 5 ways of doing it as soon as you look at even slightly larger numbers there become many more ways of doing this take for example the number 7 if we look at 7 there are 15 ways of writing 7 as sums of numbers 7 itself 6 plus 1 5 plus 2 5 plus 1 plus 1/4 plus 3/4 plus 2 plus seven ones so if we count up all the sums that we've made here we see that the total number is 15 and generally this is denoted by the shorthand P of seven equals fifteen Ramanujan and Hardy wanted to develop a formula to calculate the partitions of any number no matter how large at that time had around the turn of the century one of the great mathematical achievements was what was called the prime number theorem and this theorem gave a formula for approximating how many Prime's there were to any particular number you wanted starting with the smallest 1/2 and going up to any particular limit whether it was a million a billion or any large number it would give an approximate value although it was a tremendous achievement indeed a brilliant a piece of work it is an approximate solution consequently when people started studying the number of partitions of an integer so to speak the basic problem of addition as studying Prime's as the basic problem of multiplication the hope was that you could find a formula for this number which would be as good as this major achievement in prime number theory consequently say if you are counting the number of partitions of 200 which turn out to be around four trillion you would expect that an error around a million or so would be excellent you would probably be pleased if it was on the order of only billions but you might hope for millions Ramanujan believed her that all of this was lowering your sights much too much he believed that it would be possible to provide a formula that would be exactly correct the two of them together were able to produce this formula which they then checked against the number of ways of partitioning 200 the right answer is close to four trillion they had the major McMahon compute by hand the correct answer which took nearly a month of time prior to high-speed computers and when they compared their predicted answer to his they found that their theoretical calculations came to within point zero four of the exactly correct answer well since the answer is a whole number and not a fraction all you need to do is take their theoretical answer drop off the fractional part and you have the exact right answer and this was a revolutionary and surprising achievement the form of this formula is even more stunning it involves transcendental numbers and expressions that seem to be totally unrelated they might be appropriate say in the course on engineering or theoretical physics but for actually counting how many ways you can add up sums to get a particular number they seem absolutely incredible in fact I was stunned the first time I saw this formula I could not believe it and the experience of seeing it explained and understanding how it took shape or really I think convinced me that this was the area of mathematics I wanted to pursue you e to the -2 and I'm sure even if now you asked 99.9% of the other mathematicians they would like to prove such a result if they do not know that it actually had been done by hardly an imagined suspect they would say that this test is just out of the question there's no way one can write down such a sum of products of completed terms that actually gives you the exact value right was entirely up to Ramanujan to get it right and then hardly protein all the technical skill and he was a wonderful man I'm a dashing and he could overcome the technical difficulties but I believe Hardy was not the only mathematician who could have overcome those difficulties I'm sure that little wood could have done it probably Mordor could have done it booyah could have done it I'm sure they're quite a few people who could have played hard this role but Ramanujan role in that particular partnership and don't think could have been played at the time by anybody else the origins of Ramanujan extraordinary mathematical insight remain a mystery what did you really mean when he told Indian friends that his formulae were revealed to him in his sleep by the goddess namagiri Hardy and most other pure mathematicians will acknowledge that there are these flashes of insight that mathematics is not a game in which you sit just writing and writing and writing and things sort of slowly evolved in a deductive science as many people believe it is something where you try a problem you fail you try something else you fail you give up for a while and one morning when you're standing in the shower all of a sudden it hits you this is how the thing goes and this flash of insight sort of describes the whole panorama for you and then you go to your study and you start to write and you see clearly what was correct and you're able to write down and full justification of your insight well if one suggests that that say Ramanujan being the genius he was had more of this happened to him more often than the average mathematician and he had it and with his outlook Hindu outlook it is not inconceivable that he would attach a religious significance to it I do not believe in the immemorial wisdom of the east and the picture I want to present to you is that of a man who had his peculiarities like any other distinguished man but a man in whose society one could take pleasure with whom one could take tea and discuss politics or mathematics the picture in short not of a wonder from the east or an inspired idiot or a psychological freak but of a rational human being who happened to be a great mathematician no way even hardly could see what went on in drama no just mind he came up with his with his amazing formulae amazing relations and identities and then he had these fantastic hunches but I don't think hard because I don't know how Ramanujan came to have these - this is hunches how he came to have such well informed guesses occasionally of course in other cases Ramanujan was absolutely wrong it was very naive he he saw that mathematics is is very nice there are very few pitfalls that that was one of his strengths and also his weaknesses he didn't realize the things could go very badly wrong in the spring of 1917 Ramanujan fell ill possibly with tuberculosis a gastric ulcer or gross vitamin deficiency caused by poor nutrition no one was able to arrive at a precise diagnosis Ramanujan was ill essentially all the time in Indian in and out of bed one thing 8 or the other thing aids here he went to a host of doctors and whenever he started with the doctor he was full of confidence faith and hope and unfortunately little later when he realized the doctor couldn't help him he he went to the other extreme and he saw that this doctor was no good at all I fell into his threat how could how could I get away from me how can I run away from him My dear ramalingam the whole of last night I had fever and my temperature this morning was about 102 degrees the old cook has left this place the day before yesterday the person cook spoiled all the apple apple by scorching some of them and leaving some raw yesterday I had no dinner at all my dear Ramanujan I was exceedingly grieved to have your painful letter sorry to hear the you cook is a failure as far as you are concerned now then I will have to be a bit harsh with you I am impressed with your being so particular about your pellets but you lefty choose between controlling your pellets and killing yourself hard eh to the master of Trinity February in 1918 dear Thompson I should like to say more clearly what the position about Ramanujan is if he has not been so ill I would have deferred putting him up for a fellowship for a year or so not that there is any question of the strength of his claim but merely to let things take their ordinary course as it is I felt no time must be lost for my own part I think probably he will be alive in a year's time and that he may recover completely like all Indians he is fatalistic and it is terribly hard to get him to take care of himself everyone too is frightened of the continual illness and solitude affecting his mind in various sanatoria he was in the pain he had and the mathematics he was trying to do it was enjoying completely dominating his life you check it at some stage he had nightmares he had nightmares in which he viewed his own abdomen and he so it is a function which had very singularities and the son she had singularities at one and at minus one and lots of other in integers and he had a very strong pain at one and he had half as much pain at singularity minus one and he heard as much pain on the outside and so on so just viewed his own stomach as a mathematical object he viewed his own abdomen as a mathematical mad mathematical object and such nightmares apparently recurred so he must have been completely preoccupied with his illness and mathematics Ramanujan s condition and state of mind fluctuated wildly he even attempted suicide no one can understand Ramanujan who does not understand his passion for numbers in themselves he could remember the idiosyncrasies of numbers in an almost uncanny way it was Littlewood who said that every positive integer was one of Ramanujan friends I remember going to see him when he was lying ill in Putney I had ridden in taxi cab number one 729 and remarked that the number seemed to me rather a dull one and that I hoped it was not an unfavorable omen no he replied it is a very interesting number it is the smallest number expressible as a sum of two cubes in two different ways with the end of the war Ramanujan decided to go back to India at least for a while the work he had already done in England had secured him fellowships at both the Royal Society and Trinity the first Indian to be elected to either I Srinivasa Ramanujan elected fellow of Trinity College do hereby promise that I will loyally observe the statutes ordinances and good customs of the college and in all things endeavour to promote its welfare 22nd February 1919 yes Ramanujan five days later he left for India he would never see Trinity College again he will return to India with a scientific standing and reputation such as no Indian has enjoyed before and I'm confident that India will regard him as the treasure he is his natural simplicity and modesty has never been affected in the least by success indeed all that is wanted is to get him to realize that he really is a success you know I'm not marrying their cousin ever he used to say if you had come with me I wouldn't have fallen ill it's because you didn't come that my health failed Ramana since last year must have been a very hard one for him one of reminiscence classmates met him on his return to Madras and writes that he was very strained he was not a very happy person the way he was before he left India and he says that he looked very glum and very morose he said he had left all his maths books in England and would like to go back he also said he had five thousand rupees in savings to buy me diamond ear drops and a gold belt but in some strange way Ramanujan must have felt that his life is coming to an end coach as I am guessing because the speed with which he did work during the past year and which has been recorded in what is now called the lost notebook is according to everyone who has read it one of the most original pieces of mathematics and some ways the very best which Ramanujan did Ramanujan - Hadi Madras 12 January 1920 I am extremely sorry for not writing you a single letter up to now I have discovered very interesting functions recently which I call more theta functions unlike the false theta functions they enter into mathematics as beautifully as the ordinary theta functions he wouldn't talk to anyone who came to the house it was always maths even then he didn't care about his meals but would only do sums he sent them to England food is before he died he was scribbling he filled the box of papers and there were more people scattered around the map or among the people spent here and death and changed hands I don't know where they went for him in this universe Matz was everything the work Ramanujan did on his deathbed did reach Cambridge his notebooks restored in the Rennes library at Trinity for 50 years until professor Andrews began work on them in 1976 Ramanujan was always guided by example he would run many calculations indeed in this lost notebook probably almost half of it consists of pages that have a certain almost hysteria about them formulas are sort of started and stopped tailing off in one direction a column of figures will be added up at an angle over here something else will be written upside down nothing will be comprehensible on such a page so you get a clear feeling that he is working from example and building this up from smaller ideas into one of these grand formulas of the discoveries in this notebook I would say that prior to actually unearthing the notebook itself and seeing what was there maybe fifteen or twenty percent of these formulas had been discovered in some way or another by others but the vast majority of it is not only lay undiscovered but contains treasures of interest and significance in mathematics today so although one can feel tremendous sympathy for this man as he was dying nonetheless what he did was absolutely marvelous how does he know courtesy gonna see what many and then guys lying battle on a stick bit he told me that his name would live for a hundred years he said whether I am alive or dead you will have money he knew she was dying and said there was nothing anyone could do about it I always remember his name whenever I meditate I have just heard from India that Ramanujan is dead it is a great shock to me for I thought before he went back that he had begun to turn the corner could not Trinity do something to commemorate him permanently in a small way after all he was a most extraordinary genius of whom even Trinity may be justly proud Hardy has a plaque in the bowling-green and little woods bust stands in the combination room to which Trinity fellows still retire after dinner to drink claret and port there is no plaque or bust of Ramanujan at Trinity but Hardy did help arrange for Ramanujan mathematical papers to be edited and published as a lasting memorial to his mathematical genius even when hardly informed little of Ramana justice and lived with answered hardly from Cornwall where he was at the time most of the letter was about mathematics the letter started off saying dear H what a tragedy about art I will see what I can do about the obituaries and then number one Omega H you are proof of the lemma about Sigma from minus m to infinity minus 1 to the end and C minus S is sound in 1941 a picture post photographer took this picture of an unnamed spectator at a Twickenham rugby match it was gh Hardy a year earlier when he felt he was past his prime Hardy who wrote these words in his mathematicians apology I have never done anything useful no discovery of mine has made always likely to make directly or indirectly for good or for ill the least difference to the amenity of the world judged by all practical standards the value of my mathematical life is nil and outside mathematics is trivial anyhow the case for my life then or for anyone else who has been a mathematician in the same sense in which I have been one is this that I have added something to knowledge and helped others to add more and that these some things have a value which differs in degree only and not in kind from that of the creations of the great mathematicians or of any of the other artists great or small who have left some kind of memorial bhai them I still say to myself when I'm depressed and find myself forced to listen to pompous and tiresome people well I have done one thing you could never have done and that is to have collaborated with both little wood and Ramanujan on something like equal terms

Channel: Christopher Sykes

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Keywords: genius, mathematics, Ramanujan, Hardy, Littlewood, Chandrasekhar, Andrews, Cambridge, India, Madras, Tamil, Nadu, Kumbakonam, 1729, taxi, cab, romance, Channel, Equinox, letters, indian, clerk, Mathematician's, Apology, Kanigel, infinity, science, prime, numbers, biography, Christopher, Sykes, documentary, INCA, Karl, Sabbagh, the man who knew infinity, movie, jeremy irons, kanigel, robert kanigel, janaki, mrs ramanujan, trailer, matt brown, love, discovery, CP Snow, Freeman Dyson, Trinity College

Id: OARGZ1xXCxs

Length: 52min 15sec (3135 seconds)

Published: Sun May 13 2012

Reddit Comments

[u/cigol]

one of the greatest mathematicians ever, more like

[u/ravindrak81]

A detailed video showing the place of his birth, his close associates, friends at Oxford, relatives and other mathematicians.

Very grateful to Christopher J Sykes for creating this.

http://news.yahoo.com/mathematicians-century-old-secrets-unlocked-171554694.html#

[u/[deleted]]

I wanna be like him, but Reddit.