Srinivasa RAMANUJAN 👨‍🎓 (1887-1920)

Srinivasa Ramanujan was one of the most remarkable mathematicians of the 20th or in fact any other century even today we don't know how he got many of his results his notebooks are full of enigmatic theories and formula that will keep mathematicians busy for many years to come now to tell you some more about his life and his works [Music] you Ramanujan was born in 1887 in erode a city in Madras State now known as Tamil Nadu India he came from a working-class family and attended various local primary schools by the age of 11 when he encountered formal maths in school for the first time it was already clear that Ramanujan was operating on a different plane from his peers in his early teens he cheated other pupils quickly mastered new concepts and won a string of academic awards in 1903 as a 16 year old he got hold of a library copy of a book called a synopsis of elementary results despite the title it was actually a dense collection of about 5000 results in pure maths based on the notoriously difficult mathematical Tripos at Cambridge University Ramanujan wasn't satisfied just to absorb the books contents though he set about deriving all of the results himself with no outside help in the process he came up with a wealth of other extraordinary conclusions that seemed to spring from nowhere this almost incredible creativity became a hallmark of Ramanujan work to the end of his life he attributed all of his major insights and discoveries to a divine source the goddess namagiri who he said appeared to him in visions and dreams and revealed formulae to him after one of these experiences he wrote while asleep I had an unusual experience there was a red screen formed by flowing blood as it were I was observing it suddenly a hand began to write on the screen I became all attention that hand wrote a number of results in elliptic integrals they stuck to my mind as soon as I woke up I committed them to writing he'd also tried to prove the results that came to him in these visions and dreams but his proofs were often incomplete making it hard to check them or sometimes even to make sense of them they were also sometimes just plain wrong working in his spare time while employed as a lowly clerk in Madras now Chennai Ramanujan made new and profound discoveries in number theory or without realizing it rediscovered results that had taken mathematicians in the West centuries to obtain even when he arrived at conclusions already known he'd often do it in a totally original way by what seemed pure intuition it's possible that Ramanujan would have remained in relative obscurity had he not in his mid-20s written a series of letters to distinguished British mathematicians only one of them took him seriously fortunately that one happened to be G H Hardy famed Cambridge scholar and distinguished number theorist in Ramanujan writings hardy recognized something very special indeed some of the Indian results correspond to known maths but of a very advanced nature and arrived at by unfamiliar means other results seemed utterly new but in Hardy's opinion probably true because in his words if they were not true no one would have the imagination to invent them Hardy recognized some of the Indians formula while others as he put it seems scarcely possible to believe as far as Ramanujan theorems on continued fractions were concerned he said that he had never seen anything in the least like them before Hardy invited Ramanujan to join him and his close colleague John little would at Cambridge but it wasn't an easy decision for Ramanujan to make he'd have to leave behind his family his 13 year old wife by an arranged marriage and the lifestyle he knew and loses Brahmin status because it was taboo for members of this caste across the sea at first Ramanujan s mother was completely opposed to his going but three months later she relented after she said being told in a dream by namagiri not to stand in her son's way accompanied by another Cambridge mathematician who had been staying in India Ramanujan set sail aboard the SS neva sir bringing with him a suitcase stuffed full of notebooks containing mathematical gems he'd unearthed over the years in England Ramanujan found life difficult the weather was damp and cold the culture was alien to him and he didn't speak the language well his insistence on following a strict vegetarian diet compliant with Brahmin principles meant he had to cook all his own meals this he did irregularly and due to the outbreak of the first world war in 1914 without access to some of his customary foods he effectively became malnourished on the upside in Hardy he had a brilliant teacher who set about the delicate task of filling in some of the blanks in Ramanujan mathematical knowledge while not undermining his confidence and natural freedom of thought Hardy recalled the limitations of his knowledge were as startling as its profundity it was impossible to ask such a man to submit to systematic instruction to try to learn mathematics from the beginning once more on the other hand there were things of which it was impossible that he would remain in ignorance so I had to try to teach him and in a measure I succeeded though I obviously learnt from him much more than he learned from me for almost three years despite severe problems in adapting to his new surroundings Ramanujan prospered academically in partnership with Hardy who played a critical role in correcting his proofs and presentation he published a series of important papers filmmaker Matthew Brown who directed the 2015 film the man who knew infinity became fascinated by the relationship between Ramanujan and Hardy they are two men so fundamentally different Ramanujan was a brahmin indian from madras with no formal education who believed a formula had no meaning unless it expressed a thought of God Hardy on the other hand was a revered professor at the prestigious Trinity College at Cambridge University and also an avowed atheist it is an incredible story of how two people were able to overcome their personal differences to form one of the greatest collaborations in history of mathematics in the spring of 1917 Ramanujan fell seriously ill possibly with tuberculosis and after that he was in and out of hospital for the rest of his time in England on one occasion Hardy took a taxi to visit him in his sickbed and noted that the cab number was one seven two nine after greeting Ramanujan he remarked what a dull number 1729 seemed to be quick as a flash Ramanujan corrected him it's a very interesting number it's the smallest number expressible as the sum of two cubes in two different ways 1 7 to 9 equals 1 cubed plus 12 cubed equals 9 cubed plus 10 cubed in 1919 Ramanujan recovered enough to travel back to India where it was hoped the more familiar climate and food would help restore his health but he died the following year the height of his mathematical powers aged just 32 in his obituary Hardy wrote the Ramanujan was a mathematician of the highest quality a man of altogether exceptional originality and power on his personal scale of maths ability Hardy scored himself a modest 25 his Cambridge colleague John little would 30 and David Hilbert the most renowned mathematician of the time 80 Ramanujan he rated it 100 even today researchers continue to sift through the disorganized but fascinating notebooks that Ramanujan left behind in search of new treasures some of his final work on a subject called Mach theta functions proved more than eight years later to be important in the physics of black holes and string theory in other cases scholars are still trying to understand how Ramanujan arrived at his results and what they might mean for the future of the subject he loved [Music]

Channel: discovermaths

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Keywords: Ramanujan, Srinivasa Ramanujan, Indian mathematician, G H Hardy, Ramanujan prime, mock theta functions, Namagiri, Discover Maths, discovermaths, David Darling, Juan Medina

Id: l_-KiA2fpLw

Length: 9min 18sec (558 seconds)

Published: Wed Aug 21 2019