Srinivasa Ramanujan's Crowning Achievements

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[{"type":"txt","id":"rich_1493116928511","data":"Srinivasa Ramanujan was one of India's greatest minds, a peerless genius who was ahead of his time, surprising many eminent mathematicians from across the world. Today, his life has also been turned into a Hollywood movie starring Dev Patel in the role of the quite and shy genius of math, titled The Man Who Knew Infinity, and know he did. <\/p>So today, on the anniversary of his birth, let us take a look at his greatest contributions to Mathematics<\/p>1. Letters to G. H. Hardy<\/b> <\/p>Ramanujan, with the help of his friends, had written letters and sent his theorems to professors in England in the late 1900s and early 1910s. While many professors returned his papers without comment, G. H. Hardy couldn't believe his own eyes. Hardy at first thought that the papers from from a potential fraud, but then later concluded that nobody would posses the imagination to conjure up the theorems Ramanujan had proved. <\/p>"},{"type":"img","id":"img-uid-1493117909468","data":"58ff31a899b76"},{"type":"txt","id":"rich_1493117911991","data":"2. The Ramanujan Conjecture <\/b> <\/p>Also known as the Ramanujan - Petersson Conjecture states that Ramanujan's tau function given by the Fourier coefficients \u03c4(n) of the cusp form \u0394(z) of weight 12 (image of equation given below)<\/p>This is one of Ramanujan's most famous equation, helping in the construction of Ramanujan graphs by Lubotzky.<\/p>"},{"type":"img","id":"img-uid-1493118420177","data":"58ff2e35eddf0"},{"type":"txt","id":"rich_1493118453815","data":"3. Ramanujan Notebooks<\/b> <\/p>Following his death at the young age of 32, Srinivasa's brother collected his papers and his notebooks to publish them, which he did. It is considered one of the most important works of modern mathematics. But many of his notes were still lost and discovered later, and as such, there are 4 notebooks of his that have been published since then. The publication of the notebooks also gave rise to a popular misconception that Ramanujan couldn't solve the theorems but wrote the final result directly, but this is not true, as there is no reason for Ramanujan to write the proof in his own notes without having to explain it to someone. <\/p>"},{"type":"img","id":"img-uid-1493118536529","data":"58ff31c3937d0"},{"type":"txt","id":"rich_1493118539004","data":"4. Ramanujan's work with the infinite series<\/b> <\/p>The very series that caught G. H. Hardy's attention, amazing him enough to request Ramanujan to come to Cambridge, which he promptly refused due to resistance from parents. This has also earned him the nickname: The Man Who Know Infinity. <\/p>"},{"type":"img","id":"img-uid-1493118882723","data":"58ff2ffe89647"},{"type":"txt","id":"rich_1493118999400","data":"5. Hardy\u2013Ramanujan Number (1729)<\/b><\/p>A bit of a story, this one. During his time in England and at Cambridge University, Ramanujan would often fall sick due to various health issues. During one such period where he was sick, his Academic Advisor and fast friend G. H. Hardy went to see him in a taxicab bearing the number 1729. When Hardy remarked that 1729 was a dull number, and that he hoped it wasn't a bad omen, to which Ramanujan replied, \"No, it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.\"<\/p>Recounting his anecdote years later, Hardy quoted Professor Littlewood, his colleague and Ramanujan's other academic advisor, that 'every positive integer was Ramanujan's personal friend.'<\/p> <\/p>"},{"type":"img","id":"img-uid-1493119284522","data":"58ff31ef79aa2"}]

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