The Letter That Changed Mathematics

In January 1913, G. H. Hardy at Cambridge opened a letter from a 25-year-old clerk in Madras who had failed his college exams. It held about 120 formulas with no proofs. Some, Hardy said, defeated him completely. Within seven years the clerk, Srinivasa Ramanujan, was famous — and dead. His story: Carr's book of formulas, partitions, the infinite tower of square roots, Cambridge, the partition formula, a series for π still used by computers, illness, the taxi number 1729, and the lost notebook. 0:00 The letter 0:37 A clerk in Madras 2:28 Hardy reads it 3:22 Cambridge 4:07 Counting partitions 4:44 A formula for π 5:11 Illness 5:43 1729 6:15 The lost notebook A note on the story Every number on screen is computed: 1729 found by checking every sum of two cubes up to 12³, the partitions of 4, 5 and 6, p(n) up to n = 200 (3,972,999,029,388), his 1914 π series summed with exact integer arithmetic (6, 15, 23, 31 … correct digits), and the nested radical converging to 3. The goddess dream and some quotes are as reported by family and colleagues. The cause of his illness is uncertain; tuberculosis was suspected, and later reviews suggest hepatic amoebiasis. Sources • G. H. Hardy, Ramanujan: Twelve Lectures (1940) • R. Kanigel, The Man Who Knew Infinity (1991) • S. Ramanujan, "Modular equations and approximations to π", Quarterly Journal of Mathematics 45 (1914) • G. H. Hardy & S. Ramanujan, "Asymptotic formulae in combinatory analysis", Proc. London Math. Soc. (1918) • MacTutor History of Mathematics: Srinivasa Ramanujan; Wikipedia Images (Wikimedia Commons) Public domain / CC0: Srinivasa Ramanujan- Add. MS a947; RamanujanCambridge; Godfrey Hardy 1890s; Wren Library, Trinity College, Cambridge University; Ramanujanhome; Cauvery at Erode; Putney from the air; Trinity College Great Court Fountain Willis 1886. Creative Commons, used unmodified with credit: Srinivasa Ramanujan-Add. MS a94 version2 (cropped) (Unknown authorUnknown author, CC BY 4.0); Trinity College - Great Court 01 (Rafa Esteve, CC BY-SA 4.0); Kumbakonam Cauvery (Ssriram mt, CC BY-SA 4.0); TNK26-59-KMU-Sarangapani temple gopuram Kumbakonam 3D (VasuVR, CC BY 4.0); Madras port c1950 (Autor/in unbekannt, CC BY-SA 4.0); Narasimhaswamy temple, Namakkal (2) (Ssriram mt, CC BY-SA 4.0); Burlington House (5125727595) (Tony Hisgett from Birmingham, UK, CC BY 2.0). Narration: the channel's own cloned voice (CosyVoice3). Script and animations: original. #Ramanujan #Math #History