Hardy, Littlewood & Ramanujan, a mathematical trio

After an exchange of letters with Srinivasa Ramanujan revealed his amazing mathematical insights, two Cambridge dons, GH Hardyand John E. Littlewood, encouraged the talented but untrained young mathematical genius to come to Cambridge. There they arranged to get him a position and collaborated with him on mathematical work. 

Sadly, Ramanujan did not adapt well to the climate of England. A vegetarian, he also found it difficult to stomach the food in college. When his health began to fail, Hardy encouraged him to return to India for a holiday. He lived to see his home and family, but died in Madras of a parasitic infection. He was only thirty-three years old.

At the request of a friend, Hardy penned a memoir, A Mathematician's Apology, during his final illness. This is a seen by many as a study of the creative mind and process. Published in 1940, a year into the war, the book reveals a somewhat gloomy outlook.

JE Littlewood was a highly respected mathematician who tackled the Riemann hypothesis as assigned by his tutor, EW Barnes. Serving in the Royal Garrison Artillery during WWI, he worked out formulae that helped to ease and speed the calculation of missile trajectories. He collaborated extensively with Hardy and Rajanuman, and was also widely recognized for his own mathematical prowess, among other honours winning a Smith Medal and a Copley Medal. He was elected to the Royal Society in 1915 and awarded its medal in 1929. Though he suffered from depression at times, in old age he continued to produce mathematical work. He was ninety when he published a paper explaining a problem he had finally overcome, after thinking about it for many years. He was also the recipient of a number of international honours for his mathematical contributions.

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Alan Turing, mathematician, marathon runner, and father of computing

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David Hilbert, German mathematician