In the year 1913, G. H. Hardy received a ten-page letter from an unknown clerk from Madras, India. Like many other letters, prominent mathematician Hardy thought that the letter was no different. However, at second glance, he found ‘his’ work rather intriguing. Hardy then asked J.E. Littlewood, his colleague to take a look at the papers. Littlewood was amazed by Ramanujan’s genius. They concluded that it was certainly the most remarkable letter they had received and that Ramanujan was a mathematician of the highest quality, a man of altogether exceptional originality and power.
Thus was Srinivasa Ramanujan (1887-1920) introduced to the mathematical world. Born in South India, Ramanujan was a promising student, winning academic prizes in high school. But at age of 16, his life took a decisive turn after he obtained a book titled A Synopsis of Elementary Results in Pure and Applied Mathematics. It was in no sense a mathematical classic; rather, it was written as an aid to coaching English mathematics students facing the notoriously difficult Tripos examination, which involved a great deal of wholesale memorization. But for Ramanujan, it inspired a burst of feverish mathematical activity, as he worked through the book’s results and beyond. Unfortunately, his total immersion in mathematics was disastrous for Ramanujan’s academic career: ignoring all his other subjects, he repeatedly failed his college exams.
As a college dropout from a poor family, Ramanujan’s position was precarious. He lived off the charity of friends, filling notebooks with mathematical discoveries and seeking patrons to support his work. Ramanujan had his first paper published, a 17-page work on Bernoulli numbers that appeared in 1911 in the Journal of the Indian Mathematical Society. Still, no one was quite sure if Ramanujan was a real genius or a crank. With the encouragement of friends, he wrote to mathematicians in Cambridge seeking validation for his work. He wrote twice with no response; on the third try, he found Hardy.
Hardy wrote enthusiastically back to Ramanujan that Ramanujan has to be brought to England. Ramanujan declined Hardy’s proposal initially because his mother shunned his travel to foreign countries but she finally gave in and Ramanujan later moved to England.
Ramanujan’s arrival at Cambridge was the beginning of a very successful five-year collaboration with Hardy. In some ways the two made an odd pair: Hardy was a great exponent of rigour in analysis, while Ramanujan’s results were (as Hardy put it) “arrived at by a process of mingled argument, intuition, and induction, of which he was entirely unable to give any coherent account”. Hardy did his best to fill in the gaps in Ramanujan’s education without discouraging him. He was amazed by Ramanujan’s uncanny formal intuition in manipulating infinite series, continued fractions, and the like. Hardy quoted,” I have never met his equal, and can compare him only with Euler or Jacobi.”
Ramanujan’s years in England were mathematically productive, and he gained the recognition he hoped for. Cambridge granted him a Bachelor of Science degree “by research” in 1916, and he was elected a Fellow of the Royal Society (the first Indian to be so honoured) in 1918. But the alien climate and culture took a toll on his health. In 1917 he was hospitalized, his doctors fearing for his life. By late 1918 his health had improved; he returned to India in 1919. But his health failed again, and he died the next year.
Besides his published work, Ramanujan left behind several notebooks, which have been the object of much study. The English mathematician G. N. Watson wrote a long series of papers about them. More recently the American mathematician Bruce C. Berndt has written a multi-volume study of the notebooks. In 1997 The Ramanujan Journal was launched to publish work “in areas of mathematics influenced by Ramanujan”.
[From A Story Featured in Shasthra Snehi, on 100th Death Anniversary of Srinivasa Ramanujan]Writer- Subo
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