Hardy and Ramanujan summary
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20TH CENTURY MATHEMATICS - HARDY AND RAMANUJAN
G.H. Hardy (1877-1947) and Srinivasa Ramanujan (1887-1920)
The eccentric British mathematician G.H. Hardy is known for his achievements in number theory and mathematical analysis. But he is perhaps even better known for his adoption and mentoring of the self-taught Indian mathematical genius, Srinivasa Ramanujan.
Hardy himself was a prodigy from a young age, and stories are told about how he would write numbers up to millions at just two years of age, and how he would amuse himself in church by factorizing the hymn numbers. He graduated with honours from Cambridge University, where he was to spend most of the rest of his academic career.
Hardy is sometimes credited with reforming British mathematics in the early 20th Century by bringing a Continental rigour to it, more characteristic of the French, Swiss and German mathematics he so much admired, rather than British mathematics. He introduced into Britain a new tradition of pure mathematics (as opposed to the traditional British forte of applied mathematics in the shadow of Newton), and he proudly declared that nothing he had ever done had any commercial or military usefulness (he was also an outspoken pacifist).
Just before the First World War, Hardy (who was given to flamboyant gestures) made mathematical headlines when he claimed to have proved the Riemann Hypothesis. In fact, he was able to prove that there were infinitely many zeroes on the critical line, but was not able to prove that there did not exist other zeroes that were NOT on the line (or even infinitely many off the line, given the nature of infinity).
Meanwhile, in 1913, Srinivasa Ramanujan, a 23-year old shipping clerk from Madras, India, wrote to Hardy (and other academics at Cambridge), claiming, among other things, to have devised a formula that calculated the number of primes up to a hundred million with generally no error. The self-taught and obsessive Ramanujan had managed to prove all of Riemann’s results and more with almost no knowledge of developments in the Western world and no formal tuition. He claimed that most of his ideas came to him in dreams.
Hardy was only one to recognize Ramanujan's genius, and brought him to Cambridge University, and was his friend and mentor for many years. The two collaborated on many mathematical problems, although the Riemann Hypothesis continued to defy even their joint efforts