Some Famous Problems of the Theory of Numbers and in Particular Waring's Problem An Inaugural Lecture delivered before the University of Oxford by Hardy, G. H. (Godfrey Harold), 1877-1947
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Godfrey Harold Hardy FRS was a prominent English mathematician, known for his achievements in number theory and mathematical analysis.
Non-mathematicians usually know him for A Mathematician's Apology, his essay from 1940 on the aesthetics of mathematics. The apology is often considered one of the best insights into the mind of a working mathematician written for the layman.
His relationship as mentor, from 1914 onwards, of the Indian mathematician Srinivasa Ramanujan has become celebrated. Hardy almost immediately recognized Ramanujan's extraordinary albeit untutored brilliance, and Hardy and Ramanujan became close collaborators. In an interview by Paul Erdős, when Hardy was asked what his greatest contribution to mathematics was, Hardy unhesitatingly replied that it was the discovery of Ramanujan. He called their collaboration "the one romantic incident in my life."
Poetically written, as can always be expected from Hardy. He provides fascinating background information on Waring’s problem while allowing his personality and wit to shine through. Hardy not only references many great minds such as Polyá and Hilbert, but also expounds upon his collaborations with Ramanjuan and Littlewood. Very easily digestible read as well.