Introduction to the Theory of Numbers

Godfrey Harold(1877-1947) was a prominent English mathematician, known for his achievements in number theory and mathematical analysis. He is known for his essay in 1940 on the aesthetics of mathematics, A Mathematician's Apology, which is often considered one of the best insights into the mind of a working mathematician written for the layman. In 1914, he was the mentor of the Indian mathematician Srinivasa Ramanujan. He recognized Ramanujan's brilliance, they became close collaborators. When asked what his greatest contribution to mathematics was, he replied that it was the discovery of Ramanujan. He is credited with reforming British mathematics by bringing rigour into it. British mathematicians had remained largely in the tradition of applied mathematics, in thrall to the reputation of Isaac Newton. He was more in tune with the cours d'analyse methods dominant in France, and aggressively promoted his conception of pure mathematics, in particular against the hydrodynamics which was an important part of Cambridge mathematics. From 1911 he collaborated with J. E. Littlewood, in mathematical analysis and analytic number theory. This led to quantitative progress on the Waring problem, as part of the Hardy-Littlewood circle method. In prime number theory, they proved results and some notable conditional results. This was a major factor in the development of number theory as a system of conjectures. Hardy's collaboration with Littlewood is among the most successful and famous collaborations in mathematical history. Hardy is also known for formulating the Hardy-Weinberg principle, a basic principle of population genetics, independently from Wilhelm Weinberg in 1908. He played cricket with the geneticist Reginald Punnett who introduced the problem to him, and Hardy thus became the somewhat unwitting founder of a branch of applied mathematics. His collected papers have been published in seven volumes by Oxford University Press