HARDY, GODFREY HAROLD

born Feb. 7, 1877, Cranleigh, Surrey, Eng. died Dec. 1, 1947, Cambridge, Cambridgeshire English mathematician who solved many problems in prime-number theory. Hardy graduated from Trinity College of the University of Cambridge in 1899, became a fellow at Trinity in 1900, and lectured in mathematics there from 1906 to 1919. In 1908 he provided, concurrently with the German physician Wilhelm Weinberg, what is now known as the Hardy-Weinberg law, which resolved the controversy over what proportions of dominant and recessive genetic traits would be propagated in a large mixed population. He attached little importance to the law, but it subsequently became centrally important in the study of many genetic problems, including Rh blood group distribution and hemolytic disease. In 1912 Hardy published, with his longtime collaborator John E. Littlewood, the first of a series of papers that contributed fundamentally to many realms in mathematics, including the theory of Diophantine analysis, divergent series summation, Fourier series, the Riemann zeta function, and the distribution of primes. He also proved that when the Riemann zeta function (which is equal to the infinite series 1 + 1/2s + 1/3s + 1/4s + . . . , where s = u + iv) has a zero value, an infinite number of (although perhaps not all) values of u are equal to 1/2 when v 0. Bernhard Riemann of Germany had hypothesized that all values of u would equal 1/2 when v 0. Besides Littlewood, Hardy's other important collaboration was with Srinivasa Ramanujan, a poor, self-taught Indian clerk whom Hardy immediately recognized as a mathematical genius. Hardy brought Ramanujan to Cambridge in 1914, filled in the gaps in his mathematical education by private tutoring, and coauthored several papers with him before Ramanujan returned to India in 1919. In 1914 Hardy became Cayley lecturer at Cambridge, and in 1919 he was appointed to the Savilian chair of geometry at the University of Oxford. He returned to Cambridge in 1931 as Sadleirian professor of pure mathematics and remained there until his death.