U.S. mathematical astronomer considered by many of his peers to be the greatest master of celestial mechanics of his time. After receiving a B.A. from Rutgers College (1859), Hill joined the Nautical Almanac Office in 1861. Among his many accomplishments, Hill was the first to use infinite determinants to analyze the motion of the Moon's perigee (1877). He also developed a theory of the motion of Jupiter and Saturn. His most significant theory, dealing with the effects of the planets on the Moon's motion, is considered fundamental in the development of celestial mechanics.

For his research on the motions of the Moon, Hill received the Gold Medal of the Royal Astronomical Society in 1887, the Damoiscan Prize from the Académie des Sciences in 1898, and the Royal Society's Copley Medal in 1909. He was elected to the U.S. National Academy of Sciences (1874) and the Royal Society (1902), and from 1894 to 1896 he served as president of the American Mathematical Society. Many of his papers were republished by the Carnegie Institution in The Collected Mathematical Works of George William Hall.