Working independently and largely in isolation from the wider scientific community, he made major contributions to celestial mechanics and to the theory of ordinary differential equations.

Strong encouraged Hill to read the great works on analysis by Sylvestre Lacroix and Adrien-Marie Legendre, as well as the treatises on mechanics and mathematical astronomy by Joseph-Louis Lagrange, Pierre-Simon Laplace, Siméon Denis Poisson, and Gustave de Pontécoulant.

In 1861, Hill was hired by John Daniel Runkle to work in the United States Naval Observatory's Nautical Almanac Office, based in Cambridge, Massachusetts.

Hill lectured at Columbia University from 1898 to 1901, but he attracted few students and he ultimately chose to return his salary and to continue working alone in his home in West Nyack, rather than within academia.

[4] Hill's Collected Works were published in 1905-07 by the Carnegie Institution for Science, with a 12-page introduction by the eminent French mathematician and theoretical physicist Henri Poincaré.

[3] Of Hill's isolation from the academic community, Poincaré declared that This reserve, I was going to say this savagery, has been a happy circumstance for science, because it has allowed him to complete his ingenious and patient researches.