The family were devout Wesleyans who enjoyed music and among John's brothers, Thomas became a missionary, George a farmer, and William Grylls Adams, professor of natural philosophy and astronomy at King's College London.

[1] There he learned classics but was largely self-taught in mathematics, studying in the Library of Devonport Mechanics' Institute and reading Rees's Cyclopædia and Samuel Vince's Fluxions.

[1][4] In 1821, Alexis Bouvard had published astronomical tables of the orbit of Uranus, making predictions of future positions based on Newton's laws of motion and gravitation.

Adams believed, in the face of anything that had been attempted before, that he could use the observed data on Uranus, and utilising nothing more than Newton's law of gravitation, deduce the mass, position and orbit of the perturbing body.

While he worked on the problem back in Cambridge, he tutored undergraduates, sending money home to educate his brothers, and even taught his bed maker to read.

[7] Meanwhile, Urbain Le Verrier, on 10 November 1845, presented to the Académie des sciences in Paris a memoir on Uranus, showing that the preexisting theory failed to account for its motion.

[1] On reading Le Verrier's memoir, Airy was struck by the coincidence and initiated a desperate race for English priority in discovery of the planet.

[7] But it is also notable (and not included in some of the foregoing discussion references) that Adams himself publicly acknowledged Le Verrier's priority and credit (not forgetting to mention the role of Galle) in the paper that he gave 'On the Perturbations of Uranus' to the Royal Astronomical Society in November 1846:[9] I mention these dates merely to show that my results were arrived at independently, and previously to the publication of those of M. Le Verrier, and not with the intention of interfering with his just claims to the honours of the discovery; for there is no doubt that his researches were first published to the world, and led to the actual discovery of the planet by Dr. Galle, so that the facts stated above cannot detract, in the slightest degree, from the credit due to M. Le Verrier.Adams held no bitterness towards Challis or Airy[3] and acknowledged his own failure to convince the astronomical world:[7] I could not expect however that practical astronomers, who were already fully occupied with important labours, would feel as much confidence in the results of my investigations, as I myself did.His lay fellowship at St John's College came to an end in 1852, and the existing statutes did not permit his re-election.

However, he was "extraordinarily uncompetitive, reluctant to publish imperfect work to stimulate debate or claim priority, averse to correspondence about it, and forgetful in practical matters".

[3] It has been suggested that these are symptoms of Asperger syndrome which would also be consistent with the "repetitive behaviours and restricted interests" necessary to perform the Neptune calculations, in addition to his difficulties in personal interaction with Challis and Airy.

[10] In 1852, he published new and accurate tables of the Moon's parallax, which superseded Johann Karl Burckhardt's, and supplied corrections to the theories of Marie-Charles Damoiseau, Giovanni Antonio Amedeo Plana, and Philippe Gustave Doulcet.

[1] He had hoped that this work would leverage him into the vacant post as superintendent of HM Nautical Almanac Office but John Russell Hind was preferred, Adams lacking the necessary ability as an organiser and administrator.

[11] Later, during the eighteenth century, Richard Dunthorne estimated the rate as +10" (arcseconds/century2) in terms of the resulting difference in lunar longitude,[12] an effect that became known as the secular acceleration of the Moon.

[13] In 1820, at the insistence of the Académie des sciences, Damoiseau, Plana and Francesco Carlini revisited Laplace's work, investigating quadratic and higher-order perturbing terms, and obtained similar results, again addressing only a radial, and neglecting tangential, gravitational force on the Moon.

Small terms integrated in time come to have large effects and Adams concluded that Plana had overestimated the secular acceleration by approximately 1.66" per century.

[3] In 1858 Adams became professor of mathematics at the University of St Andrews, but lectured only for a session, before returning to Cambridge for the Lowndean professorship of astronomy and geometry.

[1] The great meteor shower of November 1866 turned his attention to the Leonids, whose probable path and period had already been discussed and predicted by Hubert Anson Newton in 1864.

[1] Newton had asserted that the longitude of the ascending node, that marked where the shower would occur, was increasing and the problem of explaining this variation attracted some of Europe's leading astronomers.

[3] Using a powerful and elaborate analysis, Adams ascertained that this cluster of meteors, which belongs to the Solar System, traverses an elongated ellipse in 33.25 years, and is subject to definite perturbations from the larger planets, Jupiter, Saturn, and Uranus.