Adams was educated at St John's College, Cambridge but this was only made possible by a number of fortuitous circumstances. His mother received a small inheritance in 1836, Adams earned money as a tutor in 1837, and he then won a scholarship to St John's College. These sources of money made a university education for him possible but financially difficult. He began his undergraduate mathematics course in October 1839 and graduated as Senior Wrangler (ranked top of the First Class) four years later having, rather remarkably, won the first prize in Greek testament every year. In the Mathematical Tripos examinations of 1843 he is said to have been awarded double the marks of the Second Wrangler which, if true, is an incredible achievement. Also in 1843 he became first Smith's Prizeman and he became a Fellow of St John's College. He did not spend all his time on research, however, for he tutored undergraduates so that he might earn money to send home to help with his brother's education. We should note that of his three brothers, Thomas Adams became a missionary, George Adams became a farmer, while William Grylls Adams became professor of natural philosophy and astronomy at King's College, London, and was elected a Fellow of the Royal Society.