 His early scholarly publications (1842-1847) were in mathematics.He had a distinguished career at Trinity, spanning over fifty-five years, as a student, fellow and professor, successively of Oratory, English Literature, Jurisprudence and Greek, LL.D, FTCD), subsequently becoming the College Librarian and ultimately its Vice Provost.During his life, Ingram was President of the Library Association of Great Britain, co-founder of the National Library of Ireland, National Library trustee, Vice-president of the Library Association of Ireland, a member of the Royal Irish Academy, co-founder of the Dublin Statistical Society, honorary member of the American Economic Association, member of the English historical school of economics and co-founder of the "Hermathena" publication.