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Abbott was born in [[Dublin]] and was educated at [[Trinity College, Dublin|Trinity College]]. He was elected a scholar in 1848, graduated in 1851 as a senior moderator in mathematics and was made a fellow of the college in 1854.<ref name=redcal>{{cite book |date=1907 |title=Dublin University Calendar, A Special Supplemental Volume for the year 1906-7 |location=Dublin |publisher=Hodges, Figgis, and Co. Ltd. |volume=III}}</ref> He obtained an M.A. and a D.Litt. (1891) from Trinity, and was ordained a minister in the [[Church of Ireland]].
In 1852 he solved a geometrical problem posed by [[J. J. Sylvester]].<ref>[https://books.google.com/books?id=kOYv0RX3Ym4C
He occupied the [[chair (academic)|chair]] of moral philosophy (1867–72), of biblical Greek (1875–88), and of Hebrew (1879–1900).<ref>"Alumni Dublinenses : a register of the students, graduates, professors and provosts of [[Trinity College, Dublin|Trinity College in the University of Dublin]] (1593–1860 [[George Dames Burtchaell]]/[[Thomas Ulick Sadleir]] p1: Dublin, Alex Thom and Co, 1935</ref><ref>{{cite book |last=Webb |first=D.A. |editor-first=Barlett |editor-last=J.R.|date=1992 |title=Trinity College Dublin Record Volume 1991 |location=Dublin |publisher=Trinity College Dublin Press |isbn=1-871408-07-5|page=}}</ref> In 1887 he was elected librarian in Trinity and, in 1900, completed catalogues of the library's manuscript holdings.<ref>[http://www.tcd.ie/Library/manuscripts/catalogues.php Catalogues – Manuscripts & Archives]</ref> He became a senior fellow in 1897. He was one of a group of Irish scholars, including [[J. P. Mahaffy]], who made significant contributions to the dissemination and study of the works of [[Immanuel Kant]]. His translation of Kant's "Critique of Practical Reason" remained the standard English version of the text well into the 20th century.<ref>[https://books.google.com/books?id=7Rnz9cDWt9kC
In June 1901, he received an honorary [[Doctor of Divinity|doctorate in Divinity]] from the [[University of Glasgow]].<ref>{{Cite newspaper The Times |title=Glasgow University jubilee |date=14 June 1901 |page=10 |issue=36481}}</ref>
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