[1] Jónas was a teacher at the Samvinnuskóli from 1952–55, archivist at the National Archives of Iceland from 1957–63, and the director of the Árni Magnússon Institute for Icelandic Studies from 1972-94 (from which position he retired upon reaching the age limit).
[4] On 31 May 1991 he received an honorary doctorate from the Faculty of Humanities at Uppsala University, Sweden.
[6][7][8] His 1972 doctoral thesis, Um fóstbræðra sögu presented new arguments about the dating of Fóstbræðra saga (arguing that it was not, as had previously been thought, relatively archaic, but relatively late).
[9] Jónas was an important editor of Icelandic texts, namely Dínus saga drambláta,[10] Viktors saga ok Blávus,[11] and a number of sagas for the Íslenzk fornrit series, on whose editorial board he sat from 1979,[1] including Svarfdæla saga,[12] overseeing the editions of the biskupa sögur with Þórður Ingi Guðjónsson,[13] and co-editing the 2014 edition of the Poetic Edda with Vésteinn Ólason.
Jónas wrote two historical novels, one of which, The Wide World, is set in Viking age North America,[citation needed] and he translated Will Durant's The Life of Greece and Arthur Miller's Death of a Salesman into Icelandic.