After passing his final examinations in 1829, Jónas moved to Reykjavík and was employed by a sheriff as a clerk, living in his home.
He began working for a law degree, but after four years switched to literature and natural sciences, excelling in both subjects.
In 1835, along with fellow Icelandic students Brynjólfur Pétursson, Konráð Gíslason and Tómas Sæmundsson, he founded the patriotic journal Fjölnir.
After graduation he was awarded a grant from the state treasury to conduct scientific research in Iceland, a project which he worked on from 1839 to 1842.
[4] Sigurjón came up against serious opposition from a number of the political élite, including Ólafur Thors, who was then Prime Minister of Iceland.
The government informed him that Jónas' bones were state property, and would be buried at the national burial ground at Þingvellir, alongside the poet Einar Benediktsson.
Sigurjón covered most of the cost, even paying for Matthías Þórðarson, the director of the National Museum, to oversee the excavation.
He drove north with them, intending to bury them in Öxnadalur in defiance of the government, but the priests there refused to perform the rites.
The coffin stood in a church for a week before being driven back south and buried in the government's chosen spot on 16 November, Jónas' birthday.